CYGNUS: Feasibility of a nuclear recoil observatory with directional sensitivity to dark matter and neutrinos
S. E. Vahsen, C. A. J. O'Hare, W. A. Lynch, N. J. C. Spooner, E. Baracchini, P. Barbeau, J. B. R. Battat, B. Crow, C. Deaconu, C. Eldridge, A. C. Ezeribe, M. Ghrear, D. Loomba, K. J. Mack, K. Miuchi, F. M. Mouton, N. S. Phan, K. Scholberg, T. N. Thorpe
CCygnus : Feasibility of a nuclear recoil observatory with directional sensitivity to darkmatter and neutrinos
S. E. Vahsen, C. A. J. O’Hare, W. A. Lynch, N. J. C. Spooner, E. Baracchini,
4, 5, 6
P. Barbeau, J. B. R. Battat, B. Crow, C. Deaconu, C. Eldridge, A. C. Ezeribe, M. Ghrear, D. Loomba, K. J. Mack, K. Miuchi, F. M. Mouton, N. S. Phan, K. Scholberg, and T. N. Thorpe
1, 6 Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA The University of Sydney, School of Physics, NSW 2006, Australia Department of Physics and Astronomy, University of Sheffield, S3 7RH, Sheffield, United Kingdom Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, I-00040, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Roma, I-00185, Italy Department of Astroparticle Physics, Gran Sasso Science Institute, L’Aquila, I-67100, Italy Department of Physics, Duke University, Durham, NC 27708 USA Department of Physics, Wellesley College, Wellesley, Massachusetts 02481, USA Department of Physics, Enrico Fermi Inst., Kavli Inst. for Cosmological Physics, Univ. of Chicago , Chicago, IL 60637, USA Department of Physics and Astronomy, University of New Mexico, NM 87131, USA Department of Physics, North Carolina State University, Raleigh, NC 27695, USA Department of Physics, Kobe University, Rokkodaicho, Nada-ku, Hyogo 657-8501, Japan Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA (Dated: August 31, 2020)Now that conventional weakly interacting massive particle (WIMP) dark matter searches areapproaching the neutrino floor, there has been a resurgence of interest in detectors with sensitivityto nuclear recoil directions. A large-scale directional detector is attractive in that it would havesensitivity below the neutrino floor, be capable of unambiguously establishing the galactic originof a purported dark matter signal, and could serve a dual purpose as a neutrino observatory. Wepresent the first detailed analysis of a 1000 m -scale detector capable of measuring a directionalnuclear recoil signal at low energies. We propose a modular and multi-site observatory consisting oftime projection chambers (TPCs) filled with helium and SF at atmospheric pressure. By comparingseveral available readout technologies, we identify high-resolution strip readout TPCs as the optimaltradeoff between performance and cost. We estimate that suitable angular resolution and head-tailrecognition is achievable down to helium recoil energies of ∼ r . Depending on the readouttechnology, an average of only 4-5 detected 100-GeV c − WIMP-fluorine recoils above 50 keV r aresufficient to rule out an isotropic recoil distribution at 90% CL. An average of 10-20 helium recoilsabove 6 keV r or only 3-4 helium recoils above 20 keV r would suffice to distinguish a 10 GeV c − WIMP signal from the solar neutrino background. High-resolution TPC charge readout also enablespowerful electron background rejection capabilities well below 10 keV. We detail background andsite requirements at the 1000 m -scale, and identify materials that require improved radiopurity.The final experiment, which we name Cygnus -1000, will be able to observe ∼ – neutrinosfrom the Sun, depending on the final energy threshold. With the same exposure, the sensitivity tospin independent cross sections will extend into presently unexplored sub-10 GeV c − parameterspace. For spin dependent interactions, already a 10 m -scale experiment could compete withupcoming generation-two detectors, but Cygnus -1000 would improve upon this considerably. Largervolumes would bring sensitivity to neutrinos from an even wider range of sources, including galacticsupernovae, nuclear reactors, and geological processes.
I. INTRODUCTION
A wide range of astrophysical observations acrossgalactic and cosmological scales indicate that dark mat-ter (DM) dominates the mass budget of the Universe.While the gravitational evidence for DM is now over-whelmingly strong (for a review, see Ref. [1]), its particleidentity remains unknown. A definitive detection of DMis expected to be a gateway to physics beyond the Stan-dard Model. Being of such fundamental importance, thequest to uncover the nature of DM remains one of themost important experimental challenges in contemporaryphysics [2].Experimental efforts in direct DM detection have largely focused on the possibility that it consists ofweakly interacting massive particles (WIMPs) whosescattering cross sections with ordinary matter are smallbut nonzero, detectable in low-background nuclear recoilexperiments. After years of incremental improvements,large swaths of WIMP parameter space are now ruledout, including those in which detections were previouslyclaimed [3–12]. As detectors become sensitive to lowermasses and weaker cross sections, the previously negligi-ble neutrino background will become important, poten-tially swamping any WIMP signal. Models with weaksignals that are hidden beneath the neutrino backgroundare said to live below the “neutrino floor”, a theoreticalboundary beyond which conventional DM detectors can- a r X i v : . [ phy s i c s . i n s - d e t ] A ug not efficiently probe.DM detectors with directional sensitivity —the abilityto reconstruct the directions of WIMP-induced nuclearrecoil events—have the potential to address two of themain challenges to current detection techniques: (1) thedifficulty of positively identifying detected interactions asbeing caused by the DM making up the galactic halo, and(2) the potential for the saturation of the signal by theneutrino background. Directionality addresses both chal-lenges by identifying the direction from which interactingparticles originate, thus distinguishing between eventscoming from the Milky Way DM halo and those originat-ing elsewhere. While this is a powerful background dis-crimination technique in principle, in practice it remainschallenging to build a directional detector that is largeenough to compete with non-directional experiments.This article lays out the science case and goals for alarge directional nuclear recoil observatory, and detailsthe challenges that need to be faced in order to achievethose goals with existing technology. The motivation forthis work draws on results summarized in three extensivereviews: the first summarized the status of existing direc-tional detection projects [13], the second detailed the fulldiscovery potential for directional detectors [14]; and thethird presented a broad summary of available direction-sensitive readout technologies [15]. Here, we combine allpresent knowledge in the field and develop a single strat-egy for a directional detector named Cygnus . This workbridges the gap between, on the one hand, theoreticalliterature on directional detection which often involvesmany idealized assumptions about detector capabilities;and on the other, purely experimental studies which arerelatively far removed from a potential future utility in acompetitive DM search.The primary goal of
Cygnus will be to discover DMeven if its cross section lies beyond the neutrino floor.WIMP sensitivity at this level also brings a secondarymotivation: the study of the neutrino background itself.There is substantial physics motivation for the detec-tion of natural or human-made neutrinos, via either co-herent neutrino-nucleus scattering (CE ν NS) or neutrino-electron scattering, both of which will be measurablein
Cygnus . In particular, directional measurements ofthese processes would be a highly-novel additional signalfor many terrestrial and astrophysical sources of neutrino.
Cygnus , therefore, retains a strong science case, even inthe absence of a positive DM signal.Observing the neutrino background and WIMP crosssections lying below the neutrino floor requires experi-ments with very large total masses. Hence the final goalfor
Cygnus will be a network of modular and multi-sitegas experiments each individually based on the strategiesset out here. Organizing the experiment in a modular andmulti-site manner alleviates some of the issues regardingthe very large volumes needed for a gas target to reachthe required mass. A schematic for a style of modular-ity is shown in Fig. 1, which shows how several smaller“back-to-back” gas time projection chambers (TPCs) can be placed within the same background shielding. Ourstudy focuses on the design of a single module that canbe scaled up in this fashion. In Fig. 2 we show the loca-tions of some of the candidate sites under consideration.A globally distributed experiment is also advantageousas it provides an additional method to deal with sea-sonal or location-dependent backgrounds as well as helpto overcome possible site-restrictions on the overall sizeof a detector.The organization of this article is as follows: in Sec. IIwe describe the advantages of directionality for the ro-bust discovery and characterization of a DM signal, andto contribute to studies of solar, supernova, atmospheric,and geological neutrinos. Section III reviews the existingand proposed detector technologies that may enable di-rectional detection, including the gas TPC, which formsthe basis of
Cygnus . In Sec. IV, we describe how dif-ferent TPC gases and readout technologies compare intheir detection capabilities while keeping in mind practi-cal considerations for construction. Section V discussesthe feasibility of achieving zero-background in large-scaleTPCs, while Sec. VI describes the requirements for detec-tor location and installation. Finally in Sec. VII, we con-clude the technological considerations described in theabove sections and outline a specific direction-sensitivedetector that is both feasible and cost-effective.
II. SCIENCE CASE FOR A LARGE NUCLEARRECOIL OBSERVATORY
Past and ongoing directional detection experimentssuch as DRIFT [16], MIMAC [17], D [18], DMTPC [19]and NEWAGE [20] have demonstrated the low-pressuregas TPC concept, and have made many impressive tech-nological advances over the years. However, currentstringent WIMP limits from non-directional experimentsdictate a significant scaling-up of these technologies,which will pose new experimental challenges. This sec-tion provides the motivation for facing those challengesby laying out the strong science case for a direction-sensitive “recoil observatory.” A. Motivation
The most popular technique to directly detect WIMPDM is to search for nuclear recoils with energies O (1 − keV [21, 22]. Experimental strategies us-ing a wide range of targets have been developed, ex-ploiting charge, light, or heat signals (for a review see e.g. Ref. [21]). After decades of progress, the tightestlimits now challenge favored models from supersymme-try [23]. Several experiments have in the past reporteddetections that are consistent with a DM interpretation,but were in tension with limits from other experiments.The only outstanding WIMP detection claim remainingis from the DAMA/LIBRA collaboration who report a
Neutron+gamma shieldingVessel
Drift direction R e a d o u t R e a d o u t C a t h o d e v e t o v e t o v e t o v e t o v e t o v e t o v e t o v e t o C YGNUS -10 m module C YGNUS -10 N m FIG. 1. Schematic of a modular N × m directional detector made up of N back-to-back TPC modules. Each module wouldhave two readout planes and a central cathode to ensure a short maximum drift distance of 50 cm. C YGNUS -UK
Boulby, UK
CYGNO
Gran Sasso, Italy C YGNUS - OZ Stawell, Aus. C YGNUS -KM
Kamioka, Japan C YGNUS -US
Lead, South Dakota C YGNUS C YGNUS - Andes
Chile/Argentina
FIG. 2. Proposed sites for a network of
Cygnus detectors.Site considerations for a large-scale TPC are discussed inSec. VI. σ annual modulation of the event rate in their NaI(Tl)crystal scintillators [24, 25]. While the annual modula-tion they observe is ostensibly DM-like, such an inter-pretation is without support from any other experiment.The annual modulation of galactic DM was often toutedas a clear signature of DM, however; the DAMA/LIBRAresult has demonstrated this approach can be entirelyfrustrated by systematics. So persistent is this disagree-ment that there are now several experiments around theworld designed to test the DAMA result in the most di-rect way possible: by replicating the experiment (DM-Ice [26], KIMS [27], SABRE [28], COSINE-100 [12, 29], ANAIS [30, 31]) and COSINUS [32, 33]. Of the cur-rently released results from ANAIS and COSINE-100,both are still consistent with a modulation amplitude ofzero. However they will need several more years of ex-posure to begin to definitively rule out the presence of amodulation at the level of DAMA.Though experience has uncovered the limitations ofthe annual modulation signature – the distribution ofrecoil directions promises more robust and convincingevidence for DM. The directional DM signature arisesfrom the motion of the Earth (and solar system) throughthe galactic halo. The flux of DM particles incidenton Earth is strongly anisotropic. This so-called DM“wind” peaks close to the star Deneb in the constella-tion Cygnus [34]. For DM-induced recoil directions, thisleads to two prominent phenomena. Firstly, in galacticcoordinates the angular distribution of recoils should be adipole pointing back towards this well-understood direc-tion. Secondly, in lab-centric coordinates, the anisotropywill cycle across the sky due to the Earth’s rotation, witha period of one sidereal day. By definition, these effectsare observable in direction-sensitive experiments, but nototherwise. The measurement of recoil directions is there-fore critical to establishing unequivocally that the sourceof some signal excess in events is due to the same particlethat makes up the DM in the Milky Way. Such a detectorwould also have a strongly-enhanced ability to removebackgrounds. In an idealized situation, directional ca-pability would make a WIMP search maximally reliableand robust by eliminating all possible backgrounds [35–37] and demonstrating the galactic origin of the detectedparticle [38].As anticipated long before the advent of ton-scale de-tectors, natural sources of neutrinos are the ultimate ir-reducible background to WIMP searches. Indeed, theupcoming generation of direct detection experiments areanticipated to be so large and so sensitive that the co-herent scattering between neutrinos and the target willalready be one of the most important backgrounds. Neu-trinos are unshieldable so without a strategy to discrimi-nate against them, the discovery of some well-motivatedlow-mass WIMP models [39] would require prohibitivelylarge exposures. However, even in the eventuality thatno WIMP signal is detected, the neutrino backgrounditself constitutes an interesting signal. A measurementof the angular distribution of neutrinos is of great inter-est in the context of supernovae [40], geoneutrinos [41],and atmospheric neutrinos [42]. Finally, we note that inthe event of a positive WIMP detection, a directional ex-periment would be able to probe some more exotic darkparticle physics as well as to map the currently unknownthree-dimensional velocity structure of the DM distribu-tion around the solar system [14, 43–47]. This latterachievement would greatly improve our understandingof the cosmological accretion and merger history of ourgalaxy, making such an experiment an instrument of as-trophysics as well as particle physics. B. Dark matter
1. WIMP scattering review
The event rate for WIMP-induced nuclear recoils isderived by integrating the product of the incoming fluxof DM and the cross section σ for the relevant WIMP-nucleus interaction. This is usually written in terms ofthe differential event rate R per unit detector mass, as afunction of recoil energy E r and time t ,d R d E r ( E r , t ) = ρ m χ m A (cid:90) v>v min vf ( v , t ) d σ d E r ( E r , v ) d v, (1)where ρ is the local DM mass density, m χ is the WIMPmass, m A is the nucleus mass and v is the DM velocityin the detector rest frame. The integral is performed forWIMP speeds v larger than v min ( E r ) = (cid:112) m A E r / µ χA which is the minimum speed kinematically permitted toproduce a recoil with energy E r . The factor µ χA is theWIMP-nucleus reduced mass. The integral over veloci-ties is weighted by the flux of DM particles vf ( v , t ) where f is the galactic distribution of DM velocities. For DMin the form of WIMPs, over the timescales of observa-tion, the velocity distribution is constant in time. Inthis formula however, it picks up a time dependence af-ter a boost into the laboratory rest frame by v lab , thevelocity with which we are moving through the galactichalo. The differential cross section is proportional to thesquared matrix element for a particular WIMP-nucleus interaction, so is therefore specifically model-dependent.However one can work with general formulae. The mostcommon approach is to divide the interaction into twopossible channels, both of which may contribute to thetotal rate,d σ d E r = m A µ χA v (cid:0) σ SI0 F ( E r ) + σ SD0 F ( E r ) (cid:1) . (2)Here, the first term describes spin-independent (SI) inter-actions such as those arising from scalar or vector WIMP-quark couplings, whereas the second includes the spin-dependent (SD) contributions from, for example, axial-vector couplings. The cross sections σ SI , SD0 are definedat zero momentum transfer, and nuclear form factors F , SD (where F (0) ≡ ) are invoked to describe thenuclear structure and its response to WIMP scatteringevents at different energies: in particular the suppressionof the rate due to the loss in coherence over the nucleusat high momentum transfers. Note that the form fac-tors depend entirely on nuclear physics, and all WIMPmodel dependence is contained in σ SI , SD0 . Keep in mindthat this is only the baseline set of WIMP interactionswhich are most commonly used to compare experimen-tal results. The list of all the physically-allowed non-relativistic WIMP-nucleus interaction operators is muchlonger than the two mentioned so far, and accountingfor them reveals a much richer array of possible signals(as will be discussed in Sec. II B 4). But for simply set-ting and comparing null results, the convention has beento focus on the SI and SD cross sections. Simplifyingthings even further, it is also commonplace to write allnuclear cross sections as proportional to those on the pro-ton σ SI , SD p , σ SI0 = (cid:12)(cid:12) Z + ( f n /f p )( A − Z ) (cid:12)(cid:12) σ SI p , (3) σ SD0 = 43 J + 1 J (cid:12)(cid:12) (cid:104) S p (cid:105) + ( a n /a p ) (cid:104) S n (cid:105) (cid:12)(cid:12) σ SD p , (4)where A is the nucleus mass number, Z is the nucleusatomic number, (cid:104) S p,n (cid:105) are the average of the proton andneutron spins in the nucleus, and J is the total nuclearspin. The ratios of the couplings to the proton and neu-tron are written as f p /f n and a p /a n for SI and SD inter-actions respectively. In the SI case, the total nuclear crosssection is enhanced by the number of nucleons squared(assuming, as we do here, isospin conserving DM where f n /f p = 1 ), meaning that large target nuclei tend tohave the potential to set the most stringent limits. Inthe spin-dependent case, the interaction probability isnot amplified by mass number, but depends instead onthe spin content of the target nuclei, hence; constraintstend to be weaker.In the case of directional detection we want to knowhow the differential event rate depends on a recoil’s di-rection as well as its energy. We can derive this by con-sidering the kinematic relationship between the incoming − WIMP mass [GeV /c ] − − − − − − − − − − − − − − − S I W I M P - p r o t o n c r o sss ec t i o n [ c m ] CRESSTCDMSlite D a r k S i d e P a n d a XX e n o n T E D E L W E I SS P I C O P I C O L DAMA C O S I N E - H e F X e Single electron threshold : 0.25 keV r [755:5 Torr He:SF ] Worst-case threshold : 8 keV r [755:5 Torr He:SF ] Search mode : 8 keV r [760 Torr SF ] k m k m Cygnus × − WIMP mass [GeV /c ] − − − − − − − − − − − − − − − S D W I M P - p r o t o n c r o sss ec t i o n [ c m ] P I C A S S O P I C O P I C O L C O U P P K I M S I c e C u b e τ ¯ τ SK τ ¯ τ ν - fl o o r : X e ν - fl o o r : F Single electron threshold : 0.25 keV r [755:5 Torr He:SF ] Worst-case threshold : 8 keV r [755:5 Torr He:SF ] Search mode : 8 keV r [760 Torr SF ] k m m m Cygnus × FIG. 3. Constraints on the spin-independent WIMP-nucleon (left) and spin-dependent WIMP-proton (right) cross sections.We show the existing constraints and detections from various experiments as labeled (see text for the associated references). Inpurple solid and dashed lines we show our projected 90% CL exclusion limits for the
Cygnus experiment operating for six yearswith 10 m up to 100,000 m of He:SF gas at 755:5 Torr (where 6 years × corresponds to a ∼ r to a very best-case minimum threshold corresponding to a single electron, 0.25 keV r . We emphasize however that we anticipateelectron discrimination well below 8 keV r . For the 100k m limits we add a third dotted line which corresponds to a mode withpurely SF gas at 760 Torr. This experiment would have a significantly higher total mass but would come at the cost of anydirectional sensitivity. This ‘search mode’ could be used to extend the high mass sensitivity to just within reach of the neutrinofloor. For the SI panel, we shade in gray the neutrino floor for helium, fluorine, and xenon targets (top to bottom), and forSD we show only fluorine and xenon. We define the neutrino floor as the cross section limit at which the rate of improvementwith increasing exposure is the slowest in standard direct detection–the effect that Cygnus aims to circumvent. This definitioncorresponds to O (100) neutrino events. WIMP velocity, v , with the outgoing recoil direction ˆ r , v · ˆ r = (cid:115) m A E r µ χA ≡ v min , (5)which can be enforced in the differential cross sectionwith a delta function,d σ d E r d Ω = d σ d E r π v δ ( v · ˆ r − v min ) , (6)where d Ω is the solid angle element around ˆ r . The eventrate then has the structure,d R d E r d Ω ( E r , ˆ r , t ) = ρ πµ χp m χ ( σ SI0 F ( E ) + σ SD0 F ( E )) × ˆ f ( v min , ˆ r , t ) , (7)where the velocity distribution now enters in the form ofits Radon transform [48, 49], ˆ f ( v min , ˆ r , t ) = (cid:90) δ ( v · ˆ r − v min ) f ( v , t ) d v . (8)The characteristic angular structure of the DM fluxon Earth is the reason why directional detection could be such a powerful means to discover DM. The pri-mary signal is a dipole anisotropy towards the direction ˆ r = − ˆ v lab , leading to an O (10) forward-backward asym-metry in the number of recoil events. The strength ofthis dipole means that in ideal circumstances ( i.e. perfectrecoil direction reconstruction) an isotropic null hypoth-esis for the recoil direction distribution can be rejectedat 90% confidence with only O (10) events [43, 50]. With O (30) recoil directions it becomes possible to point backtowards Cygnus and confirm the galactic origin of the sig-nal [44]. Secondary signals such as a ring feature at lowenergies [51], and the aberration of recoil directions overtime [52], may also aid in the confirmation of a DM sig-nal, as well as for characterizing astrophysical propertiesof the DM halo. Existing limits and projections for
Cygnus
Figure 3 shows a selection of constraints from di-rect detection experiments along with our headline re-sult: the WIMP reach of
Cygnus . Constraints ex-ist for WIMPs with masses larger than ∼ GeV c − and SI cross sections larger than ∼ − cm . Under-neath these limits lies the neutrino floor, below which − − − E threshold [keV r ] − − − − N u m b e r o f E v e n t s i n m i n y e a r s S o l a r WIMP m χ = 9 GeV Nuclear recoils
DSNBDSNBAtmosphericAtmospheric G e o G e o R e a c t o r R e a c t o r
10 kpc CCSN10 kpc CCSN s i n g l ee − e − - d i s c . He:SF
500 1000 1500 2000 2500 E threshold [keV] − − − − − − N u m b e r o f E v e n t s i n m i n y e a r s S o l a r Electron recoils
DSNBDSNB A t m o s ph e r i c A t m o s ph e r i c G e o G e o R e a c t o r R e a c t o r k p c CC S N k p c CC S N He:SF FIG. 4. Number of neutrino-nucleus (left) and neutrino-electron (right) recoil events observed in a
Cygnus -1000 m detectorfilled with atmospheric pressure He:SF at a 755:5 Torr ratio (the event rates are summed over each target nuclei). Wecalculate the expected number of observed events by integrating the event rate for each background component above a lowerenergy threshold E threshold . The background components are shown as darker and lighter shaded regions indicating the 1and 2 σ uncertainties from the predicted flux. For comparison we also show the nuclear recoil event rate expected from a m χ = 9 GeV c − WIMP with a SI WIMP-proton cross section of σ SI p = 5 × − cm as a black line. For the reactor andgeoneutrinos, we assume the entire 1000 m is located at Boulby, UK. The purple region indicates the range of expectednumbers of events from the neutrino bursts from 11–27 M (cid:12) core-collapse supernovae located 8 kpc away from Earth. To addfurther clarity we shade in gray parts of the plot which give fewer than one event in this exposure. In the left panel we alsoshow as dashed lines the 0.25 and 8 keV r best-case and worst-case thresholds respectively. WIMP models are rendered practically unidentifiable dueto the saturation of their signal by the background fromCE ν NS (to be discussed in Sec. II B 2). The limits wedisplay are from the following experiments: CRESST-II [3], CDMSLite [4], COSINE-100 [29], EDELWEISS-III [5], PICO-2L [6], PICO-60 [7], DarkSide-50 [53], Pan-daX [9], XENON1T [11], PICASSO [54], KIMS [55] andCOUPP [56]. For comparison, in the SD case we also dis-play two competitive (but model dependent) limits fromneutrino telescopes SK [57] and IceCube [58]. These lim-its are based on searches for the annihilation of WIMPscaptured by the Sun. In the SI case the closed detectionregions correspond to the disputed DAMA/LIBRA [24]annual modulation signal.Also in Fig. 3 we display the final result of this pa-per: the potential sensitivities of
Cygnus . The gas mix-ture is assumed to be He:SF at 755 and 5 Torr respec-tively. This means that the relevant target nuclei are F and He for the SI search, and just F for the SDsearch . We have assumed a detector with angular reso-lution, head/tail recognition efficiency, energy resolution, Fluorine is an attractive target for SD-proton searches since itsmost common natural isotope possesses a relatively high valueof (cid:104) S p (cid:105) . and charge detection efficiency derived for a strip-basedreadout (see Sec. IV). The shaded regions indicate limitswhen varying the hard lower cut imposed on recoil en-ergy. These range from 8 keV r (above which the electronbackground can be definitively rejected by factors greaterthan – ), down to 0.25 keV r (the smallest physicallypossible threshold as it corresponds to the detection of asingle electron). We emphasize that 8 keV is a worst-casescenario. As we will show, we expect electron rejectionto be possible down to much smaller recoil energies. Weshow several possible volumes, including the benchmark1000 m as used in our background study (see Sec. V)and a further-future 100k m . The former would beginto break into the neutrino floor at low masses whereasthe latter would allow us to further characterize the neu-trino background and study in greater detail a possibleWIMP signal if detected. Even an earlier-stage 10 m -scale experiment would already be able to set the mostsensitive limits on SD-proton WIMP-nucleus interaction,thanks to the large number of fluorine nuclei. Beneaththe largest 100k m cases we also show a hypothetical‘search mode’ limit. This corresponds to a mode in whichthe TPC contains entirely SF at atmospheric pressure.This mode would have no directional sensitivity due tothe high gas density, however the potential exclusion lim-its at high masses would greatly improve. The derivationof all the limits displayed here is the subject of the re-maining sections of this paper.
2. WIMP detection below the neutrino floor
It was anticipated in early work on direct DM detec-tion that large detectors would eventually become sen-sitive to CE ν NS [59]. For the keV nuclear recoil ener-gies observed in direct detection experiments solar, dif-fuse supernovae and atmospheric neutrinos all constitutea significant background for detector exposures beyondthe ton-year scale [60–62]. Because neutrinos are im-possible to shield against, they represent the ultimatebackground for the direct detection of WIMPs. More-over, because the nuclear recoil energy spectra induced byCE ν NS mimic the spectra for WIMPs of certain masses,the discovery of these characteristic masses is limited dueto the sizeable systematic uncertainty on the expectedneutrino flux. We give more details on CE ν NS and thevarious neutrino backgrounds in Sec. II C.The limiting WIMP-nucleon cross section below whichexperimental sensitivities are impacted by the neutrinobackground is known as the “neutrino floor” [63]. Theshape of the neutrino floor is dependent on the flux ofeach neutrino background component as well as, impor-tantly, the uncertainty on this flux. The relevant neutrinobackgrounds for WIMP searches using nuclear recoils aresummarised in the left-hand panel of Fig. 4. The mostnotable and threatening feature of the neutrino floor isthe shoulder below ∼
10 GeV c − arising from the largeflux and low energies of solar neutrinos (see Sec. II C 2).The most important of these are the neutrinos originat-ing from B decay. In a fluorine experiment the nuclearrecoil signal due to a 9 GeV c − WIMP with an SI crosssection around × − cm is well matched by recoilsfrom B neutrinos. Towards slightly larger masses (10–30 GeV c − ) the neutrino floor is set by the diffuse su-pernova neutrino background (DSNB): the cumulativeemission of neutrinos from a cosmological history of su-pernovae. The expected flux of the DSNB is extremelylow ( ∼
80 cm s − [65]) so the neutrino floor at these in-termediate masses falls by several orders of magnitude incross section. Towards masses beyond 100 GeV c − theneutrino floor is induced by the low-energy tail of atmo-spheric neutrinos from cosmic ray interactions in the up-per atmosphere. Atmospheric neutrinos (see Sec. II C 4)are the only significant background contributing neutrinoenergies above 100 MeV. The low-energy tail of atmo-spheric neutrinos is difficult to both measure and the- This shoulder extends down to very low WIMP masses, < GeV c − , where the lowest energy solar neutrino sources from pp and CNO reactions become important. These neutrinos areimportant for DM searches which rely on electronic recoils [64],but are probably out of reach for nuclear recoil analyses for theforeseeable future. oretically predict [66] so currently has uncertainties ofaround 20% [67].The shape of the neutrino floor is different depend-ing on the target nucleus, because the CE ν NS energyspectrum also depends upon m A . In this article, unlessotherwise specified, we use the definition of the neutrinofloor discussed in, for example, Refs. [42, 68]. As opposedto a limit which corresponds to a fixed expected num-ber of neutrino events, we instead show a slightly lowerfloor which corresponds to the cross sections at whichthe rate of change in a discovery limit scales the slowestwith increasing exposure. This allows us to account forthe effect of the neutrino flux uncertainty and properlydisplay which WIMP masses are most severely impactedby each background. Approximately though, the floorcan be interpreted as a limit below which an experimentwould observe more than ∼
100 neutrino events.Given that the next generation of ton-scale experi-ments are expected to become sensitive to CE ν NS, itis pertinent to search for alternative and more power-ful methods of subtracting the background. The mostbasic approach to alleviate the background is to exploitthe complementarity between target nuclei of differingmasses and nuclear content. For the SI neutrino floorit has been shown that this approach only leads to amarginal improvement in discovery limits, but in the caseof SD interactions the differences in nuclear spin contentsmake complementarity a more viable strategy [69]. Itwas also shown that the use of event time informationalso allows the low-mass neutrino floor to be overcomewith slightly lower statistics [68, 70]. This exploits boththe annual modulation of the DM signal due to the rel-ative motion of the Earth and the Sun, as well as theannual modulation in the solar neutrino flux due to theeccentricity of the Earth’s orbit.Directionality presents the most attractive prospectfor circumventing the neutrino floor because the uniqueangular signatures of both DM and solar neutrinos al-lows optimum discrimination between signal and back-ground [35, 36]. This has also been explored in non-gasTPC directional experiments, such as with nuclear emul-sions [71], spin-polarized helium-3 [72] and electron-holepair excitations in semiconductors [73]. The consensusis that: in a directional experiment there should be ef-fectively no neutrino floor, provided that directionality iswell-measured .We display the angular distribution of the DM andneutrino-nucleus recoils in Fig. 5. The crucial factor thatenables their discrimination is that over the course ofthe year the Sun does not pass through the constellationof Cygnus. The angular distance between Cygnus andthe Sun undergoes a sinusoidal modulation which peaksin September at around ◦ and is a minimum duringMarch at around ◦ . Because solar neutrino recoils canonly point with angles less than ◦ from the solar di-rection, this implies that over long periods during a yearthere are large patches of sky where the event rate ofsolar neutrinos is zero (before accounting for the finite − ◦ ◦ − ◦ ◦ − ◦ ◦ ◦ ◦ +30 ◦ ◦ +60 ◦ ◦ +90 ◦ ◦ Galacticplane E c li p t i c Galactic longitude, l G a l a c t i c l a t i t ud e , b Fluorine recoils [8–50 keV r ] September 6 . . . . . . d R / d Ω r [ t o n − s r − ] S o l a r n e u t r i n o s G e V / c W I M P FIG. 5. Total angular distribution across the sky of WIMP-induced (blue contours) and neutrino-induced (red contours) fluorinerecoils on September 6. We show the distributions in galactic coordinates ( l, b ) where the line for b = 0 corresponds to thegalactic plane. Both distributions have been integrated over recoil energy between 8 and 50 keV r . We choose a WIMP mass of9 GeV c − and a SI cross section of × − cm so that its signal is of a similar size to that of the B neutrinos. For referencewe also show the ecliptic in red: the path along which the Sun, shown by a star, moves over the year. Towards the center ofthe WIMP recoil distribution we also show the stars of the Cygnus constellation. The blue line which encircles the star Denebshows the variation in the peak direction of the DM wind over the year. angular resolution of the detector). The separation islarge enough that it is possible to discriminate the twosignals even if the recoil vectors cannot be oriented ingalactic coordinates as shown here. This would be thecase for experiments in which recoil vectors were onlymeasured after being projected on to a plane [36], or iftiming information was unavailable [37].
3. WIMP astrophysics
Predicting WIMP signals requires astrophysical inputin the form of the DM velocity distribution, f ( v ) , as wellas the local density of DM ρ . While the former is notknown concretely, the latter can be determined with as-tronomical data. Decades of attempts to constrain thisvalue have begun to settle towards ρ ≈ . GeV cm − (see, e.g. Refs. [74–78] and Ref. [79] for a review on meth-ods). However the standard value used by experimentalcollaborations is . GeV cm − . Upcoming analyses withthe extremely high and precise statistics of the astromet-ric survey Gaia [80] are expected to lead to even moretightly constrained values in the next few years. Sincethe local dark matter density only amounts to a mul-tiplicative factor which can be absorbed into the (also unknown) DM cross section , its precise value is of lowimportance before a detection is made.On the other hand the great deal of uncertainty sur-rounding the velocity distribution of the DM is generallymore important to understand. The benchmark modelassumed since the very first direct detection experimentswere conducted is the Standard Halo Model (SHM), inwhich the Milky Way’s DM forms an isothermal sphere.The motivation is that it is the simplest model that givesrise to flat rotation curves. The SHM has a Gaussian dis-tribution for f ( v ) (or Maxwellian distribution for f ( v ) ), f ( v ) = 1(2 πσ v ) / N esc exp (cid:18) − | v | σ v (cid:19) Θ( v esc − | v | ) . (9)Under the isothermal SHM, the dispersion is related tothe local rotation speed of circular orbits: σ v = v / √ .The benchmark used for this speed is the now similarlyout-of-date value of v ∼ km s − . A more recentanalysis indicates a value of v = 235 km s − [82]. As isconvention, the velocity distribution has been truncatedat the escape speed v esc , with the constant N esc used torenormalize the distribution after this truncation. Ex-perimental analyses typically have assumed v esc = 544 or km s − , the latter being the more recent RAVE Although, see Ref. [81] for a specific case where this is not true. value [83]. Again with
Gaia this is undergoing revision,however newly found high speed substructure is introduc-ing additional complexity to its determination [84]. Theescape speed in effect controls the highest energy WIMPobservable, but due to the exponential suppression thishas a marginal impact on the event rate.Astrophysical uncertainties in the form of f ( v ) im-pact the reliability of signal modeling and hence feedinto the measurements of DM particle properties [85, 86]and the calculation of exclusion limits [68, 87]. Indeedmuch effort has been spent in devising methods to in-tegrate out this uncertainty so that accurate limits canbe made. See for example the extensive literature on“halo-independent” methods for the calculation of exclu-sion limits in Refs. [88–94] and many others. Much ofthis interest has been driven by previous claims that theanomalous DAMA/LIBRA result could be explained byparticular choices for the speed distribution.Directional experiments, however, will offer a novel res-olution to the uncertainty on f ( v ) that is not present inconventional approaches. In addition to having a uniquesmoking gun signal that is difficult, or even impossible,to mimic with backgrounds, it has been shown that theprospects for directional detectors to measure the DM ve-locity structure greatly exceed that of an equal-standing non -directional detector [45, 47, 95]. This is primarilybecause recoil energy information alone cannot be usedto access the full three-dimensional form of f ( v ) and isinstead only sensitive to the one-dimensional speed dis-tribution, f ( v ) . Since our study is largely comparative innature we adopt the SHM and the out of date astrophys-ical parameter values for consistency with past studiesand limits. However in the future as more ton-scale de-tectors begin taking data, it has been advised that theSHM be updated to include recent refinements. A sum-mary of these recommendations can be found in Ref. [82].It should be emphasized additionally that the struc-ture of the local halo of the Milky Way is itself also ofgreat interest. The measurement of anisotropies in thevelocity distribution may provide insights into the ar-chaeology of the Milky Way’s formation, as well as thefundamental properties of DM. In particular, directionaldetectors are well suited to detect kinematically localizedsubstructures such as DM streams [96]. Less prominentvelocity substructures such as debris flow [97], asymme-try in the velocity ellipsoid of the Milky Way [82], andthe possible influence of the Large Magellanic Cloud [98],will all require many more events to detect, hence verylarge detectors will be essential. This is also true forvery low-mass streams from smaller DM substructuresor any other low-level structures that are likely to haveundetectable levels of influence on luminous matter; anopportunity to better understand the level of phase spaceclumpiness and non-Gaussianity of the Milky Way DMhalo is therefore a key potential advantage of directionaldetection.While it is useful to remain speculative about the kindsof structures one could hope to see in a future exper- iment, in the advent of Gaia , our concrete knowledgeabout our local distribution is improving. For instancethe expanding catalog of nearby populations of clumpsand streams as well as the overall kinematic structure ofthe stellar halo is providing us greater insight into theformation of the Milky Way halo and the constructionof its gravitational potential. In fact we already knowthat at a large chunk of the local DM halo is likely tobe part of a highly radially anisotropic feature, variouslycalled the Gaia Sausage or Gaia-Enceladus [82, 99–106].Some of the most interesting prospects for directionaldetectors are the tidal streams intersecting our galacticposition [107, 108]. These have been discovered recentlythanks to
Gaia , some prominent examples are the localstreams S1 [109] and S2 [110, 111], see also the examplesstudied in Ref. [112]. Streams will be subdominant con-tributions to the local density ρ , hence will be secondarysignals. However their unique characteristics relative tothe bulk of the halo DM are almost entirely washed out intheir eventual nuclear recoil signals–unless one has direc-tional information [82, 109, 110]. The ability to resolvethese substructures is another major advantage of such adetector [96].
4. Particle models and directionality
As well as simply detecting DM, we also require that afuture large-scale experiment be able to uncover proper-ties of the particle itself. This is particularly challengingas there are many competing models that may be de-generate with respect to the signals they produce in theusual direct detection schemes. Various classes of par-ticle models give rise to unique directional signals thatwould go undetected in a conventional experiment. Weoutline a few of these here.Inelastic DM (IDM) models are those in which DM canhave a lower or higher energy excited state to which it candown- or up-scatter via a nuclear recoil event. IDM mod-els were proposed to reconcile the DAMA annual modu-lation signal [113]. The availability of excited states andthe suppression of elastic scattering means that heaviernuclei are favored, the low energy recoil spectrum is mod-ified, and the annual modulation is enhanced. It has alsobeen shown that IDM models can give rise to enhancedsignal discrimination power in directional detectors [114].This is because the recoils are more focused in the for-ward direction, since slower WIMPs cannot scatter withenough energy to induce an excited state.Directional detectors can also disentangle elastic andinelastic scattering events in DM models that allow forboth [115], and if the detector is equipped with any pho-todetector technology then the luminous decay of the ex-cited state may also be observed [116]. In this latterexample, the sensitivity to this process is facilitated bythe large volumes of gas-based detectors, as opposed toonly their directional sensitivity. This is also the casefor proposals for super-heavy DM particles with masses0extending up to the Planck scale and beyond [117].Another possibility is if DM exists in the form of “dark-onium” bound states composed of two or more particles(as is predicted in some configurations of asymmetric DMmodels). It has been shown that there may be angularsignatures observable in directional experiments that canconstrain the properties of these bound states [118].Several years ago a novel scheme to generalize the cal-culation of signals in direct detection experiments wasdeveloped. This uses a non-relativistic effective field the-ory description of the DM-nucleus interaction to posita set of operators that describe general processes be-yond the simple spin-independent and spin-dependent.The basic operators include all Hermitian, Galilean, androtation-invariant interactions constructed out of the lowenergy degrees of freedom involved in a WIMP-nucleusinteraction [119]. Certain examples, those which are de-pendent on the DM particle’s transverse velocity v ⊥ = v + q / µ χA ), give rise to unique ring-like angular signa-tures [120, 121]. This means that directional detectorswould be more powerful than conventional experimentsin distinguishing between these particular operators. Animportant consequence of these features is that it enablesan experiment to distinguish spin-0 DM particles fromspin-1/2 or 1 [122]. The information which permits thisturns out to be found in the angular dependence of cer-tain effective field theory operators. However, many non-standard operators tend to be suppressed, meaning eventrates are inherently low. Large scale detectors will there-fore be required for studying the complete phenomenol-ogy of DM.
5. Axions
Direct detection experiments searching for WIMPs arenot limited to a single class of DM candidate. Anothervery popular class of candidate is the axion and its gener-alization, the axion-like particle (ALP). The motivationfor axions originates in the dynamical solution of Pecceiand Quinn [123] (PQ) to the strong-CP problem of quan-tum chromodynamics (QCD), see e.g.
Ref. [124] for a re-cent review. The ALP is inspired phenomenologically bythe QCD axion but could come from a variety of theoret-ical origins when spontaneously broken PQ-like symme-tries are embedded in higher energy theories. This is thecase most notably in string theory where both the QCDaxion and a slew of phenomenologically similar particlesare predicted [125]. The masses of axions and ALPs canspan many orders of magnitude but their extremely weakcouplings to the Standard Model make them attractiveDM candidates. Axions produced non-thermally in theearly Universe via vacuum misalignment [126–128], de-caying topological defects [129, 130] or in the form of ax-ion stars [131] or miniclusters [132–134] have been shownto be able to match the required properties and cosmo-logical abundance of cold DM (see e.g.
Ref. [135]). Ax-ions and ALPs are by construction coupled to the Stan- dard Model through quark loops which gives rise to anumber of potentially observable interactions: for exam-ple, axion-photon conversion inside magnetic fields, ab-sorption by atomic electrons (the axioelectric effect) andspin-precession of nuclei. In the case of the QCD axionthe strength of the coupling and its linear relationshipto the axion mass is prescribed by theory, but for thegeneralized ALP, the coupling may take any value. SeeRef. [136] for a recent review of experimental searches foraxions.Existing WIMP direct detection experiments suchas LUX [137], XENON [138–140], EDELWEISS [141],CDMS [142] and PandaX [143] have already constrainedaxions and ALPs in the search for their interactions withelectrons via the axioelectric effect [144–146]. The cou-pling most accessible to a WIMP experiment is the axion-electron coupling g ae , as opposed to the photon couplingmeasured in the most mature axion experiments usingresonant cavities such as ADMX [147] and CAST [148](although in QCD axion models these couplings are re-lated). Note that most of these analyses can also berecast as constraints on vector bosonic dark matter par-ticles, the dark photon being the most notable exam-ple [149].ALPs may be searched for as both a DM candidate aswell as solely a modification to the Standard Model. IfALPs with masses in the range m a ∼ − keV comprisea significant fraction of the local DM density, then theyshould stream into a detector and induce electron emis-sion from target atoms with a sharp spectrum locatedat m a . Since the spectral width of this signal would bewell below the energy resolution of any detector, astro-physical uncertainties might only be resolved with theangular spectrum. Cygnus may also be particularly ad-vantageous in this regard because of the excellent elec-tron/nuclear recoil discrimination that could be achiev-able at low energies. It should be mentioned that thekeV-mass QCD axion couplings are already ruled out, solow-background recoil experiments would only be able todetect DM in the form of an ALP and not an axion.On the other hand, these experiments may in the fu-ture be able to see the QCD axion, since it is expectedthat they should be produced in the Sun with ∼ keV en-ergies, and their precise incoming flux and spectrum iswell understood [150]. As is the case with solar ax-ion telescopes such as CAST, if the ALP mass is muchless than a keV c − the axions are produced relativisti-cally and the signal is dominated by the energy of thesolar emission. This means an experiment is consistentlysensitive over a large range of arbitrarily small masses.Even in the event of the detection of a DM or solar ALP,a large directionally-sensitive experiment could be novel Recently an excess of electronic recoil events below 7 keV wasreported by XENON1T [140] with a similar spectrum to the solaraxion flux. However the size of the excess would require couplingsin violation of astrophysical bounds [151–153]
C. Neutrinos
1. Coherent neutrino-nucleus scattering CE ν NS was predicted over 40 years ago with the real-ization of the neutral weak currents [156]. This Standard-Model process went unobserved for many years due todaunting detection requirements: ∼ keV nuclear recoilthresholds, kilogram to ton-scale target masses, and lowbackgrounds. Recently COHERENT has made the firstmeasurements of the CE ν NS cross section in agreementwith the Standard Model [157–159]. Due to the smallweak charge of the proton, the coherence results in anenhanced neutrino-nucleon cross section that is approxi-mately proportional to the square of the number of neu-trons in the nucleus. A few years after the CE ν NS pre-diction, and ironically before the conception of the firstDM direct detection experiments, the possibility of usingthis enhanced process to develop a “neutrino observatory”was put forward [160]. A cornucopia of physics searcheswas envisioned using neutrinos from stopped-pion beams,reactor neutrinos, supernovae, solar neutrinos, and evenneutrinos of a geological origin. See e.g.
Ref. [161] for asummary of natural sources of neutrino.Shortly thereafter, the first generation of DM exper-iments began to search for the scattering of WIMPs,where the signature was a low-energy nuclear recoil. To-day the irony lies in the fact that the unshieldable recoilsthat result from CE ν NS will soon be a source of back-ground for the next generation of DM direct detectionexperiments. But an experiment that can successfullyseparate and identify these neutrino events can not onlyproceed past the neutrino floor, but can also realize thelong-awaited vision of a “neutrino observatory”. A de-tector with directional sensitivity has the potential to dojust that.In CE ν NS, coherence is only satisfied when the initialand final states of the nucleus are identical, limiting thisenhancement to neutral current scattering. The coher-ence condition, where the neutrino scatters off all nucle-ons in a nucleus in phase, is also only maintained whenthe wavelength of the momentum transfer is larger thanthat size of the target nucleus. A high level of coherenceacross all recoil energies is only guaranteed for low energyneutrinos: less than tens of MeV, depending on the massof the target nucleus. The Standard Model total crosssection for the process can be approximated (neglectingsubdominant axial-vector terms that arise from unpairednucleons) as σ = G F π (cid:2) A + Z (4 sin θ W − (cid:3) E ν F ( E r ) , (10) where G F is the Fermi constant, θ W is the Weinberg an-gle and E ν is the energy of the incoming neutrino [156]. Itis evident that the cross section increases with the squareof the energy of the neutrinos; however, while the form-factor condition, which comes in as | F ( E r ) | , is easilysatisfied for solar neutrinos, the total cross section be-gins to suffer from decoherence for supernova and atmo-spheric neutrinos. As can be seen in Fig. 4, a detectorwith an energy threshold of zero can expect to see severalhundred to a few thousand recoils from solar neutrinosper ton-year of exposure, depending on the mass of thetarget nucleus [160].The differential cross section with recoil energy can beapproximated as [156]:d σ d E r = G F π (cid:2) Z (4 sin θ W −
1) + N (cid:3) m A (cid:18) − E r m A E ν (cid:19) . (11)Assuming a F target, for example, and a 5 (10) keVthreshold for observing nuclear recoils. This results inan expectation of ∼
90 (15) background recoils per ton-year, from solar neutrinos alone [162].
2. Solar neutrinos
On Earth, the most prominent source of neutri-nos is our Sun with a total flux at Earth of . × cm − s − [163]. Due to the eccentricity of theEarth’s orbit, the Earth-Sun distance has an annual vari-ation leading to a modulation in the solar neutrino flux Φ , d Φ( t ) d E ν d Ω ν = d Φ d E ν (cid:20) e cos (cid:18) π ( t − t ν ) T ν (cid:19)(cid:21) × δ (ˆ r ν + ˆ r (cid:12) ( t )) , (12)where t is the time from January 1st, e = 0 . isthe eccentricity of the Earth’s orbit, t ν = 3 days is thetime at which the Earth-Sun distance is minimum, T ν =1 year, ˆ r ν is a unit vector in d Ω ν , and ˆ r (cid:12) ( t ) is a unitvector pointing towards the Sun. The directional eventrate is found by convolving this directional flux, with thedirectional cross section for CE ν NS. The cross sectionwith respect to the lab-frame recoil angle θ can be writtenas [156, 160]d σ d (cos θ ) = G F π (cid:2) Z (4 sin θ W −
1) + N (cid:3) E ν (1 + cos θ ) . (13)The resulting recoils are thus biased to the forward di-rection, away from the location of the Sun.The spectra of solar neutrinos d Φ / d E ν come in variousdistinct forms depending on the nuclear fusion reactioninvolved in their production. Neutrinos from the initialproton-proton fusion reaction, pp , make up 86% of thesolar emission [164]. Despite the huge flux of pp neutri-nos, they yield nuclear recoils well below the threshold ofany direct detection experiment; however they would be2the dominant source of electron recoils. Secondary fusionof p + e − + p and He + p produce neutrinos, labeled pep and hep , extend to energies beyond pp neutrinos but withlower flux. There are also two monoenergetic lines associ-ated with Be electron capture with E ν = 384 . keV and861.3 keV. The latter of these is principally responsiblefor limiting WIMP discovery for m χ < GeV c − [165].At higher energies there are neutrinos due to the decayof B which extend up to E ν ∼ MeV and within thereach of nuclear recoil WIMP searches, as already dis-cussed. Finally, extending to relatively high energies butwith much weaker fluxes, are neutrinos arising from thecarbon-nitrogen-oxygen (CNO) cycle labeled by the de-cay from which they originate: N, O and F.The theoretical uncertainties on the solar neutrinofluxes range from 1% ( pp flux) to 14% ( B flux). Forall except B, the theoretical uncertainty is smaller thanthe measurement uncertainty. The theoretical uncer-tainty originates largely from the uncertainty in the solarmetallicity, and in order to establish a self-consistent setof solar neutrino fluxes one must assume a metallicitymodel. The Standard Solar models (SSMs) of Grevesse& Sauval [166] are generally split into two categories:“high-Z” and “low-Z,” based on the assumed solar metal-licity. Both models have historically disagreed with someset of observables such as neutrino data, helioseismology,or surface helium abundance [167]. More recent gener-ations of SSMs [168] have a mild preference towards ahigh-Z configuration, though neither are free from somelevel of disagreement with the various solar observables.DM detection experiments may shed further light on thesolar metallicity issue (see e.g.
Refs. [165, 169, 170]). Themeasurement of CNO neutrinos will be essential for this,and may be possible in future DM experiments [170, 171].Recently CNO neutrinos were measured for the very firsttime by Borexino [172], though currently with insufficientstatistics to resolve the solar metallicity problem. Theadvantage of directional detection in performing thesescience goals is the vastly improved background rejectioncapabilities and the ability to reconstruct neutrino ener-gies on an event-by-event basis.In Fig. 4 we show the expected neutrino backgroundfor all components mentioned in this section, for both nu-clear and electron recoils (although the latter do not enterinto the main discussion of the paper). As in later exam-ples we assume a 1000 m gas TPC located at Boulby Un-derground Laboratory with a He:SF gas mixture heldat atmospheric pressure with a ratio of 755:5 Torr. Again,the justification for this choice of target, volume and siteare the subject of the remaining sections of the paper.We show the expected number of events as a function ofthe lower limit of integration in recoil energy, i.e. a hard The Boulby mine is the site of the DRIFT experiment, and isone of several candidate labs for future
Cygnus detectors, seeFig. 2. threshold but with detection efficiency and resolution ig-nored.As we have discussed, solar neutrinos are expected—and indeed desired—to be the dominant background for
Cygnus . In the case of nuclear recoils, the majority ofthe event rate above reasonable O (1 – keV r ) thresholdsoriginates from B component of the flux. One could ex-pect up to 100 events in six years if the threshold canbe lowered to 0.25 keV r . Electron recoils are sensitive tomuch lower energy neutrinos, so all components of thesolar flux contribute to the background leading to a verylarge event rate that persists even at high energies. Ifnon-neutrino electron recoil backgrounds are able to besuppressed to low levels (see Sec. V) then one would ex-pect pp and Be neutrinos to contribute significantly tothe electron recoil signal in
Cygnus . In fact it is possiblethat these fluxes could be measured to even lower ener-gies than in Borexino. We have shown the spectrum ofneutrino-electron recoils for reference and future interest.The directionality of neutrino-electron recoils is notstudied here, but will be crucial to understand if theyare to be extracted from the large background of elec-tron recoils from other sources. Nevertheless, the elec-tron recoils at the energies shown in the right-hand panelof Fig. 4 will have very long tracks in a gas target, sotheir directions should be easily measurable [173, 174].A full investigation of neutrino-electron recoil signals in
Cygnus will be the subject of follow-up work.
3. Supernovae
Another potential signal of interest in directional DMdetectors is the enormous burst of neutrinos from a core-collapse supernova (CCSN), which sheds the binding en-ergy of the resulting compact remnant almost entirely inthe form of neutrinos over a timescale of a few tens ofseconds. Such a collapse-induced burst is expected a fewtimes per century in the Milky Way. The neutrinos ina supernova burst will have a few to a few tens of MeVof energy, and will include all flavors of neutrinos andantineutrinos with roughly equal luminosity [175, 176].Dark matter detectors with low recoil energy thresh-olds are sensitive to supernova neutrino bursts viaCE ν NS [177]. The order of magnitude is a handful ofevents per ton of detector material for a supernova at ∼
10 kpc (just beyond the center of the galaxy, and closeto the most likely distance to the supernova [178]). Ob-served numbers of events scale as the inverse square ofthe distance to the supernova. In Fig. 4 we showed theexpected number of neutrino events in
Cygnus for sucha typical CCSN. We source total neutrino luminositiesand moments of the energy spectra from the 1d simu-lations of Ref. [179] and compute the neutrino spectrausing the fitting formulae from Ref. [180]. We show therange of expected event numbers for the explosions ofstars with masses between 11 and 27 M (cid:12) which cov-ers most of the range of possible supernova-progenitor3masses. For Cygnus -1000 m the typical galactic super-novae at 10 kpc would be just out of reach, however > nuclear or electron recoil events could be observed forsupernovae closer than 3 or 0.5 kpc respectively. All ofthe neutrino burst events would be concentrated arounda O (10 s) period. For very close supernovae, at sub 100pc distances, there may even be detectable pre-supernovaneutrino events generated ∼
10 hours prior to the explo-sion during the dying star’s silicon burning phase [181].A detection of a supernova explosion via CE ν NS wouldbe valuable due to its sensitivity to the total, all-flavorburst flux. Most other detectors that are currently on-line are primarily sensitive to either the ¯ ν e (in water andscintillator detectors) or ν e (in argon and lead detectors)components of the flux [176, 182]. Furthermore, someneutrino spectral information and therefore properties ofthe supernova could be reconstructed from the measuredrecoil energy spectrum [183].The advantages of directionality for the detection of su-pernova burst neutrinos via CE ν NS are several: first, andmost clearly, directional information about the sourcewill be of value to observers in electromagnetic wave-lengths and multimessenger channels who want to makeprompt observations of the supernova event in real-time.Currently, only detectors able to make directional mea-surements of elastic scattering on electrons have goodpointing ability [184, 185] (and Super-Kamiokande isthe only current instance) [186]. Even if there is no ob-viously bright supernova event (as may be the case fora failed supernova), directional information will be help-ful to narrow down the possible progenitors. Finally, ifthe direction to the supernova is known via astronomi-cal measurements, then the neutrino direction informa-tion can be used to reconstruct neutrino energies on anevent-by-event basis.The diffuse supernova neutrino background (DSNB) isalso of interest as an astrophysical target [65, 187–189].A measurement of the DSNB flux would be an indepen-dent probe of cosmology, as well as representing an aver-age of supernova bursts. Unfortunately, both the nuclearand electron recoil rates are expected to be immeasurablysmall in
Cygnus . This can be seen in light-blue curvesin Fig. 4; clearly an increase in detector size of severalorders of magnitude from 1000 m would be needed torealistically observe the signal. Even then, since the fluxis expected to be very close to isotropic, isolating theDSNB would be difficult, and is therefore not a primarygoal for Cygnus .
4. Atmospheric neutrinos
Cosmic ray interactions in the upper atmosphere havelong been a reliable flux of 10 MeV–PeV neutrinos. At-mospheric neutrinos principally originate from the decaysof π and K mesons in hadronic showers created by colli-sions between high-energy cosmic rays and air molecules.The emission of atmospheric electron and muon neutri- nos and antineutrinos has been well-studied for energiesabove 100 MeV, and was important historically in thediscovery of neutrino oscillations. The spectrum in the10 GeV – TeV region is roughly a power law with E − . ν .However at low energies, especially < ∼ MeV, the ge-omagnetic field causes suppression in the flux [66, 67].Current studies of atmospheric neutrinos are based onMonte Carlo simulations such as HKKM [67], Bartol [190]and FLUKA [191], which are informed by cosmic raydata and atmospheric nuclear interaction models. Re-cent observations by Super-Kamiokande [192] and Ice-Cube [193] measure the spectrum between 100 MeV–10TeV with uncertainties now comparable to the models,enabling tight constraints on sterile neutrinos [194, 195]and non-standard interactions [196–198]. The limitedavailability of secondary muon data at low energies makethe flux uncertainty for the 10 MeV–1 GeV neutrino tailmuch larger [62], but a nuclear recoil observatory wouldbe most sensitive to atmospheric neutrinos in this veryregion. The nuclear recoil rate above these energies isvery small due to the falling flux and nuclear form factorsuppression. A future measurement of the low-energyflux by a nuclear recoil experiment would be beneficialfor the improvement of atmospheric neutrino flux mod-els. This is important as atmospheric neutrinos at theseenergies will be a background for future studies of theless well-understood diffuse supernova background. Aswith solar neutrinos, a key advantage of observation vianuclear recoils is the sensitivity to the three-flavor flux,improving the measurement of the total normalization.In addition to spectral information, the angular distri-bution of atmospheric neutrinos is also of great interest.The flux is known to peak towards the horizon over thefull energy range due to the longer flight path for primarycosmic rays through the atmosphere. The directionalityof neutrinos is also controlled by the cutoff in the geo-magnetic rigidity ( pc/Ze for a particle with momentum p and atomic number Z ), which sets the minimum en-ergy required for a cosmic ray to have been deflected toa given direction. For the higher energies when cosmicrays are generally more energetic than the rigidity cut-off, the flux is symmetric in zenith angle about the hori-zon; however for low energies below the cutoff, the fluxis expected to become enhanced in upward-going direc-tions [67]. The spatial dependence of the rigidity cutoffalso induces an east-west dipole asymmetry in both ν e and ν µ directions as well as a strong dependence in theflux normalization on latitude. The subsequent nuclearrecoil distributions therefore also weakly depend on an-gle: a calculation relevant for directional detectors can befound in [42]. A measurement of these angular featuresat new locations would serve as an additional test for fluxsimulations as well as again supplying an enhanced back-ground rejection capability for a directional experiment.The science case for a nuclear recoil observatory and at-mospheric neutrinos is therefore well motivated. How-ever the relevant flux at low energies is still extremelysmall, ∼ cm − s − [67], with roughly 10-20% uncer-4tainties (see the green curves in Fig. 4). This would yielda nuclear recoil rate in a 5 keV r threshold F target ex-periment around of 0.1 ton − year − . Due to the highenergies of the atmospheric neutrino flux, the electronrecoil rate on the other hand is negligible. Atmosphericneutrinos may be measurable via nuclear recoils if furtherrefinements to these calculations put the flux in the up-per end of the current uncertainty, but this would still bea late-stage goal of a Cygnus -like experiment, requiringDUNE-sized [199] ∼ scale volumes.
5. Geoneutrinos
The radioactive decay of uranium, thorium and potas-sium in the Earth’s crust and mantle is believed topower a large fraction of the internal heat flow of theEarth [200, 201]. Such decays will also be a significantsource of antineutrinos for energies below 4.5 MeV. Theimpact of these geoneutrinos on DM experiments hasbeen discussed in the past [60], but as a backgroundthey are subdominant when compared with the largeflux of solar neutrinos at similar energies. Recently how-ever, Ref. [41] explored the science potential of direc-tional geoneutrino measurements in particular. Natu-rally, the flux of neutrinos originating from the Earth willbe strongly anisotropic in an upward going direction, ap-proximately azimuthally symmetric and constant in time.As with a DM search, the distinct angular signature andthe lack of modulation for geoneutrinos (with respect tosolar neutrinos for instance) would give a directional ex-periment strong background rejection capabilities in thiscontext.As shown in Fig. 4 (left) the CE ν NS recoil rate fromgeoneutrinos in
Cygnus (assuming a location at Boulby)is expected to subdominant, and difficult to observe with-out lowering the threshold significantly. However theremay be scope for using electron recoils as can be seen inFig. 4 (right). The event rate for electron recoils fromgeoneutrinos is around 1–10 per 10,000 m in six years.Boulby in fact has a relatively low flux of geoneutrinoscompared with alternative sites [202]. The main issue inobserving this flux would be the fact that the electron re-coil rate is completely swamped by solar neutrinos. Thisis precisely why directional experiments would be desir-able, since the geoneutrino and solar neutrino fluxes arealmost completely separable in zenith angle during thedaytime, assuming head/tail recognition.The physics motivation for studying geoneutrinos issubstantial. Past measurements of U and
Thgeoneutrinos by KamLAND [203] and Borexino [204]have relied on antineutrino capture by protons. How-ever the 1.8 MeV threshold for free proton inverse betadecay has rendered neutrinos from the decays of K and
U undetectable in this manner. A measurement ofthe threshold-free neutrino-electron scattering from theselower energy sources could tighten the constraint on theradioactive contribution to the Earth’s surface heat flow, which currently stands at ± [205]. A better un-derstanding of the heat flow from an improved knowledgeof the abundance and spatial distribution of radioactivesources would be invaluable for tracing the thermal his-tory of the planet. Since inverse beta decay measure-ments have a very weak angular dependence, a directionalgeoneutrino search would again be particularly advanta-geous in this regard. In Ref. [41] it was found that a 10ton-scale detector operating for 10 years would be capa-ble of a 95% CL measurement of the K flux. With evenlarger detectors the angular recoil spectrum of geoneutri-nos would provide insight into the source of the Earth’smagnetic field. Crucially this requires knowledge of thecomposition and distribution of radioactive elements inthe core. Distinguishing neutrinos from the core and themantle is not possible without directional information.Detecting geoneutrinos will therefore be an importantsecondary goal of a
Cygnus -100,000 m scale experi-ment, particularly if this total volume is distributed overmultiple sites.
6. Science with source and detector
Artificial sources of neutrinos can be used in conjunc-tion with a CE ν NS-sensitive detector for multiple physicspurposes. Potential artificial sources include— in approx-imately increasing order of neutrino energy— radioactivesources (typically ∼ MeV or less), nuclear reactors [206](several MeV), isotope decay at rest [207] ( ∼ < MeV),stopped-pion neutrinos [208] (up to 52 MeV) and low-energy beta beams [209] (tunable, up to tens of MeV ormore). Many of these were first proposed in Ref. [160]in 1983. For neutrino-nucleus interactions to be dom-inated by CE ν NS, the momentum transfer Q must beless than the inverse nuclear size, which is largely thecase for medium-size nuclei for neutrino energies up toaround 50 MeV.Physics possibilities with an artificial-neutrino-sourceCE ν NS experiment are extensive [208]. They includeStandard Model tests [210–214], neutrino electromag-netic properties [211, 215, 216], sterile neutrino oscil-lation searches [217, 218], as well as nuclear form fac-tor [219, 220] and neutron radius measurements [221].For some experimental setups, light DM produced at thesource can be probed [222–225].In Fig. 4 we showed the expected number of nuclearand electron recoil events in
Cygnus over six years fromnearby nuclear reactors. The rates shown here are rela-tively large since the Boulby site benefits from its closeproximity to the Hartlepool nuclear power station. Aswith geoneutrinos, the major advantage of a direction-ally sensitive experiment is in its ability to reject theotherwise irreducible background from other sources ofneutrinos, namely the large rate of solar neutrinos at sim-ilar energies. As with natural sources, the measured re-coil directions of artificial neutrinos, in combination withthe known source location would enable event-by-event5reconstruction of neutrino energies and improve back-ground rejection. The improvements brought by direc-tionality would in general enhance sensitivity to any ofthe array of physics measurements accessible to artificial-source CE ν NS experiments [226].Of the various artificial neutrino source possibilities,the currently-available ones are reactors, which offer hugefluxes of ¯ ν e , and stopped-pion sources. The latter hasyielded the first measurementS of CE ν NS [157–159] bythe COHERENT experiment. Stopped-pion sources pro-duce neutrinos from the weak decays of charged pions atrest. They emit neutrinos with a well-understood spec-trum with a maximum energy of half the mass of themuon, . MeV, overlapping well with typical supernovaneutrino energies. These neutrinos are produced copi-ously at accelerators when ∼ GeV-scale protons collidewith matter, producing pions; when the predominant π + decay after stopping in the matter, they yield monochro-matic 30 MeV ν µ and muons; these at-rest muons decayon 2.2 µ s timescales to create ¯ ν µ and ν e with a few tensof MeV. Stopped-pion sources have been used in exper-iments in the past [227, 228]. Currently the SpallationNeutron Source (SNS) at Oak Ridge National Labora-tory, [211, 229] is in use for CE ν NS measurements [208],and other potential sources might be available in the fu-ture [220]. The SNS produces about × neutrinosper flavor per second with few-hundred-ns pulse width at60 Hz, which results in a factor of − backgroundrejection. While no current detector there has directionalcapability, this source would be suitable for such exper-iments. This setup could serve as a detector technologytest, given that the expected recoil distributions are wellknown.
7. Exotic models
DM experiments will also be able to explore novel neu-trino sector physics. The recently measured CE ν NS crosssections [157–159] appears to agree with the StandardModel prediction currently, but there may be additionalnon-standard interactions that would affect the recoil en-ergy spectra observable in future DM experiments. Forexample Ref. [170] explored the prospects for ton-scaleexperiments to perform novel solar neutrino measure-ments, such as measuring the pp or B flux via the neutralcurrent, as well as constraining the running of the elec-troweak mixing angle and the possible existence of addi-tional mediators from some light dark sector. By mod-ifying the recoil energy spectra, additional exotic inter-actions involved with both DM and neutrinos will affectthe shape of the neutrino floor [230, 231]. Certain me-diators may also increase the number of expected eventsfrom the neutrino background by several orders of mag-nitude [232]. This further emphasizes the need for di-rectional experiments with low energy sensitivity. If theCE ν NS cross section is enhanced in this way by non-standard interactions then potentially a much greater range of WIMP cross sections at low masses are satu-rated by the neutrino background. It was also shownin Ref. [169] that direct detection experiments would beable to make complementary constraints on sterile neu-trinos if both coherent nuclear and electron scattering ofsolar neutrinos is measurable. Again, the fact that theinitial directions of solar neutrinos are known means thata directionally sensitive experiment can reconstruct theneutrino energy spectrum on an event-by-event basis.
D. Summary of science case
A large-scale directional nuclear recoil detector like
Cygnus will offer many opportunities in a great num-ber of research avenues, both in particle physics and as-trophysics. We have described the major goals for suchan experiment functioning as an observatory for DM aswell as neutrinos. As a DM detector, a recoil observa-tory offers one of the most sensitive tests of the putativeWIMP in the sense that it can attain the most powerfulbackground rejection capabilities and confirm the galac-tic origin on the detected signal. Additionally, we havediscussed here that such an experiment will also be ca-pable of searching for other candidate particles for DM,probe non-standard and exotic particle interactions andmap the local DM phase space structure of the MilkyWay galaxy around us. Furthermore, while we woulddesirably have the experiment detect the DM, we em-phasize that the presence of the unavoidable neutrinobackground in nuclear recoil experiments brings with itnovel opportunities for discovery in its own right.
III. EXISTING DIRECTIONAL DETECTIONTECHNOLOGIES
The directions of nuclear recoils can be inferred in adetector by direct or indirect means. A direct reconstruc-tion of the recoil track, such as in a tracking detector, canbe achieved if the nuclear recoil geometry is measurable.An indirect measure on the other hand may be possible ifthere exists some proxy for the recoil direction, such as adetector response that depends upon some angle betweenthe recoil and a detector axis. In this section we summa-rize the various available readout methods based on thesetwo broad ideas. In doing so we outline and provide refer-ences to the experimental data that supports the simula-tion parameters used in the following Sec. IV. For a moredetailed and critical assessment of these technologies, in-cluding those not under consideration for
Cygnus , seeRef. [15].
A. Detectors with recoil track reconstruction
All currently active directional experiments aim to re-construct the geometry of recoil tracks. Most of these6make use of a low-pressure gas time projection cham-ber (TPC), in which the mm-scale track geometry ismeasured in 1, 2, or 3 dimensions. In addition to gas-based TPCs, track reconstruction at the 100 nm scale hasbeen demonstrated in solid-state nuclear emulsions [233].More exotic, and at this point unvalidated, technologiessuch as nitrogen-vacancy centers in diamond [234], DNAstrands [235], and columnar recombination [236] havealso been proposed.
1. Gaseous TPCs
The low-pressure gas TPC is the most mature direc-tional detection technology. In this scheme, the WIMP-induced recoil generates a track of ionization in the gasvolume, and an electric field transports the resultingcharge to an amplification and readout plane. The fullthree dimensions of a recoil track can be reconstructed bycombining the 2d measurement of the ionization chargedistribution on the readout plane, with the third dimen-sion inferred by sampling the transported signal as afunction of time. The projection of the track along thisthird dimension, parallel to the drift field, is found bymultiplying the duration of the signal with the knowndrift velocity of the charge in the gas. In some designs,the ionization electrons can be transported directly. Inothers, a target gas with high electron affinity is usedwhere the ionization electrons rapidly combine with sur-rounding gas molecules near the interaction site to formnegative ions which instead drift to the readout plane.This latter method, so-called ‘negative ion drift’ (NID),can help suppress the diffusion of the ionization track tothe thermal limit and thus preserve more of the track ge-ometry prior to readout [237]. Recent work has exploredNID operation at atmospheric pressure as well [238].Given the O (keV) energies expected for WIMP-induced nuclear recoils, and the typical energy requiredto create an electron-ion pair in gas targets, W ≈ eV,a recoil will produce O (10 – ) primary ionizationelectrons. To enhance this signal, a gas amplificationdevice is used, consisting of a carefully designed region ofhigh electric field where avalanche multiplication occurs.In some cases, this amplification device is integral to thereadout—Multi-Wire Proportional Chambers (MWPCs)and Micromegas for instance—while in others, the gasamplification and readout are distinct, like with siliconpixel chips or an optical readout. Indeed, multiple gasamplification techniques, and readouts, may be usedtogether in the same detector. The recoil measurementmay combine charge readout with other detectionchannels. For example, if the gas target scintillatesduring amplification, then optical readout can be usedwith, or in place of, charge readout. a. Multi-Wire Proportional Chambers Early workin directional detection used MWPCs, which provideboth gas amplification and spatial information. The DRIFT collaboration pioneered this method [239, 240],and currently holds the leading DM limit set by adirectional detector [241, 242]. DRIFT-IId achievedzero-background operation over more than 100 live-daysusing a low-pressure gas mixture (30:10:1 Torr ofCS :CF :O ) in a back-to-back TPC configuration, eachwith drift length of 50 cm. An energy resolution of40%, a threshold for head/tail recognition for fluorinerecoils (in a statistical sense, not event-by-event) of40 keV r , and a fluorine recoil detection energy thresholdof 20 keV r , were all achieved experimentally. The energythreshold was ultimately limited by the achievable gasamplification of ∼ [243, 244]. The spatial resolutionin the readout plane is given by the amplification wirespacing, or pitch, of 2 mm. Mechanical instabilitiesarising from inter-wire electrostatic interactions preventsmaller wire spacings. The spatial granularity along thedrift direction, on the other hand, is substantially finer: µ m, for a 1 MHz sampling rate and negative ion driftspeed of 60 µ m/ µ s. In an MWPC, the capacitance perwire is very low ( (cid:28) pF for a wire length of 1 m), andthe noise will depend on the readout electronics. Forexample, using front-end ASICs developed for LAr TPCs[245] coupled to a custom digitizer, a noise of 250 e − with a 10 µ s averaging time has been demonstrated [246].Based on previous experience, a × m MWPC wouldcost approximately US$15k. b. Micro-Patterned Gas Detectors with strip read-out
The development of micro-patterned gas detectors(MPGDs) [247, 248] has enabled improved spatial reso-lution relative to MWPCs, which enhances the track re-construction capability of gaseous TPCs. MPGDs are de-fined as high spatial granularity gaseous devices with sub-mm gaps between their anode and cathode electrodes,fabricated using microelectronics technology. Examplesinclude the µ -PIC [249], and the Micromegas [250].Large-area MPGDs have become commodity items.For example, a × m resistive-strip micromegas with2d strip readout (200 µ m pitch) is available for purchasefrom CERN for US$30k [251]. The measured strip ca-pacitance is 500 pF per meter [251]. A vigorous R&Deffort is underway to produce low-background MPGDsfor rare-event searches (see e.g. Ref. [252]).MPGDs with segmented readout are in use for di-rectional dark matter detection already. For example,the MIMAC collaboration [17, 253] uses a low-pressureelectron-drift gas mixture of CF , CHF , and C H (70%/28%/2% at 50 mbar) in a back-to-back TPCconfiguration with 25-cm drift length. MIMAC demon-strated an event detection threshold of 1 keV ee , andan energy resolution of 10% at 5.9 keV ee for a gasamplification of 20,000 [254]. In addition, the NEWAGEcollaboration [255], uses a µ -PIC with 400 µ m pitch anda readout sampling time of 10 ns. To enhance the gasamplification, a Gas Electron Multiplier (GEM) [256]is used, for a typical total gas gain of 6000. NEWAGEhas run a TPC with 40 cm drift length and CF gas7at 100 Torr. They have achieved an energy resolutionof 16% ( σ/µ ), and an angular resolution of 40 ◦ attheir recoil energy threshold of 50 keV ee with an under-ground detector [255]. NEWAGE has also demonstratedhead/tail sensitivity down to 75 keV ee with a testchamber [257]. c. MPGD with pad readout Driven by the needsof large-scale LAr neutrino detectors, the communityhas seen new developments in large-area MPGDs. Forexample, a segmented readout plane with integratedreadout electronics has been developed [258]. Thepad pitch of 3 mm is large compared to the needs fordirectional DM detection, but the pad geometry couldbe optimized in the future. The model considered herehas a pitch of 3 mm, a pad capacitance of 0.25 pF,and an rms readout noise of 375 e − in a 1 µ s samplingwindow, with an estimated cost of US$5k per squaremeter readout plane [259]. d. Pixel chips Even finer spatial resolution thanMPGDs can be obtained with pixelated silicon chips.Examples of pixel-based readouts include the FE-I4bATLAS chips [260], QPIX [261] and Medipix [262]pixel chip families, which provide spatial granularity asfine as 50 µ m. Rapid digitization of the readout planeprovides spatial information along the drift direction.The fine spatial resolution and low per-pixel capacitance(0.01–0.2 pF) are clear strengths of this technology,though a drawback is the small size of each chip (thecurrent-generation ATLAS pixel chip is . × . cm).Building a square-meter area readout plane would behighly costly and complex, though certainly possible.For example, the ATLAS Phase II pixel detector willemploy enough chips to cover more than 10 squaremeters of readout area [263]. R&D work has demon-strated the capability of pixel chips for directionalDM detection. For example, in a TPC filled with oneatmosphere of He:CO (70:30) — an electron-drift gas— and using double GEMs for gas amplification, anenergy resolution of 20% and single electron threshold(for primary ionization) was demonstrated [264–267].Presently, the cost of the ATLAS pixel chips (modelRD53B) is US$90k/m , not inclusive of the cost of a gasamplification device or readout system. e. Optical imaging The ionization from charge am-plification in the gas may be accompanied by the emis-sion of photons, which can be imaged optically ( e.g. witha CCD or CMOS camera). This was the first approachused in 1994 for directional dark matter detection withTPCs [268]. The technique was then revived in the2000s [269], and was employed by the DMTPC collabora-tion [270–272] who used four CCD cameras (Apogee AltaU6, × pixels, × µ m each) to image a TPCwith 27 cm drift length filled with CF at 60 Torr (typi-cal). The proven energy resolution was 35% at 80 keV r ,with a recoil energy threshold of 20 keV ee . The angu- lar resolution was 15 ◦ at 20 keV ee , with head/tail sensi-tivity above 40 keV ee [271]. The DMTPC cameras had10 e − readout noise. More recent high-end commerciallyavailable cameras ( e.g. Hamamatsu ORCA-Flash4.0 V3CMOS, costing US$9k) could offer substantial perfor-mance improvements.Exposure and readout times of cameras are long com-pared to the signal generation in the detector, so a disad-vantage of optical readouts is that only a 2d projectionof a recoil track in the readout plane is measurable. Onewould need to combine this slow imaging technique witha faster readout (e.g. photomultipliers) to recover thethird dimension of the track [273–275]. Another draw-back is that the ratio of photon production to chargeproduction can be low, e.g. one photon per three elec-trons in CF [276]. More importantly, the geometric ac-ceptance for photons is very small because very few pho-tons produced in the amplification region make it ontothe image sensor. Orders of magnitude more gas ampli-fication are therefore required to compensate, relative tocharge readout. However, cameras do have advantagesover charge-based readouts, in particular a lower burdenon radiopurity since the cameras are located outside ofthe active volume of the detector. Additionally, high 2dspatial resolution is possible, and data acquisition is triv-ial, e.g. a USB cable to a PC.Optical readouts are not a major focus of this pa-per. Instead, the CYGNO project [277, 278] is work-ing with and alongside Cygnus to investigate separatelythe prospects of optically based readouts and electrondrift. CYGNO employs a CMOS camera coupled to aTPC with triple thin GEMs for gas amplification in a60:40 He:CF mixture at 1 bar [275]. This configura-tion provides the necessary high gas gain of O (10 ) , withabout one photon produced for every ten electrons [279].An energy threshold of 2 keV ee and 20% energy reso-lution at 5.9 keV ee has been demonstrated [280]. InLEMOn, the largest CYGNO prototype, the drift lengthis 20 cm, achievable thanks to the low electron diffusionin He:CF . Fiducialization may also be possible becausethe high spatial granularity can allow the diffusion ofionization cloud to be measured, which in turn is de-pendent on the absolute track position along the driftdirection. Preliminary measurements with LEMOn havedemonstrated directional and head/tail sensitivity downto about 20 keV ee [281].
2. Nuclear Emulsions
The nuclear emulsion most well developed for low en-ergy applications consists of silver halide (AgBr) crys-tals with a 2.7 eV semiconducting band dispersed in apolymer. The crystal grains work as sensors of chargedparticles by producing several-nanometer diameter sil-ver clusters in response to a nuclear recoil track. Theemulsions need to be developed successively with a cat-alytic process, so that a two-dimensional projection of8the track trajectory onto the surface can be eventuallyreconstructed with an optical or x-ray microscope. Re-cently, Nagoya University managed to produce a super-high-resolution nuclear emulsion called a Nano-ImagingTracker (NIT), with a mean crystal size of 20-40 nm [282].Currently no head-tail sensitivity has yet been demon-strated in nuclear emulsions.The Nuclear Emulsions for WIMP Search project(NEWS) is a directional DM experiment with NIT anda fully automated optical scanning system. It demon-strated absolute tracking efficiencies for carbon recoils at60, 80, and 100 keV of 30 % , 61 % and 73 % , respectively,by implanting collimated monoenergetic ions ( e.g. C, O,Kr, F, B etc.). With a directional analysis based on theuse of plasmon resonance [283] and a prototype micro-scope, NEWS managed to establish a position accuracyof 10 nm for a single grain [233] for 100 keV C ions. Back-ground discrimination methods are under investigationto suppress the high expected C contamination presentin the gelatin producing β decays: the current rejectionpower is 10 − , but the required is 10 − . An R&D exper-iment of 10 grams of NIT is currently being prepared forinstallation at LNGS.Since the measurement of the nuclear emulsion must beperformed after the exposure time of the experiment, anydirectional signal will be washed out by many rotationsof the Earth during that time. NEWS have proposedmounting the experiment on an equatorial telescope butat great financial cost. It was shown in Ref. [37], however,that there is still a directional signal present after time-integration, but the strength of the anisotropy is reduced.A factor of 2–3 more events would be required to distin-guish the WIMP signal from an isotropic background ifthe mounting strategy were not implemented.
3. Crystal defect spectroscopy
Nitrogen vacancy (NV) centers in diamond are quan-tum systems that are highly sensitive to nearby magneticfields as well as to localized crystal strain. A recent pro-posal suggests that this emerging technology could beused for directional DM detection [234]. WIMP-inducednuclear recoils in the diamond target would create a dam-age trail in the crystal. The trail alters the strain patternwhich could be measured using spectroscopic interroga-tion of nearby NV centers. This technology has the ben-efit of being solid-state, so a large potential target mass.With ultra-fine nanometer-scale spatial resolution, pre-liminary calculations suggest a sensitivity to a head/tailsignature as well, though no experimental work has beenreported yet.
4. Graphene targets
Nuclear recoil directions in 3d (bulk) targets often getscrambled through multiple interactions with the sur- rounding medium. The recoil direction may be moredirectly measured in 2d targets. Such targets could befabricated from semiconductor materials in which the ex-citation energy is on the order of ∼ eV, allowing evenMeV-scale WIMPs to initiate electronic excitations. Arecent proposal suggests that 2d graphene could serve asa directional detector of sub-GeV WIMPs [284]. This isa particularly interesting idea, especially given that noother directional technology can probe this WIMP massscale. There has not yet been an experimental demon-stration of this technology, although it may be possiblewithin the PTOLEMY relic neutrino search [285]. B. Detectors that indirectly determine the recoildirection
1. Anisotropic scintillators
Solid scintillators ( e.g.
NaI and CsI) are commonlyused in particle detection, and specifically in DM detec-tion. Because of their large target mass and high nucleoncontent, they are ideal for SI WIMP searches. Some scin-tillators, such as ZnWO and stilbene, have been shownto exhibit a response that depends on the recoil ion di-rection relative to the crystal axes. In principle, thisscintillation anisotropy can be used to infer the nuclearrecoil track direction without direct reconstruction of thetrack geometry. Several groups have explored the possi-bility of using anisotropic scintillators for a directionaldark matter search [286–291], though the magnitude ofthe anisotropy is too small (less than 10%) for anythingparticularly sensitive. Moreover, none of these studieshave demonstrated anisotropic scintillation for nuclearrecoils at low enough energies. Therefore, all quoted en-ergy resolutions, thresholds, and general performancesare for general detection of alpha, beta, and gamma ra-diation and not necessarily relevant for discussion in thecontext of DM.
2. Columnar recombination
When a recoil ionizes the detector medium, a trackof electrons and ions is created. If no electric field ispresent, these ionization products recombine, produc-ing scintillation light and suppressing the charge signal.With an external electric field, the amount of light pro-duced will depend on the relative orientation of the recoiltrack and the field: a large angle results in a small re-combination fraction, which enhances the charge signalrelative to the light signal. A precise measurement ofthe charge-to-light-ratio could be a proxy for recoil trackdirection [236, 292].Evidence for columnar recombination with high-energyalpha tracks was observed long ago in dense xenongas [293]. Recent simulations [294] suggest that it couldbe present for tracks as short as 2 µ m (corresponding to a9threshold of 30 keV r at a pressure of 10 bar), if the ionizedelectrons are properly thermalized. This is not possiblehowever in pure Xe due to the lack of inelastic scatteringbelow 7 eV. Early experimental efforts to cool ioniza-tion electrons with trimethylamine strongly suppressedthe primary scintillation light, so that a columnar recom-bination measurement was not possible [295]. In liquidargon, however, there has been a marginal detection ofthe signature of columnar recombination for nuclear re-coils with energies above 57 keV [296]. If the effect wasshown to be strong enough in liquid noble experimentsthen it may marginally help in extending the discoverybelow the neutrino floor at WIMP masses around 100GeV c − and above [42]. R&D work on columnar recom-bination is ongoing (see e.g. Ref. [292]), but given the lowtechnological readiness at this time, we do not evaluateit further here.
3. Carbon nanotubes
Single-wall aligned carbon nanotubes (CNTs) havebeen recently proposed as a DM target due to their ex-pected anisotropic response to neutral particles [297].Under the right conditions, when a C ion scatters off ofthe CNT walls it sees the tube as empty and can travelwith nearly no loss of energy: an effect known as channel-ing. Different orientations of the CNT axis with respectto the DM wind would give different channeling prob-abilities and therefore produce significantly different Cion currents at the end of the nanotube. The proposeddetector concept in Ref. [297] is a brush of CNTs arrayclosed at one end and open at the other, inserted in a(low-pressure) TPC to detect the outgoing C ions downto ∼
10 keV. An R & D effort is currently underway in Italyto test the channeling hypothesis for neutral particle scat-tering and the TPC detector approach.
IV. DETERMINING THE DIRECTIONALSENSITIVITY OF CYGNUS
To determine and optimize the directional sensitivityof a large scale experiment like
Cygnus , we will focus ongas TPCs, which constitute the most mature directionaldetection technology. In the previous section, we haveseen that a large number of TPC readout technologieshave already been successfully demonstrated on smallerscales. Our primary goal here therefore, is to determinethe most appropriate TPC readout technology to realizethe science goals set out in Sec. II.Previous theoretical work already compared the abilityof directional detectors to discover galactic dark matter,and to set limits beyond the neutrino floor [14, 36]. Herewe go one step further, by simulating TPCs with specificreadout technologies from the ground up, accounting forinevitable physics and detector effects such as nuclearstraggling, diffusion of drift charge, readout quantization, and readout noise. This allows us to obtain an energy-dependent description of the detector performance in-cluding angular resolution, head/tail efficiency, energyresolution, and detection efficiency. The gradual varia-tion of the detector performance with recoil energy is ulti-mately what will determine how well
Cygnus can utilizerecoil directions to distinguish between dark matter andneutrinos, or between dark matter and an unexpectedbackground of nuclear recoils. There is also the questionof electron background rejection, which is also stronglyenergy-dependent, and which will determine the recoilenergy threshold above which
Cygnus can be expectedto remain background free. We will use the TPC simu-lations to estimate electron rejection factors, which willinform the later discussion (see Sec. V) of backgroundsfor a 1000 m scale experiment. To further inform ourreadout choices for Cygnus , we will also evaluate thecost of each simulated technology. Ultimately the idealdetector is the one the maximizes science sensitivity perunit cost. This will be the manner in which we arrive ata final readout decision.
A. Choice of gas
The parameter space for gas TPCs is large, as a num-ber of readout technologies, gas mixtures, and opera-tional parameters are possible. Furthermore, for eachreadout technology the spatial segmentation can be var-ied, for each gas mixture the pressure can be varied, andthere are many operational parameters such as drift fieldstrength, avalanche device voltage, and gas temperature.Our goal here is to identify the optimal choice of read-out, with the goal of uniting investigators in the field topursue a single, optimal, detector design. This is com-plicated by the fact that the optimal choice of readoutdepends somewhat on gas mixture and operating param-eters. For example, the gas mixture and pressure affectthe maximum avalanche gain and recoil length, which af-fect the charge sensitivity and segmentation required ofthe readout, respectively.To make progress, we partition the problem, and herecompare multiple existing charge readout technologieswith typical performance parameters while holding thegas mixture and detector avalanche gain constant.As mentioned in Sec. III A 1, NID gases are well knownto improve the performance of dark matter TPCs bylimiting diffusion of the drift charge. Moreover, it hasalso been discovered that minority carriers in NID gasescan enable fiducialization in the drift direction. Full 3dfiducialization in NID was first demonstrated with CS gas [298], and more recently with SF gas [299]. Thisability to locate events within the detector volume is cru-cial for background rejection. SF gas also has a num-ber of additional properties that when combined makeit a particularly suitable TPC fill gas for a DM search:is non-toxic, non-corrosive, and contains F–one of themost powerful targets to set limits on the SD WIMP-0proton cross section. For these reasons, the NID gas SF has received substantial recent interest from the direc-tional dark matter detection community [238, 300–302].One potential drawback of SF , is that it tends to re-sult in approximately two orders of magnitude lower gasavalanche gains than is typical for commonly used elec-tron drift gases. As a result, fixing SF as a design choicebiases our comparison of TPC readouts in favor of moresensitive charge readout technologies. This is importantto mention because alternative design strategies based onelectron-drift gases may also be competitive. In detectorsusing electron drift, the substantially higher avalanchegain will generally lead to greatly improved charge sensi-tivity and performance of low mass WIMP and neutrinoexperiments. With a high-resolution charge readout, 3dfiducialization is also possible in electron drift detectors— albeit with different techniques [264]. However chargetends to diffuse more in electron drift detectors which re-duces directionality at the O (1 – keV) energies neededto detect light WIMPs and solar neutrinos. This aspecttherefore favors NID gases.A new approach for this paper — one which is alreadyunder experimental investigation by the authors [280,303] — is the addition of helium to the fill gas. Weexpect this to greatly improve WIMP sensitivity and di-rectionality at the lowest recoil energies. When used as ascattering target, helium has greater energy transfer thanfluorine for particle masses near the proton mass. Thismeans our DM mass sensitivity could be extended downto very light and unconstrained ∼ c − WIMPs,while increasing the solar neutrino event rate. Heliumgas has a much lower mass density than fluorine at thesame pressure, so its inclusion does not greatly affect thetrack lengths of fluorine recoils. Finally, helium ions havelower specific ionization than heavier nuclei and thereforelonger tracks, further improving directionality at low re-coil energies. For these reasons a He:SF or He:CF mix-ture may be optimal as it could both improve the direc-tional sensitivity in general as well as extend the darkmatter search into unexplored parameter space.In this work, we have focused on He:SF mixtures, andthe final gas mixture was identified iteratively. Three dif-ferent mixture were simulated, using the gas parametersin Table I, and the performance was evaluated. The an-gular resolution for nuclear recoils depends strongly onthese gas parameters (see Ref. [267], Eq. 5): the angularresolution is proportional to the readout point resolu-tion and inversely proportional to the track length. Thepoint resolution in turn grows with diffusion, and thetrack length is inversely proportional to the gas density.Hence angular resolution improves with smaller diffusionand with lower mass-density. In addition, recoil lengthat fixed energy also increases as the nuclear mass is low-ered. Hence angular resolution can also improve whenlow-mass target nuclei are introduced, as long as othergas parameters do not degrade.The first gas simulated, pure SF , has been used exten-sively experimentally, but we found here that the simu- lated fluorine recoils do not have satisfactory angular res-olution at low recoil energies relevant to WIMP sensitiv-ity near the solar neutrino floor. We then added heliumto arrive at a 740:20 Torr He:SF mixture. This leads totwo improvements: The helium recoils have substantiallybetter angular resolution than the fluorine recoils, andan atmospheric pressure gas mixture would negate theneed for low-pressure vessels, reducing cost. We found,however, that the addition of helium increased the massdensity to a point where angular resolution for low en-ergy recoils was still worse than desirable. For that rea-son, we performed a third set of simulations with a 755:5Torr He:SF gas mixture. This mixture has the com-bined benefits of low mass density, high helium content,and atmospheric pressure, enabling good directional per-formance at low recoil energies while keeping cost low.The final readout comparison and sensitivity analysishere is therefore performed with the 755:5 He:SF gasmixture. Due to substantial computing time required toperform detector simulations, not all the other studiesbelow have been performed for all gas mixtures. Resultswith pure SF and 740:20 He:SF should be consideredlower limits on performance.Improved performance and sensitivity per unit cost islikely to result from further optimization of the gas mix-ture. The final choice of gas mixture is also constrainedby operational stability, which cannot be reliably simu-lated. An experimental investigation of gases suitable fordirectional recoil detection, for electron drift gases at at-mospheric and sub-atmospheric pressures, can be foundin Ref. [266]. B. Simulation
Our simulation of a directional detector consists of thefollowing stages: (1) nuclear and electron recoil momen-tum vectors are generated from the expected distributionof WIMP and neutrino event rates; (2) primary ioniza-tion distributions are generated for each generated recoilevent; (3) the primary ionization is propagated throughthe detector; and finally (4) the simulation of the gainstage and charge readout. Each stage is described inmore detail below. Once we have obtained a simulationof the signal measured by each readout technology un-der consideration, a fit to obtain a recoil direction foreach event is performed, and the result is put throughan analysis framework to derive physics results. Theselatter steps will be detailed in the subsequent sections.
1. Momentum vector generation
WIMP nuclear recoil vectors are generated assuminga Gaussian velocity distribution Eq.(9), with circular ve-locity v = 220 km s − , escape speed v esc = 533 km s − and DM density ρ = 0 . GeV cm − at the solar system.For SI recoils, we assume the standard Helm form fac-1 Nuclear recoils (20 keV r ) Helium in 20 Torr SF P o s t d r i f t P r e d r i f t
25 cm drift 25 cm drift
Fluorine in 20 Torr SF FIG. 6. Distribution of recoil ionization for 20 keV r helium (left column) and fluorine (right column) nuclear recoil eventsin 20 Torr of SF , generated with TRIM. Both recoils start out at ( x, y, z ) = (0 , ,
25 cm) with initial velocity vectors in thedirection of the positive x axis. The top row displays the primary ionization prior to drift, and the bottom row displays thenegative ion distribution after 25 cm of diffusion. The recoil direction of the helium nucleus is better preserved after diffusionof drift charge than the fluorine recoil. This is mostly because helium recoils are longer than fluorine recoils of the same energy.In addition, helium nuclei suffer smaller energy losses to nuclear collisions, which results both in more visible ionization andstraighter recoils. tor (although in the case of helium this has a negligibleimpact on the distribution). For fluorine SD recoils, wetake the two-body corrected values for (cid:104) S p (cid:105) = 0 . and (cid:104) S n (cid:105) = 0 . from Ref. [304] combined with a shell modelform factor calculation [305]. We assume equal SI and SDcouplings to protons and neutrons. Fluorine and heliumrecoils from coherent elastic neutrino-nucleus scattering,on the other hand, are generated using the analytic ex-pression for the angular differential event rate calculatedin Ref. [36]. We again use the Helm form factor and as-sume a B flux normalization in accordance with a globalanalysis of solar and terrestrial neutrino data [306]. WIMP and neutrino nuclear recoil vectors are gen-erated in the lab (North-West-Zenith) coordinate sys-tem at the latitude and longitude of Boulby, UK(54.5534 ◦ N, 0.8245 ◦ W). We use the full computationof v lab ( t ) and ˆ r (cid:12) in this system (see Ref. [14]) whichensures the vector generation automatically includes an-nual and daily modulation signals for both WIMPs andneutrinos. The events are generated assuming uniformup-time throughout the calendar year. The simulatedposition distribution of recoils in the detector is uniform.Electron momentum vectors finally, are generated uni-formly in the detector and isotropically with respect to2 Electron recoils (20 keV)
20 Torr SF
200 Torr SF P o s t d r i f t P r e d r i f t
25 cm drift 25 cm drift
FIG. 7. As in Fig. 6 but now for 20 keV electron recoil events in SF , generated with DEGRAD. The left- and right-handcolumns compare two different pressures: 20 Torr and 200 Torr respectively (note the different spatial scales between the twocolumns). Then, as in the previous figure, the top row displays the primary ionization prior to drift, and the bottom rowdisplays the negative ion distribution after 25 cm of diffusion. In 20 Torr, the electron recoil is essentially preserved after thediffusion of drift charge, but when the pressure is increased to 200 Torr the topology is washed out. This illustrates that a gaswith low mass density improves not only directionality but also particle identification. this coordinate system.
2. Generation of primary ionization distributions
To generate the primary ionization distribution of nu-clear recoils and electron recoils, we utilize the event gen-erators TRIM [307] and DEGRAD [308], respectively.Both generators take as input the momentum vector ofthe particle to be simulated, and configuration files thatspecify the gas mixture. DEGRAD directly outputs a 3ddistribution of ionized electrons, while the TRIM outputneeds to be post-processed. At low energies, ionization from secondaries cannot be neglected. To estimate thefull ionization distribution for individual recoils, we gen-erate TRIM recoils in the most detailed mode and con-figure TRIM to output all primary and secondary col-lisions. From the detailed collision output, we recon-struct the trajectories and momenta of all particles inthe recoil cascade, from which the 3d ionization is esti-mated. Further details on this procedure are available inRef. [309]. The top rows of Figs. 6 and 7 show examplesof generated events as they appear at this stage. Figure 8then shows distributions of resulting event-level quanti-ties that can be computed at this stage: the quenchingfactor for nuclear recoils (left), and the fitted length of3the charge cloud versus the deposited ionization energy(right). The track lengths versus energy show clear sepa-ration between helium, fluorine and electron recoils. Thiswill be important later in this Section when we discusselectron discrimination.
3. Simulation of diffusion and gain
Gas mixture SF He:SF He:SF Pressure [Torr] 20 740:20 755:5Density [kg/m ] 0.16 0.32 0.20 W [eV/ion pair] 35.5 38.0 40.0Trans. diffusion [µ m / √ cm ] 116.2 78.6 78.6Long. diffusion [µ m / √ cm ] 116.2 78.6 78.6Drift velocity [ mm / µ s ] 0.140 0.140 0.140Mean avalanche gain × × × TABLE I. Various gas-dependent parameters assumed in theTPC detector simulation. The values are sourced as follows:the W factor for pure SF is from a measurement with alphaparticles [310], while the W factors for the He:SF and He:CF mixtures are calculated using Eq.(1) of Ref. [266]. The dif-fusion values and drift velocity in 20 Torr of pure SF weremeasured in Ref. [299]. For the He:SF mixtures, no mea-surements or reliable simulations exist, so we use the 40 Torrpure SF diffusion from Ref. [299] and then assume the electricfield can be adjusted to keep the drift velocity constant. Theavalanche gain assumed for pure SF has been achieved withTHGEMs in Ref. [311] and triple thin GEMs in Ref. [312],and is also used for He:SF mixtures. After generating primary ionization distributions, weassume that all electrons attach to fluorine atoms, con-verting into negative ions, and then drift towards thereadout plane. We simulate the combined effect of thisattachment, the drift of individual ions, and the subse-quent gas avalanche multiplication in the TPC using thediffusion and gain parameters listed in Table I. For pureSF , these parameters have already been experimentallyestablished. For the He:SF mixture, although the exactgas parameters have not been measured, SRIM predic-tions for recoil properties are similar to what is obtainedby simulating helium and fluorine recoils in pure SF ofthe same total density. In the diffusion and gas gain sim-ulation, we assume that by adjusting the electric fieldstrength and the gain stage, the same diffusion, drift ve-locity, and gas gains as measured in pure SF can beachieved. Experimental work has shown the feasibility ofobtaining gain in He:SF and He:CF :SF mixtures, atboth low ( ∼
100 Torr [313]) and high ( ∼
600 Torr [238])pressure.The simulated drift length of each electron (negativeion in the case of NID) differs. The distance of the WIMPinteraction vertex position to the readout plane is pulledfrom a uniform distribution ranging from 0 to
50 cm .Each electron (ion for NID) in the generated recoil isthen placed at the appropriate position in the detectorand smeared with a Gaussian diffusion dependent on its distance to the readout plane. Edge effects in the driftdirection are included by deleting charges that start out-side the fiducial volume. Amplification is also simulatedat the single electron (or ion) level, using an exponentialdistribution with mean equal to the avalanche gain. Thisproduces an energy-dependent fractional gain resolutionat the event level, which in turn results in an energy-dependent energy resolution, with σ E /E ∼ O (10%) at . ee , typical for gas detectors. Readout noise broad-ens this resolution further, and is discussed later. Foreach gas, the diffusion and gain parameters from Table Iare fixed for all readouts to ensure a fair comparison.This means that we are essentially comparing detectorswith identical gain stages, but different charge readouttechnologies. While many combinations of gain stagesand readouts are possible, we keep the gain stage fixedso as to focus on how the readout affects the final direc-tional performance.Figure 6 shows 20 keV r helium and fluorine recoils in
20 Torr of SF gas. After
25 cm of drift the fluorine recoildirection is rather washed out, but it can still be approxi-mately determined by eye in the case of the helium recoil.Figure 7 shows a
20 keV ee electron event before and af-ter the initial ionization distribution has drifted
25 cm in the detector. For a gas pressure of
20 Torr , the eventtopology is still preserved after diffusion of drift charge,and can be reconstructed with a detector capable of high-resolution charge readout. For a gas pressure of
200 Torr ,such an electron event would have a reduced range, andthe topology is therefore mostly washed out by diffusionafter
25 cm of drift.Comparing the bottom rows of Figs. 6 and 7 it canbe seen that nuclear and electron recoils with similaramounts of ionization (accounting for the quenching fac-tor) differ both in the length and topology of the chargecloud. In particular the charge cloud from the electronrecoil is longer and less uniform. Together these re-sults show that in
20 Torr SF , the ionization distribu-tion can be used to determine the recoil direction anddiscriminate between nuclear and electron recoils–evenafter charge diffusion from realistic drift lengths. Heliumis a preferable target for extending our low WIMP massreach. When adding helium, we must keep the overallmass density low, to preserve recoil lengths and hence di-rectionality and particle identification capabilities. Herewe accomplish this by maintaining atmospheric pressureand reducing the partial pressure of SF . An alternativestrategy is to operate at sub-atmospheric pressure.
4. Simulation of charge readout
A realistic detector requires a charge readout that iscapable of preserving at least part of the topology of thecharge cloud. We compare the performance of six chargereadout technologies in doing this. We discuss the advan-tages and disadvantages of each technology below, in or-der of increasing cost, complexity and performance (the4 ] r VRecoil energy [ke Q u e n c h i ng f ac t o r Helium in He:SF Fluorine in He:SF
FIG. 8. Two different features of the primary ionization at generator level.
Left : quenching factors for TRIM fluorine (blue)and helium (red) recoils in 755:5 He:SF gas, versus recoil energy. Error bars indicate the standard deviation of the quenchingfactor, resulting from fluctuations of the primary ionization. Right : track length versus ionization energy for DEGRADelectron recoils (black) and TRIM fluorine (blue) and helium recoils (red). Track length is defined as the projected length ofthe primary ionization distribution along a 3d track fit. Neither diffusion nor detector effects are included at this stage.Readout type Dimensionality Segmentation ( x × y ) Capacitance [ pF ] σ noise in 1 µ s Threshold/ σ noise planar 1d ( z ) 10 cm ×
10 cm 3000 18000 e − yz ) 1 m wires, 2 mm pitch 0.25 800 e − xyz ) 3 mm × e − xyz ) µ m × µ m n/a 2 photons 5.77strip 3d ( xyz ) 1 m strips, 200 µ m pitch 500 2800 e − xyz ) µ m × µ m 0.012 - 0.200 42 e − . × − photons per avalanche electron is used to account for the combined effects of photon yield, geometric opticalacceptance, optical transparency, and quantum efficiency. parameters used to simulate each one are also summa-rized in Table II). Planar denotes a simple but cost-effective readout whereonly the time-dependence of the avalanche charge isrecorded, with 10 ×
10 cm segmentation. This results ina signal that is effectively a 1d projection of the chargecloud. One implementation of such a readout would be todirectly read the signal from the gain stage, for instanceusing a GEM with a digitizer. This approach has theadvantage of having very low cost per unit area but alsohas several drawbacks resulting from the low segmenta-tion transverse to the drift axis. This leads to reduceddirectionality, reduced electron rejection, and high capac-itance, which in turn means high readout noise and highenergy thresholds.
Wire readouts are traditional MWPCs (see Sec. III).They are of interest because they can be made highly radiopure, and have very small capacitance and hence lowreadout noise. One drawback however is that constraintson wire spacing limit the minimum segmentation of thereadout plane.
Pad readouts with mm-scale feature size are under con-sideration for liquid-argon neutrino detectors [258]. Thesmaller segmentation leads to much lower noise, but alsomuch higher channel counts and higher instrumentationcost than for planar readout. The transverse feature sizeis still larger than ideal for directional detection of WIMPand neutrino nuclear recoils.
Optical readouts (CCDs or CMOS) can be used to im-age scintillation light from the amplification region. Thisapproach may lead to lower backgrounds because thecameras can be placed outside optical ports in the gasvessel. Optical sensors provide exceptionally high seg-mentation and low noise but have comparatively poor5 predrift postdrift z [ c m ] ] - e c ha r ge [ planar - - x [ c m ] z [ c m ] ] - e c ha r ge [ wire N o . o f pho t on s - - x [cm] - y [ c m ] optical - x [ c m ] - y [ c m ] z [ c m ] pad - x [ c m ] - y [ c m ] z [ c m ] pad - - x [ c m ] - y [ c m ] z [ c m ] strip - - x [ c m ] - y [ c m ] z [ c m ] strip - - x [ c m ] - y [ c m ] z [ c m ] pixel - - x [ c m ] - y [ c m ] z [ c m ] pixel FIG. 9. Simulated 25 keV r helium recoil event in 740:20 Torr He:SF gas before drift (top left), after 25 cm of drift (topright), and as measured by six readout technologies (remaining plots as labeled). Readout noise and threshold effects havebeen disabled. temporal resolution. As a result, such readouts integratethe signal in the drift direction, resulting in a 2d pro-jection of the charge cloud. TPCs with optical readoutare cost-effective in that they need only a few camerasper unit readout area, but the effective charge collectionefficiency consequently suffers due to geometric photonacceptance losses which can be as severe as O (10 − ) . Strip readouts, for example strip micromegas or µ PIC,use the coincidence of signals in orthogonal strips to cre-ate 3d hits. Such readouts are a good compromise be-tween performance and cost.
Pixel readouts with application-specific integrated cir-cuit (ASIC) chips generally have the lowest noise andhighest performance, but are the most costly. Due to therelatively small O (cm ) area of typical ASICs, the fullreadout plane for Cygnus would require a substantial number of chips and be quite labor-intensive to imple-ment.We note that readouts can be combined, for instance,Optical 3d readout can be achieved by combining the sig-nal from 2d CCD or CMOS sensors with an independent1d measurement of the time-dependence of the avalanchecharge. See Section IV E.Our aim here is to compare these quite different chargereadout technologies in a fair and unified simulationframework, without invoking any technology-specific sig-nal processing or reconstruction algorithms. In thatspirit, we assume that the amount of charge arriving ateach detection element can be recorded at 1 µ s inter-vals. For readout technologies that have already beenconstructed and characterized, we scale known readoutnoise levels to 1 µ s. For readouts that do not yet exist,6 predrift postdrift z [ c m ] ] - e c ha r ge [ planar - - - x [ c m ] z [ c m ] ] - e c ha r ge [ wire N o . o f pho t on s - - x [cm] - - y [ c m ] optical - - - x [ c m ] - - y [ c m ] z [ c m ] pad - - - x [ c m ] - - y [ c m ] z [ c m ] pad - - x [ c m ] - - y [ c m ] z [ c m ] strip - - x [ c m ] - - y [ c m ] z [ c m ] strip - - x [ c m ] - - y [ c m ] z [ c m ] pixel - - x [ c m ] - - y [ c m ] z [ c m ] pixel FIG. 10. Simulated 20 keV electron event in 740:20 Torr He:SF gas before drift (top left), after 25 cm of drift (top right), andas measured by six readout technologies (remaining plots as labeled). Readout noise and threshold effects have been disabled. such as the planar readout, we estimate the readout noisefor this time interval from the typical capacitance of a de-tection element and the noise curves of a candidate chargesensitive preamplifier [245]. Capacitance values and thenoise estimates used in the simulation are summarized inTable II. We assume that before event reconstruction ahard threshold is applied to the recorded signal in eachchannel. This threshold is set so that for each readoutthe expected rate of noise hits is equal to − / ( cm µ s).As a result, the ratio of the threshold to the noise level,threshold/ σ noise , varies from approximately three for theplanar readout to about six for the pixel ASIC readout.The threshold/ σ noise values resulting from these noise re-quirements are larger for the more segmented readouts,which agrees with common practice in the field.Since the optical readout cannot be sampled at thesame speed as the other readouts, the same procedure cannot be used to determine an analysis threshold. InTable II we instead set a requirement of − / cm noisehits per event on average, but the optical readout per-formance depends strongly on this threshold. For thatreason, a fair comparison of optical and charge readout isnot straightforward. In the comparisons that follows, wetherefore focus only on charge readout, and have a shortseparate discussion of optical readout in Section IV E.Figure 9 shows how a 25 keV r helium recoil in 740:20Torr He:SF gas that has drifted 25 cm and is subse-quently detected by each of the six readout types. Theevents are shown after simulation of gain, gain resolu-tion, and spatial quantization into detection elements,using the parameters from Table II. Noise has been dis-abled for this particular visualization, otherwise noisehits obscure the 3d event displays. Similarly, Fig. 10shows a 20 keV ee electron in the same gas mixture and7with the same detector simulation. In all cases, the de-tected event topology or waveform differs visibly fromthose of the typical nuclear recoil in Figure 9. For a 755:5Torr He:SF mixture, the main change is that the recoillengths approximately double, improving directionalityand discrimination between nuclear recoils and electronrecoils. This suggests electron rejection is achievable inthe O (1 – keV) energy range, perhaps even with verysimple readouts like the planar. We extend this discus-sion quantitatively in Sec. IV H. C. Analysis methodology
In order to analyze the data from the different readouttechnologies in a uniform way, we turn the simulated out-put of each readout into 3d spatial points as follows. Af-ter the gain and noise simulation, charge above thresholdin each detector element and temporal sampling intervalis quantized by dividing the charge by the mean gainand turning the results into an integer. This quantizedcharge is then assigned an absolute ( x, y ) (transverse todrift) coordinate based on the location of the center ofthe detector element, and a relative z (parallel to drift)coordinate based in the detection time relative to the firstcharge above threshold in the event.Once the reconstructed spatial distribution of thecharge cloud has been obtained, its primary axis is foundvia singular value decomposition (SVD). At this stage thereconstructed primary axis vector has an arbitrary sign,so we only have axial-vector information. The sign ofthe vector is reconstructed based on the projection of thepositions of the quantized charges onto the primary axis.Each charge is assigned to one half of the track, basedon whether the charge is closer to the charge with theminimum or maximum projection onto the reconstructedprimary axis. We assume that the kinetic energy of therecoiling nucleus being reconstructed is sufficiently lowso as to be below the Bragg peak; so we take the trackend with the largest assigned charge as the tail. Ouranalysis methodology neglects all charge below thresh-old, but it could be partially recovered with a more so-phisticated noise suppression algorithm. This would im-prove reconstruction performance further, therefore allresults on the directional performance do stand to im-prove. However such an algorithm would likely need to bereadout-specific, while here we aim to be readout-generalto first establish the optimum technology for Cygnus .The implementation and optimization of a bespoke trackreconstruction algorithm would be the next step once thistechnology is chosen.
D. Low-level performance of electronic readouts
We first look at the efficiency, energy resolution, anddirectional performance of each readout type, when de-tecting individual nuclear recoil events. All performance estimates are made at the end of the simulation chain,after the energy thresholds in Table II have been applied,data have been digitized, and 3d space points have beenreconstructed as discussed above. We evaluate the per-formance in 1-keV steps, and fit the results with analyt-ical functions. These functions will allow us to performhigh-statistics simulations of WIMP and neutrino detec-tion scenarios, where the energy spectrum is continuous,without re-running the computationally expensive detec-tor simulation. The parameterized detector performanceversus energy may be useful for studies by the wider com-munity, and the fit parameters are available from the au-thors by request. As mentioned earlier, a fair comparisonof optical and electronic charge readout is not straight-forward. We therefore compare only electronic readouts.Optical readout is discussed separately in Section IV E.
1. Detection efficiency
Figure 11 shows the event-level detection efficiency ofeach readout. Here, an event is counted as detected ifthe reconstructed avalanche charge above threshold isequivalent to at least one electron of ionization beforegain, and if at least three space points have been recon-structed. Such criteria should ensure that some minimaldirectional information can be inferred. A very loose re-quirement, but one that is simply intended to give anindication of the lowest possible recoil energy sensitiv-ity that could be achieved with each technology at thesimulated gain. The energy dependence is obtained byfitting the function a/ (1 + e − b ( E − c ) ) to the data pointsvia χ minimization. Here, a , b , and c are floating fitparameters and E is the recoil energy.We find that all readouts except planar have an effi-ciency higher than 50% above 3 keV r , even for the lowgain of 9000 simulated (with electron drift, gains of or-der − and drastically lower energy thresholds areexpected.) The efficiency is primarily determined by thenoise level of each readout, so that the pixel readout endsup being the most sensitive at low recoil energies, fol-lowed by the pad, wire, strip, and planar readouts. Thisbegins to inform us of the hierarchy in our collection ofreadouts, but electron background rejection and obtain-ing good event-level directional information will typicallyrequire significantly more detected charge per event, aswe discuss below.
2. Energy resolution
Figure 12 shows the energy resolution for each read-out. Since each readout has been simulated with thesame gain stage, the energy resolution differences seenare due to the charge readout. The energy depen-dence is obtained by fitting the functional form σ E /E = (cid:112) ( a /E + b /E + c ) to the data points via χ mini-mization. Here, a , b , and c are floating fit parameters8 Energy [keVr] - -
10 1 E v e n t d e t ec ti on e ff i c i e n c y Planar Wire Pad Strip Pixel 0 2 4 6 8 10
Energy [keVr] - -
10 1 E v e n t d e t ec ti on e ff i c i e n c y Planar Wire Pad Strip Pixel
FIG. 11. Event-level detection efficiency of each readout for fluorine (left) and helium (right) recoils in a 755:5 Torr gas mixtureof He:SF . Error bars are binominal standard deviations, assuming the efficiency measured is the true efficiency.
10 20 30 40 50 60 70 80
Energy [keVr] / E E s F r ac ti on a l e n e r gy r e s o l u ti on , Planar Wire Pad Strip Pixel 0 10 20 30 40 50 60 70 80
Energy [keVr] / E E s F r ac ti on a l e n e r gy r e s o l u ti on , Planar Wire Pad Strip Pixel
FIG. 12. Fractional energy resolution of each readout for fluorine (left) and helium (right) recoils in a 755:5 Torr gas mixtureof He:SF . Error bars indicate the RMS variation in the recoil sample analyzed. Note that the curves for the pad readout arevery close to the pixel and wire cases so are not easily visible here. and E is the recoil energy. For pixel, wire, and pad read-out, the low readout noise does not noticeably affect theenergy resolution. As a result, these three readouts haveidentical energy resolution, limited by the resolution ofthe gain stage. For strip and planar readout, the highernoise floor increases energy resolution above the gain res-olution. It is possible that this could be improved with amore clever energy determination at the algorithm level.If not, somewhat higher gain than simulated would be beneficial for these two readouts.
3. Angular resolution and head/tail recognition
We quantify and compare the directional performanceof each readout by computing their angular resolutionsand head/tail recognition efficiencies.We define angular resolution to be the mean difference9
10 20 30 40 50 60 70 80
Energy [keVr] A ngu l a r r e s o l u ti on [ d e g r ee s ] Planar Wire Pad Strip Pixel Post drift Pre drift 0 10 20 30 40 50 60 70 80
Energy [keVr] A ngu l a r r e s o l u ti on [ d e g r ee s ] Planar Wire Pad Strip Pixel Post drift Pre drift
FIG. 13. Angular resolution of each readout for fluorine (left) and helium (right) recoils in a 755:5 Torr gas mixture of He:SF .Each color denotes a different readout as shown in the legend. Data points show the mean mismeasurement of the recoil axisdirection determined from two hundred pseudo-experiments. Error bars show the statistical uncertainty of this mean. Linesare analytical functions fit to the data points, used to parameterize performance versus energy. The resolution that can beobtained with a perfect readout before (black) and after (red) charge diffusion during drift is also shown for comparison. between the initial recoil axis and the reconstructed re-coil axis. Two randomly oriented 3d axial vectors will onaverage be separated by an angle of 1 radian or 57.3 ◦ .Hence this value corresponds to no angular sensitivity.The energy dependence is obtained by fitting the func-tional form a/ (cid:112) ( b + E c ) + d to the data points via χ minimization. Here, a , b , c , and d are floating fit param-eters and E is the recoil energy. The angular resolution(Fig. 13) of the pixel readout is superior. For other read-outs, the angular resolution gradually gets worse withincreasing feature size and noise floor, as expected fromthe performance ordering in Table II. The performanceof the pixel readout is essentially as good as the perfor-mance obtained by analyzing the primary charge distri-bution immediately after diffusion (indicated as postdriftin Fig. 13). This implies that there is no need for anyfiner segmentation of this readout.At low energies, the effective resolution obtained byfitting the charge cloud before diffusion (pre drift) is sub-stantially better than the post drift performance. Thistells us that the performance at low energies becomeslimited by the track length being short compared to thediffusion scale. This occurs below ∼
20 keV r for heliumrecoils and below ∼ keV r for fluorine. The differencearises because helium recoils are longer than fluorine re-coils of the same energy. In this comparison, helium re-coils also benefit from two additional effects: they de-posit more ionization due to a higher quenching factor,and they exhibit less straggling. The latter limits theangular resolution before diffusion (pre drift). Furtherimprovements may be achievable with a curved track fit to account for straggling, but this is not explored here.Figure 14 shows the head/tail recognition efficiency ofeach simulated readout type versus recoil energy. A ran-dom head/tail assignment will be correct in 50% of thecases, so a value of 0.5 corresponds to no sensitivity. Theenergy dependence is obtained by fitting the functionalform a/ (1 + e − b ( E − c ) ) + d to the data points via χ min-imization. Here, a , b , c , and d are floating fit parametersand E is the recoil energy. In the case of fluorine, the effi-ciency is quite poor for all readouts, even at the higher re-coil energies. We see that before diffusion, some head/tailinformation is still present in the charge cloud, but mostof this information appears to be lost after diffusion. Incontrast for helium recoils, the head/tail information ata given energy is much higher both before and after dif-fusion, and the readouts are able to measure head/tailwith some significance down to energies of order 5 keV r .Because head/tail recognition and angular resolutionat low energies are critical for detecting a WIMP signal,the findings here support utilizing helium as a target nu-cleus. Even with helium, the directionality gradually be-comes diffusion-limited at the lowest recoil energies. Thiseffect starts below 20 keV r for the angular resolution, andbelow approximately 35 keV r for the head/tail recogni-tion. This suggests that the design simulated here is notyet fully optimized. We anticipate further improvementsin performance at low recoil energies by lowering the dif-fusion and/or increasing the recoil length further. Low-ering the gas pressure, lowering the drift length, imple-menting readout-specific reconstruction algorithms, andusing hydrogen target nuclei are examples of possible0
10 20 30 40 50 60 70 80
Energy [keVr] C o rr ec t h ea d t a il fr ac ti on Planar Wire Pad Strip Pixel Post drift Pre drift 0 10 20 30 40 50 60 70 80
Energy [keVr] C o rr ec t h ea d t a il fr ac ti on Planar Wire Pad Strip Pixel Post drift Pre drift
FIG. 14. Head/tail recognition efficiency versus recoil energy and readout type, for fluorine (left) and helium (right) recoilsin a 755:5 Torr gas mixture of He:SF . Each color denotes a different readout as shown in the legend. Data points showthe efficiency determined from two hundred pseudo-experiments. Error bars are binomial standard deviations, assuming theefficiency determined is the true efficiency. Lines are analytical functions fit to the data points, used to parameterize performanceversus energy. The performance that can be obtained with a perfect readout before (black) and after (red) charge diffusionduring drift is also shown, for comparison. strategies that should be pursued. Improving this lowenergy performance will be crucial for maximizing theWIMP/solar neutrino discrimination. E. Optical readout
For optical readout, we find that the simulated perfor-mance depends strongly on the exact value of the opticalloss factor, the noise rejection signal threshold, and thereconstruction algorithm. Our overall finding is that op-tical readout looks challenging with the specific assump-tions given in Table II. Optical readout can be compet-itive, however, if the yield of detected photons per pri-mary electron is increased. This increase can be achievedwith improved amplification structures for negative iondrift gases, by utilizing an electron drift gas, or by bring-ing the optical sensor closer to the amplification plane,thereby reducing the optical loss factor. It is also possi-ble to increase the photon yield via electroluminescence[314].To get a feel for the capabilities of optical readout withmore favorable assumptions, Fig. 15 shows the simulatedperformance when the loss factor and noise are both dis-abled in the simulation. Then, 2d optical readout byitself has similar head/tail recognition as charge readout,but reduced angular resolution when compared to three-dimensional charge readout. This is as expected due tothe 2d nature of the sensor. The angular resolution canbe improved by combining the 2d optical signal with a 1d signal from a PMT. If we assume the PMT perfectlymeasures the true z -width and the true sign of the z com-ponent of the recoil vector (green data points and lines inFig 15), this 2d+1d optical reconstruction performs quitewell in terms of angular resolution, though not quite aswell as true 3d reconstruction. Note that the head/tailperformance in unrealistically good when assuming thisperfect z-measurement. If we simulate a realistic PMT,with performance loosely based on Ref. [275], the per-formance somewhat degrades, but is still substantiallybetter than optical 2d by itself. It may be possible toimprove the optical 2d+1d readout performance substan-tially with more sophisticated algorithms, which wouldutilize not only the PMT signal width, but its detailedtime structure. This has already been demonstrated bythe CYGNO collaboration for electron tracks [275].If we turn on either the optical loss factor or the sig-nal noise, performance does not degrade substantially.However, if we turn on both effects, the optical 2d signalsuffers strongly. For such a scenario, a readout specificnoise-rejection algorithm will be required. This is cur-rently being investigated by the CYGNO collaboration[315].In summary, we find that the optical readout perfor-mance is strongly dependent on the algorithm that com-bines the PMT and optical 2d signal, and on the algo-rithm that rejects the noise. Optical readout also favorssubstantially higher gain than what is simulated here.For these reasons we conclude that a fair comparisonagainst charge readout is not easily possible, and leave1the evaluation of optical readout for future work. F. Directionality threshold
We have seen that there is substantial variation inthe energy-dependent angular resolutions and head/tailrecognition efficiencies of the different readouts consid-ered. The optimal readout, however, is not the one withthe best performance, but rather the one with the bestcompromise between performance and cost, so that thephysics reach per unit cost is maximized. Different sig-nals will have different ranges of relevant recoil ener-gies, so the best compromise may depend on the specificphysics goal.As a first step towards a final cost-performance analy-sis, we quantify the directional performance versus recoilenergy in a way that combines both the angular resolu-tion and head/tail recognition efficiency. This is done byestimating how many recoils each readout needs to de-tect in order to discriminate between a monodirectional(“signal”) delta function (all recoils have initial momen-tum vectors in the same 3d direction) and an isotropic(“background”) recoil distribution. The goal here is toprovide an intuitive result that clearly shows the recoilenergy range where each technology has good direction-ality. Note that a 3d delta function is a hypotheticalscenario with maximum directionality. In any real phys-ical scenario, the recoil distribution is always broadenedby the non-zero scattering angles.Several discovery variables and test statistics have beenproposed in the literature for detecting anisotropic recoildistributions for WIMP searches [14]. The most powerfulvariables are those which depend on the angle betweenthe recoil direction and the direction of Cygnus (or poten-tially the direction of the Sun when the principal back-ground is neutrinos). Not all of our simulated readouts,however, have a dimensionality which allows these anglesto be measured at all times. Our 3d delta function pointsalong the negative z direction, which is the direction thatdrift charge is traveling in the detector. This is the mostsensitive direction for the less segmented readout tech-nologies. Our discovery variable in this case is the polarangle, θ , with respect to the vertical z -axis. Our gener-ated signal peaks at cos θ = − , while our background isflat in cos θ . The detected cos θ distribution for the pixelreadout is shown in Fig. 16 for fluorine and helium recoils.As discussed earlier, the helium recoils are more stronglydirectional than fluorine recoils of the same energy. Thisis a consequence of the performance difference we saw forthe two recoils species in Fig. 13, and primarily causedby helium recoils producing longer tracks than fluorine.Also note that the helium mono-directional signal re-coil distribution in Fig. 16 is significantly more asymmet-ric than the equivalent fluorine distribution, because thehead/tail is assigned correctly more often for helium, aspreviously shown in Fig. 14: at 20 keV r , the simulationpredicts a correct head/tail reconstruction of only ∼ in fluorine, while it is ∼ for helium.In general the reconstructed signal will differ even morefrom the background at higher recoil energies when thedirectional performance is better. The cos θ signal distri-bution is also more asymmetric at higher energies. Forlower energies than 20 keV r the contrast between the sig-nal and background distributions becomes gradually lessdefined, and at the lowest energies simulated here theyare essentially indistinguishable. We saw this in Figs. 13and 14 where all readout curves converged to 1 rad an-gular resolution and 0.5 head/tail efficiency respectively,corresponding to no directional sensitivity.To quantify the physics reach corresponding to thedirectional performance of each readout, we perform aKolomogorov-Smirnov test [316] comparing each signaland background cos θ distribution. Figure 17 shows howmany monodirectional signal events are required to re-ject the isotropic background hypothesis at the 90% con-fidence level (CL) when there are zero background eventspresent. To fairly compare readouts, we count the num-ber of interacting events, meaning that we also countthose that go undetected due to finite reconstruction ef-ficiency. For higher recoil energies, as little as two-threeevents are sufficient to exclude isotropy for the highest-performing readouts.For lower recoil energies however, the number of re-quired events diverges as the directional sensitivity andevent-level detection efficiency deteriorates in all read-outs. To quantify these observations with a single num-ber, we define a directionality threshold : the recoil energyat which ten or more interacting events are required toexclude isotropy. Note that the choice of ten events isan arbitrary choice made to allow an easy comparisonof readout — therefore the directional threshold is notto be interpreted as a hard threshold, and there is stilldirectional sensitivity below this threshold.With those disclaimers made, the directionality thresh-olds for pixel, strip, pad, wire, and planar readouts areapproximately 4 keV r , 6 keV r , 17 keV r , 22 keV r , and42 keV r , respectively, for helium recoils. We note thatto get such good performance at low recoil energies, thelow mass density of the 755:5 Torr He:SF gas mixturewas required. For a 740:20 mixture (not shown here), thedirectional thresholds were approximately a factor of twohigher.Comparing Fig. 17 left and right, we see that for flu-orine recoils, the directional thresholds are more thana factor of three higher than for helium recoils. Sinceour “signal” is maximally anisotropic here, these thresh-olds estimate the limit for good directional sensitivity.It should be noted however we have used a very simplemeasure of directionality. Directional sensitivity can beimproved by performing statistical tests that use all re-coil angles and their correlation with recoil energy, forexample in a likelihood-based analysis. Furthermore,as noted earlier, the pixel and to some extent the stripreadout, are diffusion-limited below 20 keV r for helium,and 50 keV r for fluorine recoil. Hence the directional-2
10 20 30 40 50
Energy [keVr] A ngu l a r r e s o l u ti on [ d e g r ee s ] Optical 2d Opt. 2d + PMT Opt. 2d + true 1dStrip Post drift Pre drift 10 20 30 40 50
Energy [keVr] C o rr ec t h ea d t a il fr ac ti on Optical 2d Opt. 2d + PMT Opt. 2d + true 1dStrip Post drift Pre drift
FIG. 15. Angular resolution (left) and head/tail recognition efficiency (right) for helium recoils in 755:5 Torr He:SF gas,detected with various optical readout technologies, with optical loss factors and detector noise disabled in the simulation. Stripreadout and maximum achievable performance before and after diffusion are also shows, for comparison. See text for discussion. - - - - - q cos F r ac ti on o f e v e n t s / b i n Mono-directional signalIsotropic background - - - - - q cos F r ac ti on o f e v e n t s / b i n Mono-directional signalIsotropic background
FIG. 16. Reconstructed polar angle distribution for 20 keV r fluorine (left) and helium (right) recoils detected with a pixelreadout for a hypothetical mono-directional recoil signal (red) and isotropic recoil distribution background (blue). ity threshold and WIMP sensitivity should improve evenfurther with a detector operating point (gas pressure anddrift field) fully optimized for these high-resolution read-outs. That optimization is beyond our scope, but will bean important part of the next stage, a technical designfor a large directional detector. G. Directional WIMP/neutrino discrimination andenergy threshold requirements
Given that WIMP and neutrino recoils produce keV-scale energies and steeply falling energy spectra, it isclear that the directionality thresholds of different read-outs will have a major effect on the WIMP and neutrinosensitivity. Figure 18 (left) shows the mean number ofWIMP-helium recoil events required to exclude a back-3
Energy [keVr] N u m b e r o f e v e n t s r e qu i r e d Planar Wire Pad StripPixel Post drift Pre drift
Energy [keVr] N u m b e r o f e v e n t s r e qu i r e d Planar Wire Pad StripPixel Post drift Pre drift
FIG. 17. Mean number of mono-directional fluorine (left) or helium (right) recoil events required to reject an isotropic recoilhypothesis at 90% CL, in the case of zero background events, for a 755:5 Torr gas mixture of He:SF . Each color denotes adifferent readout as shown in the legend. Data points show the mean number of recoils required, based on pseudo-experiments,with errors indicating the uncertainty due to finite simulation statistics. The performance that can be obtained with a perfectreadout before (black) and after (red) charge diffusion during drift is also shown, for comparison. Energy [keVr] N u m b e r o f e v e n t s r e qu i r e d Planar Wire Pad StripPixel Post drift Pre drift
Energy [keVr] E xpo s u r e r e qu i r e d [ a r b it . un it ] Planar Wire Pad StripPixel Post drift Pre drift
FIG. 18. Mean number of 10-GeV-WIMP-helium recoils (left) and exposure (right) required, in order to exclude isotropy ingalactic coordinates at 90% CL, versus energy threshold, for a 755:5 Torr gas mixture of He:SF . Each color denotes a differentreadout as shown in the legend. Data points show the mean number of recoils required, based on pseudo-experiments, witherrors indicating the uncertainty due to finite simulation statistics. See text for further details on this and following plots,including why some data points are not drawn. ground recoil distribution that is isotropic in galactic co-ordinates, versus recoil energy threshold. The number ofevents required for exclusion falls with energy, becausethe angular resolution and head/tail efficiency both im-prove with higher energy, so that the WIMP recoil distri- butions become more asymmetric. Because the WIMPrecoil rate falls with energy, however, the best strategyfor an experiment is not simply to raise the energy thresh-old. To get a feel for the energy threshold that minimizesthe exposure need to exclude isotropy, we also show the4 Energy [keVr] N u m b e r o f e v e n t s r e qu i r e d Planar Wire Pad StripPixel Post drift Pre drift
Energy [keVr] E xpo s u r e r e qu i r e d [ a r b it . un it ] Planar Wire Pad StripPixel Post drift Pre drift
FIG. 19. Mean number of 10-GeV-WIMP-helium recoils (left) and exposure (right) required to exclude a neutrino backgroundhypothesis at 90% CL, versus energy treshold, in the case of no detected neutrino background events, for a 755:5 Torr gasmixture of He:SF . Each color denotes a different readout as shown in the legend. Data points show the mean number ofrecoils required, based on pseudo-experiments, with errors indicating the uncertainty due to finite simulation statistics. Energy [keVr] N u m b e r o f e v e n t s r e qu i r e d Planar Wire Pad StripPixel Post drift Pre drift
Energy [keVr] E xpo s u r e r e qu i r e d [ a r b it . un it ] Planar Wire Pad StripPixel Post drift Pre drift
FIG. 20. Mean number of 100-GeV-WIMP-fluorine recoils (left) and exposure (right) required, in order to exclude isotropy ingalactic coordinates at 90% CL, versus energy threshold, for a 755:5 Torr gas mixture of He:SF . Each color denotes a differentreadout as shown in the legend. Data points show the mean number of recoils required, based on pseudo-experiments, witherrors indicating the uncertainty due to finite simulation statistics. exposure required for exclusion versus energy thresholdin Fig. 18 (right). Note that the unit we use as a proxyfor exposure is actually the number of recoil events be-fore the energy threshold - so while these exposure unitscan be used to compare readouts, they are arbitrary inthe sense that they cannot be used to compare scenarioswith different target nuclei or different WIMP masses, i.e. different figures in this article.An important result in Fig. 18 (left) is that only threeto four recoils above 20 keV r are sufficient to excludeisotropy for the two highest-performing readouts, pixelsand strips, respectively. This appears consistent withprevious idealized studies such as Ref. [43], which foundthat 5 to 9 events are required for exclusion of isotropy5 ] WIMP mass [GeV/c N u m b e r o f r ec o il e v e n t s Planar Wire Pad StripPixel Post drift Pre drift ] WIMP mass [GeV/c N u m b e r o f r ec o il e v e n t s Planar Wire Pad StripPixel Post drift Pre drift
FIG. 21. Mean number of WIMP-helium recoil events with energy greater than 6 keV r required to exclude an isotropic (left)and neutrino (right) background hypothesis at 90% CL, versus WIMP mass, in the case of no detected background events. Thetarget gas simulated is a 755:5 Torr mixture of He:SF . Each color denotes a different readout as shown in the legend. Datapoints show the mean number of recoils required, based on pseudo-experiments, with errors indicating the uncertainty due tofinite simulation statistics. at 90% CL in 90% of the cases, which is a stricter statis-tical requirement than ours. Fig. 18 (right) shows thatthe exposure required to exclude of isotropy plateaus be-low 6 keV r for all readouts, but the required exposure isone order of magnitude lower for pixels and strips thanthe other readout technologies. This leads to two ma-jor conclusions: First, directional detectors with strip orpixel readout have about one order of magnitude higherdirectional WIMP sensitivity per unit of exposure thanother readouts studies here. Second, to maximize direc-tional sensitivity to 10-GeV c − WIMPs, we should aimto achieve an energy threshold of 6 keV r or lower.Before moving on, we give more detail on exactly howFig. 18 is produced, as the same procedure is also usedto produce Figs. 19 through 22. We perform 400 pseudo-experiments for each readout and energy threshold com-bination. For each experiment, we record the numberof events required to achieve exclusion at 90% CL, us-ing only the observed recoil direction cos θ as a discrim-inant. The number of events required to achieve ex-clusion at 90% CL is a highly asymmetric distribution,with a significantly larger high-side than low-side tail.In Fig. 18 we conservatively plot the mean, which tendsto be significantly larger than the median. The errorbars shown are the asymmetric statistical uncertaintieson that mean. For cases with limited directionality andlow energy thresholds, sometimes a very large numberof events is required for exclusion, requiring impracti-cally long computations. To reduce computational time,we skip these scenarios: if any of the 400 pseudoexperi-ments require more than 5000 detected events to achieve exclusion, we abort that particular simulation and do notdraw a data point. This is the reason, for example, whythere are no data points for the less directional readoutsin Fig. 18 (right) for the lowest energies. In this simu-lation, we orient the detector so that the WIMP windis aligned with the TPC drift axis ( z ). This is equiva-lent to putting the detector on an equatorial mount, andcontinuously rotating the drift axis towards the expectedWIMP wind direction. For the 3d pixel and strip read-outs, this subtlety is unimportant as these readouts haveclose to isotropic performance. However this is a choicethat will artificially improve the sensitivity of less seg-mented readouts with anisotropic performance or lowerdimensionality, though only mildly.Figure 19 shows the analogous analysis, but now with B neutrino recoils as the background hypothesis. Wemaintain the recoil angle distribution in galactic coordi-nates as the WIMP/neutrino discriminant. Compared tothe isotropic background case, slightly fewer events arerequired to exclude the neutrino background hypothesis.Improved discrimination is possible by including the en-ergy spectrum, event time, and signal normalization asdiscriminants, to be included in Sec. IV I.Figure 20 shows the case of 100 GeV c − WIMPs. Forthe readouts with the best performance, five or fewer flu-orine recoils at high energy are sufficient to exclude anisotropic background hypothesis at 90% CL. Note that inthis case the plateau in the exposure required for exclu-sion occurs around 30 keV r , while for the other scenariosstudies here this plateau occurred around 6 keV r . Thismeans that for a directional detector optimized specifi-6 Number of neutrino-recoil background events N u m b e r o f W I M P -r ec o il e v e n t s r e qu i r e d Planar Wire Pad StripPixel Post drift Pre drift
FIG. 22. Mean number of 10 GeV c − WIMP helium-recoilevents with recoil energy greater than 6 keV r required to ex-clude a neutrino background hypothesis at 90% CL, versusnumber of neutrino background events in the detected eventsample. The target gas simulated is a 755:5 Torr mixture ofHe:SF . Each color denotes a different readout as shown inthe legend. Data points show the mean number of recoils re-quired, based on pseudo-experiments, with errors indicatingthe uncertainty due to finite simulation statistics. The linesshow χ -minimizations of the functional form a + b √ n to thedata points, with a and b being floating fit parameters and n being the number of neutrino background events. cally for high-mass WIMPs, a higher energy threshold isacceptable.In summary, we have found that a 3d readout withgood vector tracking capability, e.g. pixel or strip read-out, can rule out an isotropic background or neutrinoswith as few as three to ten recoils above an energythreshold of 20 to 50 keV r , depending on the exact sce-nario. The required exposure for exclusion is typicallyminimized, however, with an energy threshold of about6 keV r . Figure 21 provides a compact summary of thenumber of helium recoils required to exclude the isotropicor neutrino background hypotheses for 10, 100, and 1000GeV c − WIMPs, using this 6 keV r energy threshold. Inthat case typically between ten and twenty recoil eventsare required for exclusion via directionality only. Thefindings here are consistent with past theoretical works,summarized in Ref. [14].Finally, Fig. 22 shows how the number of WIMPevents required to exclude the neutrino-only hypothesisincreases with neutrino background events present in thedetected event sample. For a 10 GeV c − WIMP, thenumber WIMP-recoils required (in this case for an energythreshold of 6 keV r ) grows only slowly with the number ofneutrino events, illustrating the power of directionality indiscriminating against even large a neutrino background. H. Electron background rejection
Electron backgrounds (i.e. gamma-recoils) are a keyissue for
Cygnus in that they will effectively determinethe energy threshold. In our background simulations of astrawman
Cygnus -1000 design (Section V) we find thatthe electron energy spectrum is dominated by Comptonscattering, with a flat energy spectrum in the O (kev) region where we expect the WIMP recoil signal. Ourdesign goal, which we show can be met for the lowest-background readouts, is an electron background rate of keV ee − year − . We will quantify the ability to rejectelectrons via the electron rejection factor, R , defined as R = N all /N surv , (14)where N all is the number of electron background detectedin a given energy range, and N surv is the subset of thoseevents that survive an electron-veto algorithm that re-tains 50% of nuclear recoils. R is thus the factor by whichwe expect to suppress detected electron background viaoffline selections. We will see that the electron rejectionfactor in Cygnus is high and rises exponentially withenergy. Assuming a six-year exposure and a flat elec-tron background energy spectrum at a rate of keV ee − year − , if we assume a hard energy threshold at thecenter of the first 1-keV ee energy bin where R > × ,then (due to the steep rise of R with energy) Cygnus willessentially be free of electron backgrounds. This is some-what conservative; the electron rejection factor also risesstrongly if we accept lower nuclear recoil efficiency, sothat a real experiment can probably remain backgroundfree at even lower energies by accepting some efficiencyloss. To quantify this lower-energy performance, we alsodefine the electron rejection turn-on as the lowest energywhere >90% of electrons can be rejected while retaininghalf of the nuclear recoils. This corresponds to the energywhere R = 10 .The charge density distributions of electronic and nu-clear tracks in gas are very different in both shape andscale, as demonstrated by Figs. 6 and 7. This suggeststhat good electron discrimination should be possible. Asa first step, the linear charge density is a simple, yet pow-erful discriminant than can be obtained from the chargedistributions. Lines of constant charge density corre-spond to lines of constant slopes through the origin inFig. 8 (right). Furthermore, we can expect the discrimi-nation between electrons and fluorine recoils to be betterthan between electrons and helium recoils. Fluorine re-coils have higher specific ionization and therefore differmore from electron recoils than helium recoils do. InFig. 23, we show the electron rejection factor R that canbe achieved using only this simplest linear charge den-sity. Before diffusion (data points with blue error bars),we obtain significant discrimination down to the lowestenergy studied (1 keV ee ) for fluorine. The electron rejec-tion factor rises quickly with energy, and exceeds × ] ee VEnergy [ke E l ec t r on r e j ec ti on f ac t o r Fluorine, before diffusionFluorine, after diffusion 0 1 2 3 4 5 6 7 8 9 10 ] ee VEnergy [ke E l ec t r on r e j ec ti on f ac t o r Helium, before diffusionHelium, after diffusion
FIG. 23. Electron rejection factors for fluorine recoils (left) and helium recoils (right) in 755:5 Torr of He:SF . Only the simplestobservable, the fitted-track length at a given ionization energy, is used to discriminate between electrons and nuclear recoils.Within each energy bin we apply a variable minimum track length that retains 50% of the nuclear recoils. Error bars showcombined uncertainties due to finite simulated electron and nuclear recoil statistics. The electron rejection rises exponentiallywith energy. For the higher energy bins, where no data point are shown, all simulated electron events were rejected, and theelectron rejection factor exceeds . at approximately 3.5 and 7.5 keV ee for fluorine and he-lium recoils respectively. We also see that the electronrejection turn-on occurs at order 1 keV ee and 2.5 keV ee forfluorine and helium, respectively.The data points with red errors bars in Fig. 23 show theresult after diffusion corresponding to
25 cm of drift. Wesee that the discrimination power remains high even afterthis amount of diffusion, and that the electron-rejectionturn-on moves up to about 4 keV ee . It should be notedthat the diffusion simulated here is more than the aver-age for a
50 cm long maximum drift length (due to the √ distance scaling), and that for recoils with short driftlength the electron rejection will be closer to the pre-driftcase. This result is remarkable because conventional di-rect detection experiments based on ionization signalstypically run out of discrimination power at these lowenergies.An important limitation of this study worth remark-ing upon can be seen in the absence of pre-diffusion datapoints above 4 keV ee (fluorine) and 9 keV ee (helium).This is an artificial effect due to the finite Monte Carlosamples; in fact all simulated electron events were re-jected for these bins. In reality we expect the exponen-tial increase of the electron discrimination factors to con-tinue. It is clear from Fig. 8 (right) that the discrimina-tion should continue to rapidly improve with energy, butstudying this further will require substantial CPU time.For similar reasons, we have not studied the readout de-pendence of electron discrimination, unlike previous re-sults in this section. Nevertheless, from results such as Fig. 13, we can expect that the most segmented readouts(pixel and strip) will have rejection factors quite close towhat we report here.While already promising, we expect these electron re-jection factors to only improve from here. Preliminaryexperimental and simulation work by some of the au-thors has already achieved improved discrimination withmore sophisticated shape analysis of the detected re-coils [317, 318]. For example, deep learning neural netstudies at the University of Hawaii achieved an impres-sive electron rejection factor of R = 10 at 3 keV ee for740:20 He:SF mixtures and helium recoils with 100 µ mof diffusion included. We expect this to improve byone additional order of magnitude in the lower-density755:55 He:SF mixture. In these preliminary results, theneural networks are not fully optimized, but already wesee background rejection better than chance at 1 keV ee .With additional tuning, we expect to see good discrim-ination at energies less than 1 keV ee [319]. Putting allthis together, we expect to achieve R of order at3 keV ee for helium recoils, which corresponds to 7.5 keV r ,for a 50% helium recoil efficiency. Based on this esti-mate, we should remain background free at substantiallylower energies, but more work is required to establish theexact threshold electron-background-free operation. Inour reach curves, we draw 8 keV r as the highest possiblethreshold line. Because we expect high electron rejectionat substantially lower recoil energies, and some electronrejection even at 1 keV r , we also show a number of lowerenergy thresholds.8Future work will therefore be devoted to experimen-tal verification of the electron rejection factors reportedhere, followed by the implementation of discriminationmethods using the detailed charge density distribution. I. WIMP sensitivity below the neutrino floor
Following our discussion of the directional performanceof each readout technology, we now examine how thisperformance translates into sensitivity to WIMP crosssections. To do this we build a signal and backgroundmodel for the WIMP and neutrino recoil distributionsbased on the theoretical input described in Sec. II. Then,all energy-dependent angular resolutions and head/tailefficiencies from Figs. 13 and 14 are applied, as well asthe event-level energy resolutions and efficiencies fromFigs. 12 and 11. For the threshold, a hard cut on recoilenergy is imposed at a range of values up to 8 keV r , butthe Gaussian energy resolution is applied to the under-lying d R/ d E r before this cut is made. A harder cut of0.25 keV r is applied first however, to address the uncer-tainty in determining the readout performance for ener-gies below the single electron level.Then we use our signal and background models to cal-culate median 90% CL exclusion limits using the stan-dard profile likelihood ratio test (see e.g. Ref. [320] forthe statistical formalism, but the WIMP+neutrino anal-ysis here closely follows Ref. [36]). Each neutrino back-ground flux normalization is accounted for as a nuisanceparameter using a Gaussian parameterization. No otheruncertainties or backgrounds are accounted for, so ourhard threshold effectively enforces the assumption thatperfect electron discrimination can be achieved above it.The resulting limits on the SI and SD parameter spacesare shown in Fig. 24 for a 1000 m experiment and foreach readout. We also include several additional the-oretical limits with improved directional sensitivity tohighlight the room for improvement. The limits labeled‘predrift’ are similar to those introduced earlier. We as-sume the energy resolution and efficiency of the pixelreadout, but the angular resolution and head/tail effi-ciency is as though we were able to measure the tracktopology before diffusion (this emphasizes the impact ofdiffusion on the sensitivity).We also introduce in this plot a limiting case labeled“ideal”, which takes the predrift sensitivity and simplysets the angular resolution to zero and the head/tailrecognition to 100%. This is a theoretical ideal, not pos-sible in practice, but our fully simulated readouts arepromisingly close already. This limit corresponds to al-most perfect discrimination between WIMPs and neu-trinos, a feat that should be possible in principle basedon their angular distributions (see Fig. 5). We ignorethe ‘postdrift’ curve here (which was shown in previousresults), since its corresponding limits are nearly identi-cal to the pixel readout. As demonstrated by the factthat most of the curves converge at high masses, the di- rectional information is playing a subdominant role insetting limits when compared with statistics alone. In-terestingly the poor energy resolution of several readoutsdoes enable them to set limits at lower masses than thosewith superior resolution, but at the cost of poorer sen-sitivity over larger masses due to the lack of ability toperform signal characterization. This demonstrates thatfor a Cygnus -1000 experiment the sensitivity is muchmore sensitive to the number of events than the overlapbetween the signal and background distributions. There-fore the hard threshold is something that should be con-sidered carefully.Fig. 25 shows in more detail how the limits of two sep-arate cases, predrift (top) and strip (bottom), depend onthe imposed electron discrimination threshold. Lower-ing the threshold down to 3–4 keV, can claim a gener-ous portion of unconstrained low-mass WIMP parameterspace. Attempting to lower this threshold even a smallamount is therefore highly motivated, even though thedirectionality at low energies is poorer. Unfortunately,for 1000 m of He:SF at atmospheric pressure, the lowtarget mass only allows the experiment to just reachthe neutrino floor, although there is an expected neu-trino event rate greater than one. To see this explicitlywe show 1-neutrino event lines rather than the neutrinofloor (which typically corresponds to O (100) expectedneutrino events). Limits intersecting these boundaries(for the relevant target) observe more than one neutrinoevent. The current electron discrimination threshold of 8keV r in fluorine is extremely close to the tail of the solarCE ν NS recoil spectrum; anything slightly larger wouldnot observe the background and not cut into the floor.In fact the improvement brought about by directionality,comparing the top and bottom row, is relatively minor incomparison to the substantial benefit at low masses whenlowering the threshold. In other words, the 1000 m ex-posure is still statistics limited. For larger experimentsthis conclusion will change, as we show next.In Fig. 26 we show two discovery limits for individualWIMP masses as a function of the number of expectedneutrino background events. The readout assumed ineach case is the same (pixel) but we compare severalanalyses which use all, or a subset of the available in-formation. The region outlined by dotted lines assumesonly the recoil event time information is used, so thatonly event counts and the annual modulation enable sen-sitivity. The dashed lines assume that recoil energy in-formation is also used. The dot-dashed lines assume thatthe directional information is used with directional per-formance curves simulated for the pixel readout. Thelowest, solid lines correspond to the pixel readout if itwere able to measure the track before diffusion, so as tohighlight how much of the sensitivity is limited by diffu-sion.Until now we have considered a Cygnus -1000 bench-mark volume. Comparing the limits at this point inFig. 26 we can see that, as hinted by the previous fig-ures, we are still in a regime where the sensitivity gains9 − WIMP mass [GeV /c ] − − − − − − − − − S I W I M P - p r o t o n c r o sss ec t i o n [ c m ] H e F X e PlanarWirePadStripPixelPixel (pre-drift)Pixel (ideal)
Cygnus × E th = 8 keV r E th = 0 .
25 keV r WIMP mass [GeV /c ] − − − − − − S D W I M P - p r o t o n c r o sss ec t i o n [ c m ] ν - fl o o r : X e ν - fl o o r : F PlanarWirePadStripPixelPixel (pre-drift)Pixel (ideal)
Cygnus × E th = 8 keV r E th = 0 .
25 keV r FIG. 24. Expected SI-nucleon (left) and SD-proton (right) 90% CL exclusion limits for
Cygnus -1000 using He:SF at 755:5Torr over an exposure of six years ( ∼ ton-year exposure). The solid lines all correspond to limits assuming an 8 keV r threshold whereas the dashed are for 0.25 keV r . We compare all readouts that have been simulated in this section, as well astwo theoretical limits labeled “predrift” and “ideal” which are included to highlight the role of the directional performance inlimiting the sensitivity. The two additional examples both assume the charge detection efficiency and resolution of the pixelreadout, but have their directional performance modified. The “predrift” limits correspond to cases already shown in previousresults, i.e. the angular resolution and head/tail efficiency of the track as if it were measured before diffusion. The “ideal”limit corresponds to an angular resolution of 0 ◦ and a head/tail efficiency of 100%. The combination of all existing SI and SDexclusion limits are shown as a green and red filled region respectively. We also show the neutrino floors for helium, fluorineand xenon targets in grey. more from the improved threshold via statistics, thanfrom directionality. For larger experiments however thedirectional sensitivity adds a considerable benefit. Inan experiment without directional information that alsoobserves a sizable neutrino background, the sensitiv-ity scales with detector volume at a rate much slowerthan the standard Poissonian background subtraction of V − / . However, directional limits scale much faster.This information can improve limits by almost an or-der of magnitude when the directionality is good (seethe predrift solid lines). This is also the case for themore realistic directional performance of the full read-out accounting for diffusion (dot-dashed lines), howeverthe conclusion again seems to be that diffusion is thedominating factor in restricting better sensitivity. Wereiterate that the only difference between the predriftand postdrift lines is an improved angular resolution andhead/tail recognition. This figure makes clear how muchour sensitivity could stand to improve. J. Summary of readout performance andconclusion on cost-optimal readout choice
Table III summarizes the main detector performanceparameters resulting from the detector and readout sim-ulation. We define each of these parameters in turn. We define the event detection threshold as the recoilenergy at which the event-level detection efficiency ex-ceeds 50%. This threshold is mainly determined by theavalanche gain and the readout noise floor, and the noisefloor is in turn determined by the capacitance of thereadout elements. Even with the modest gain of 9000assumed in this study, the readouts with the lowest ca-pacitance per readout element (pixels, pads, wires) havehigh efficiency at 1 keV r , the lowest recoil energy sim-ulated. The strip and planar readouts have larger de-tector elements with larger capacitance and noise, andrequire higher thresholds to compensate. The thresholdare slightly lower for fluorine than helium recoils, becausethe former have higher charge density.The directionality threshold , defined as the recoil en-ergy where ten events are sufficient to identify a maxi-mally directional source, is determined by the recoil tracklength, energy threshold, readout segmentation as well asthe nuclear straggling and diffusion of drift charge. Wenote that without diffusion or readout effects simulated,this directionality threshold is below 1 keV r . After diffu-sion but before detection, the directionality threshold isabout 15 keV r for fluorine and 4 keV r for helium, mainlybecause the helium recoils are longer, which helps over-come the diffusion. Comparing the different readouts, wesee that the pixel readout directional threshold is nearlyidentical to what is seen after diffusion. This means that0 − WIMP mass [GeV /c ] − − − − − − − − − − − S I W I M P - p r o t o n c r o sss ec t i o n [ c m ]
90% CL N wimp = 1 Cygnus -1000 m × Predrift E th [keV r ] X e n o n ( ν ) H e l i u m ( ν ) F l u o r i n e ( ν ) − WIMP mass [GeV /c ] − − − − − − − − − − − − S D W I M P - p r o t o n c r o sss ec t i o n [ c m ]
90% CL N wimp = 1 Cygnus -1000 m × Predrift E th [keV r ] X e n o n ( ν ) F l u o r i n e ( ν ) − WIMP mass [GeV /c ] − − − − − − − − − − − S I W I M P - p r o t o n c r o sss ec t i o n [ c m ]
90% CL N wimp = 1 Cygnus -1000 m × Strip E th [keV r ] X e n o n ( ν ) H e l i u m ( ν ) F l u o r i n e ( ν ) − WIMP mass [GeV /c ] − − − − − − − − − − − − S D W I M P - p r o t o n c r o sss ec t i o n [ c m ]
90% CL N wimp = 1 Cygnus -1000 m × Strip E th [keV r ] X e n o n ( ν ) F l u o r i n e ( ν ) FIG. 25. Expected SI-nucleon (left column) and SD-proton (right column) 90% CL exclusion limits for
Cygnus -1000 as afunction of the hard recoil energy threshold. We focus on the analyses corresponding to the predrift directional sensitivity (toprow) and the strip readout (bottom row). We vary the threshold again from 0.25 keV r (single electron) to 8 keV r (electrondiscrimination). In contrast to the previous figure we now show the 1-neutrino event lines for helium, fluorine and xenon targetsin grey, as opposed to the neutrino floor. This allows us to see that the 8 keV r threshold only just observes a non-zero neutrinobackground–highlighting the importance of improving electron discrimination. the pixel readout essentially extracts all relevant infor-mation from the diffused ionization distribution. Thesegmentation of this readout is thus sufficient, and finersegmentation would not improve the directional perfor-mance further, unless we also achieve lower diffusion.This may be possible with NID at larger electric fieldstrengths, which should be explored. Note that the per-formance ordering of the detectors is different for direc-tionality threshold than for energy threshold, especiallyfor strip readout. The reason is that strip readout hashigh capacitance per readout element, which raises theenergy threshold, but excellent segmentation once x/y strip coincidence is utilized, which lowers the direction-ality threshold.We define the electron rejection turn-on threshold asthe detected energy at which at least 90% of electronbackground events can be rejected while maintaining a50% nuclear recoil detection efficiency. This threshold isless than 1 keV ee (fluorine) and 2.5 keV ee (helium) beforediffusion, and approximately 4 keV ee after diffusion forthe 755:5 Torr He:SF gas mixture where we have simu-lated electrons. At higher energies, the electron rejectionpower improves exponentially. We take these electron re-jection turn-on thresholds as upper limits, as we expect1 Charge readout predrift postdrift pixels strips pads wires planarEvent detection threshold (F) [keV r ] n/a n/a < < < r ] n/a n/a < < < r ] < <
14 25 > > > Directionality threshold (He) [keV r ] < < ee ] < < - - - - -Electron rejection turn-on (He)[keV ee ] < . < - - - - -Exp. penalty, exclude isotropy, 10-1000 GeV c − WIMPs (F) 4.7 12 14 22 186 151 166Exp. penalty, exclude neutrinos, 10-1000 GeV c − WIMPs (He) 4.5 11 11 17 76 109 215Average relative exposure penalty factor n/a n/a 1 1.6 10 10 15Approx. cost per unit readout area [US $/m ] n/a n/a 400k 22.5k 5k 5k 0.050kTotal readout cost (US $) n/a n/a 800M 71M 105M 104M 2MTotal volume cost (US $) n/a n/a 25M 39M 262M 261M 382Mtotal detector cost, constant WIMP sensitivity (US $) n/a n/a 825M 111M 367M 365M 384Mtotal detector cost, volume (US $) n/a n/a 825M 70M 35M 35M 25MTABLE III. Summary of main performance parameters and estimated detector cost at equal directional sensitivity, for thesimulated TPC charge readout technologies. Results assume a 755:5 He:SF gas mixture at atmospheric pressure, roomtemperature operation, a gain of 9000, charge diffusion of . µ m / √ cm , and maximum drift length of
50 cm . improved electron rejection, and consequently even lowerenergy thresholds, are possible with more sophisticatedselections. Preliminary work on this is highly encourag-ing, see Section IV H. A full analysis of electron rejectioncapabilities of different readouts, with more sophisticateddiscriminants, is important for future experiments, andshould be followed up in future work.We have seen that ruling out an isotropic background(in galactic coordinates) or neutrino background hypoth-esis using only the directional distribution of detectedevents, is possible at 90% CL with as few as three recoilswith energy E greater than 20 keV r or of order ten recoilswith E > keV r , for the highest performance readouts(pixels and strips), for WIMP masses of 10, 100, and1000 GeV c − . To fairly compare readouts with differ-ent energy thresholds and directional performance, wereport in Table III the exposure penalty , defined as thenumber of WIMP interactions with E > keV r thatmust take place, in order to detect sufficient events torule out the background hypothesis. This would be thefirst step towards confirming the cosmological origin ofa tentative WIMP dark matter signal. In order to reachidentical WIMP sensitivity in this context, detectors withdifferent readouts need to have an exposure proportionalto their respective exposure penalty. We find that thispenalty does not depend very strongly on whether thebackground is isotropic or due to neutrinos. The penaltyis also roughly the same for 10, 100, and 1000 GeV c − WIMPs.We see that it instead increases with the directionalitythreshold, which makes sense, given the falling energyspectrum of WIMP recoils. Quantitatively, we find thata pixel readout needs the lowest exposure to rule outa background via directional measurements. Hence weaverage the penalty factors for the six scenarios (threeWIMP masses and two background hypotheses for each),and normalize them to the pixel readout, to arrive at the average relative exposure penalty factor. We find that strip, pad, wire, and planar readouts require on average1.6, 10, 10, and 15 times higher exposures, respectively,to reach the same directional WIMP sensitivity as thepixel readout.Next, we estimate cost. Given that pixel readout hasthe lowest exposure penalty, we take a detector with avolume of and with pixel charge readout as abaseline scenario. For each of the other readout technolo-gies, we set the volume equal to the product of and the average relative exposure penalty factor for thatparticular technology. This way, we are comparing de-signs with identical expected directional sensitivity. Forall designs, we assume a drift length of
50 cm , so thatthere are two readout planes per unit cell of thedetector.We consider two cost components: The first compo-nent is total readout cost , which we take to be the prod-uct of three factors: , the readout cost per squaremeter , and the average relative exposure penalty factor.The two latter factors both depend on readout choice,and vary substantially. Interestingly, the two effects can-cel to some degree, so that the variation in total read-out cost is not as large as one might have expected.Strip readout and planar readout have the lowest to-tal readout cost. For the strip readout, the cost in-cludes $12,500/ m for strip micromegas or similar charge-readout and $10,000/ m for readout ASICs (10,000 read-out channels per m at a cost of $1/channel).The second cost component considered is cost per unitvolume, which is independent of readout type and as-sumed to be US $ 5000 ($5k). This cost term accountsfor all volume-dependent cost other than the charge read-out itself: the vacuum vessel, field cages, shielding, gas,the charge avalanche device, and downstream data ac-quisition. For the pixel readout, we base the cost on avolume of , resulting in a total volume cost of US$ 5 million ($5M). For the other readouts, we increasethe volume (and thus the volume cost) by the relative2 Volume [m ] − − − − − S I W I M P - p r o t o n c r o sss ec t i o n [ c m ] [Time][Energy+Time][Postdrift Directionality+Energy+Time][Predrift Directionality+Energy+Time]0.251.02.03.04.05.06.07.08.0 − Number of B neutrino events E th [keV r ] I n f o r m a t i o n m χ = 9 GeV /c FIG. 26. Minimum excludable SI WIMP-nucleon cross sectionat 90% CL, for a 9 GeV c − WIMP, as a function of detectorvolume. The colored bands correspond to energy thresholds inthe same range used in the previous two figures. The numberof B neutrino events observed for each threshold as a functionof volume is displayed in the upper colored horizontal axes.The various regions correspond to the performance of the pixelreadout when different levels of information are used in settingthe limits. The four sets of limits display various levels ofinformation used from the least powerful to the most powerful.The solid lines correspond to the theoretical optimum for agas detector whereas the dotted lines use only the minimumamount of available information (event times). exposure penalty factor. The resulting estimated totalvolume cost is quite high for the less directional readoutchoices, such as pad, wire and especially planar readout.While cost-effective per unit readout area, these read-out choices would require expensive and large detectorvolumes to reach the desired directional sensitivity.Strip readout emerges as the technology with the low-est cost at equal directional sensitivity, or equivalently,as the technology with the highest directional sensitivityper unit cost. The latter is shown graphically in Fig. 27,normalized to pixel readout. A strip readout TPC with afiducial volume of about , would have total costof about $70M, with about two thirds of that cost beingassociated with the specific charge readout. This totalcost is similar to the cost of a typical HEP detector, butmuch less than the cost scale of a particle collider. Thisseems like a reasonable scientific investment compared toothers in the field, given that it would allow us to makeunique experimental progress on one of the most signifi-cant unsolved problems in physics (dark matter). Such adetector could rule out isotropy of a detected recoil dis-tribution from 10 to 1000 GeV c − WIMPs at 90% CLwith 22 WIMP-helium-recoils above 6 keV r , or with only TPC charge readout technology D i r ec ti on a l s e n s iti v it y / c o s t [ a r b . un it s ] FIG. 27. Estimated directional sensitivity per unit cost fordifferent TPC readout technologies. Pixel readout, which hasthe highest performance, is taken as the reference, with direc-tional sensitivity per unit cost equal to unity by definition. Wefind that strip readout provides the optimal tradeoff betweencost and performance. Note that non-directional nuclear re-coil detectors score zero on this performance metric. r .A detector based on pixels would be an order of magni-tude more expensive, but have better performance. Withthe lowest exposure penalty, it would require the small-est detector for a given physics reach, but the cost is cur-rently dominated by the relatively expensive pixel ASICs.The number of pixel chips, and hence cost of pixel chipreadout planes, could potentially be greatly reduced viaso-called charge focusing – electrostatic focusing of thedrifting ionization before detection [321]. Alternatively,the cost of pixel chips may be considerably lower with fu-ture semiconductor manufacturing processes or chip de-signs. In either case, pixel chip readouts, or similar ultra-high-resolution charge readouts could then become themost cost-effective readout options. With further reduc-tions in diffusion, which would need to be demonstrated,a pixel-based design is likely to be the most competitiveoptions at WIMP masses of order 1 GeV c − and lower.As it stands, pad, wire, and planar score similarly interms of directional sensitivity per unit cost. These read-outs are performance-limited due to relatively coarse seg-mentation. For planar readout, large segmentation isinherent to the design and cannot be reduced. Planarreadout may still prove somewhat more competitive byutilizing a dedicated discriminant, as opposed to the gen-eral event reconstruction utilized in the comparison here.A detector based on wires or pad technologies could be-come substantially more cost competitive if a reductionin feature size is possible, which would lower the direc-tional threshold and exposure penalty, while maintainingthe relatively low readout cost. Here, pads have the ben-efit of offering full 3d directionality, while wires have thebenefit of lower backgrounds.This brings us to out next topic: we note that the3cost/performance analysis here does not directly considerthe effect of electron discrimination. As discussed above,it appears likely that pixel and strip readout will havethe best electron background rejection capabilities due totheir high segmentation. However the wire readout hasless intrinsic radioactive backgrounds, so that a smallerelectron rejection factor will be required.Taking a step back, we note in closing that a higher-gain TPC with electron drift gas could also be compet-itive. That option should be studied further, but is be-yond the scope of this article. V. ZERO BACKGROUND FEASIBILITY
Direct DM search experiments typically strive tocontrol backgrounds to less than one expected eventwithin the fiducial volume over the anticipated expo-sure time and energy range (so-called zero background).As we have discussed in previous sections, directionaldetectors—more-so than non-directional detectors—arein principle able to tolerate a non-zero level of nuclearrecoil background, for example from neutron or neutrinointeractions, while still being able to positively identifya DM signal. However, any backgrounds will negativelyimpact the sensitivity, so this level of tolerance will de-pend on the capabilities of the detector technology.For
Cygnus we aim for zero electron background fromradioactivity of the detector and surrounding materials,and neutron recoil background that is a factor of foursmaller than the expected nuclear recoil count from neu-trinos. This section describes the feasibility of this fora 1000 m TPC. The simulations and preliminary resultwith machine learning previously discussed suggest thatan electron background of order 10 yr − keV − could betolerated even for energies below 10 keV. Given the quickrise of electron rejection with energy, this means that fora six year exposure, Cygnus will be background freeabove the energy at which the electron rejection crosses6 × . We also saw in earlier sections that we expectapproximately 40 nuclear recoils above a 1keV r thresholdover a six year exposure, or about 4 per year (see Fig. 4).We therefore set the following, preliminary, back-ground design goals for Cygnus : (1) an intrinsic electronbackground rate of 10 yr − keV − , (2) one nuclear recoilabove 1 keV r from neutrons per year, and (3) any otherbackgrounds from other sources, notably radon, shouldbe controlled to at least this level. This then leaves neu-trino induced recoils as the only non-negligible nuclearrecoil background. In what follows we must verify if thesedesign goals are achievable. To streamline a detailed dis-cussion of all anticipated backgrounds for Cygnus weset a benchmark nuclear recoil threshold of 1 keV r andcalculate background rates above this value. This willinform the amount of shielding required and the level ofmaterial radiopurity needed to reach the design goals.As discussed in Section IV A, we have been iterating onthe Cygnus target gas during the conceptual design pro- cess. While the final results presented here are for a 755:5Torr He:SF mixture, the discussion on backgrounds be-low will also iterate through a number of gases, and scalebackgrounds from one to the next.To start out, we make a few simplifying assumptions.For the vessel and gas we assume that the TPC is a × × m cube filled with 20 Torr of SF . This choiceallows detailed exploration of a basic, large, low-densitynegative ion gas configuration, but one for which thedata can reasonably be extrapolated to estimate back-grounds in other gas mixtures and pressures, includingthose used elsewhere in this paper. We assume a singleaverage thickness for the vessel wall, rather than indi-vidually simulating the support structures that would beneeded in a real vessel. Then, for the readout we assumeit is configured as in the TPC design of Fig. 1, with a50 cm drift distance (following the previous section). Thetotal readout area is therefore 2000 m . The laboratoryenvironment is based on the salt rock found at Boulby,UK. This site has certain advantages such as a low rockgamma flux, but we leave the discussion of the varioussite considerations to Sec. VI.Sections V A–V D detail all neutron, gamma, radon-related and cosmogenic backgrounds respectively. Wethen describe in Sec. V E how the results can be extrap-olated to the atmospheric pressure He:SF gas mixturecurrently envisaged for Cygnus . We give our final back-ground summary and recommendations in Sec. V F.
A. Neutron backgrounds
Neutrons produce nuclear recoil events in the samerange of energies as those expected from WIMPs. Theneutron background is therefore one of the most prob-lematic for all direct detection experiments. However,mitigating against it in a low-density gas TPC is dis-tinct from the methods used in solid or liquid-based de-tectors. The low density of gases means that neutronsare less likely to undergo double or multiple scattering,reducing the potential to veto on this basis. Estimat-ing neutron backgrounds by extrapolation from existingbackground simulations for massive xenon or bolometricdetectors [322] for example is therefore not appropriate.Instead, we must perform a dedicated Monte Carlo sim-ulation for
Cygnus , for which we use Geant4 [323]. Wesimulate the neutron background from the rock, shield-ing, vessel, and internal readout components using neu-tron energy spectra obtained from SOURCES [324]. Thespectra include neutrons originating from the
U and
Th decay chains due to spontaneous fission and ( α, n ) reactions. For neutrons due to cosmic ray muons inter-acting with the detector or surrounding materials, we usethe simulation code MUSUN [325]. We now detail therate calculation for each of these components in turn.4 Neutron energy [MeV] . . . . . . N e u tr o np r o du c t i o n r a t e Th U Total
Boulby, UK [ − M e V − c m − s − ] FIG. 28. Neutron energy spectrum from the salt rock cav-ern surface at Boulby. The blue and orange curves show thespectra due to
U and
Th respectively, and the black lineshows the sum of the two.
1. Rock neutrons and passive shielding
Concerning the salt rock at the Boulby site we use themeasured values of ± ppb of U and ± ppbof Th [326]. Figure 28 shows the energy spectrumof the neutron flux from isotopic decays of these nuclei.Since the flux saturates beyond 3 m, it is sufficient toonly simulate the rock to this depth to accurately repli-cate the laboratory neutron flux. We then simulate theresulting nuclear recoils in the gas volume. To reduce thecomputational burden the simulations assumed 600 Torrof gas and then used the linear relationship between thenuclear recoil rate and the gas pressure to scale each re-sult to 20 Torr. This should hold well assuming that thedouble scattering of neutrons in the gas remains negli-gible. Nevertheless, we have crosschecked that the ratesat the nominal and increased pressure are consistent withthis scaling. Water was selected for the neutron shieldingand is simulated at different thicknesses surrounding the
Cygnus gas volume. The rock, water and gas material issimulated using a cubic geometry enclosing each respec-tive volume. No space is simulated between the volumesas this was seen to have a negligible effect on the results.We find that a 75 cm thickness reduces the rate to anacceptable < ∼ . yr − (90% CL). Possible contamination of the water by radionuclei is not ac-counted for here as the background rate is likely to be subdomi-nant. See for example Ref. [326], which lists water radioactivitymeasured as low as 10 − ppb for both U and
Th.
2. Vessel neutrons
The vacuum vessel—the TPC component with by farthe largest mass—has the potential to dominate the neu-tron background. Here we consider the possibilities ofvessels constructed of steel, titanium, copper or acrylic.For each material, we consider a thickness, T , rangingfrom 5-30 cm, and compute the neutron recoil rate, R n ,in the gas volume using the formula, R n = N r N tot Φ n V a . (15)Where N r /N tot is the ratio between the number of neu-tron recoils that occurred within the gas volume and thetotal number simulated. The rate is proportional to thematerial volume, V ( T ) , and the neutron production ratewithin the vessel material, Φ n , which is expressed as V − s − a − , where a is the contamination of the vessel mate-rial by radioisotopes. The values of a used here for Uor
Th isotopes within each material under considera-tion are listed in Table IV.
Material U Th K ReferenceSteel 0.27 0.49 0.40 LZ [327]Titanium <0.09 0.23 < 0.54 LZ [327]Copper < 0.012 < 0.0041 0.061 NEXT-100 [328]Acrylic 0.029 0.039 2.1 SNO+ [329]Silicon < 12.35 < 4.07 < 6.81 UKDMC [326]Aluminum < 0.52 1.94 < 6 [330]Polyimide < 36.79 < 27.52 < 410 NEWAGE [331, 332]Kapton < 98.77 < 36.59 58.82 UKDMC [326]TABLE IV. Published material contamination levels and up-per limits (in mBq kg − ), used for our background simulation. In some cases the published upper limits on a for cer-tain materials will likely give background rates exceedingour requirements. In these cases we rearrange Eq.(15) tofind the value that would be required to give R n < yr − .The values of R n and required purities are summarized inTable V. Note that in this and subsequent tables the up-per limit is inherited from the isotope measurement andthe error is the statistical error from the Monte Carlosimulation.Some initial conclusions can be extracted from the re-sults in Table V. Based on the most recent low back-ground limits reported, both acrylic and copper producesignificantly fewer neutron recoils than either steel or ti-tanium of the same width. Acrylic in particular has aneutron self-shielding property due to its relatively highhydrogen content. However, while the construction of a5–10 cm thick copper vessel or a 5–30 cm thick acrylicvessel would keep the neutron recoil rate within 1 peryear, this may not be practical. In reality, a steel or tita-nium frame could be needed to support the vessel. Theexact structure of such a frame is not explored here butfrom a background perspective, if this frame were to av-erage 5 cm in width, then the U and
Th content5
Material Thickness Rate
U limit
Th limit(cm) (yr − ) (mBq kg − ) (mBq kg − )Steel 5 21 ± ± × − × −
20 177 ±
25 1.8 × − × −
30 242 ±
36 1.5 × − × − Titanium 5 < 11 ± ± × − × −
20 < 88 ±
15 2.9 × − × −
30 < 200 ±
28 1.2 × − × − Copper 5 < 0.39 ± (cid:51) (cid:51)
10 < 1.0 ± (cid:51) (cid:51)
20 < 2.0 ± × − (cid:51)
30 < 2.6 ± × − (cid:51) Acrylic 5 0.11 ± (cid:51) (cid:51)
10 0.17 ± (cid:51) (cid:51)
20 0.21 ± (cid:51) (cid:51)
30 0.17 ± (cid:51) (cid:51) TABLE V. Neutron recoil rate for different vessel materialsat different thicknesses. We display a checkmark where theexisting
U and
Th limits give rates of less than one recoilper year. In cases where they do not, we instead give the valueof radiopurity that would. would need to be reduced by a factor of 17 and 26, re-spectively for steel, or 7 and 15 for titanium. It is worthremarking that the
U activities for titanium and cop-per are upper limits, so further screening tests may revealthem to be within the limit.An alternative solution for improving the radiopuritywith steel or titanium would be to use an internal acrylicshield of around 10 cm. This width would not contributesignificantly towards the total neutron background but itwould help to shield against neutrons produced by a steelor titanium support frame. Running at atmospheric pres-sure may also reduce the vessel neutron background sinceit would require thinner walls and less support structure,as we explain in Sec. V E. Overall we can summarize thatthere is a good prospect for reaching a design of TPC ves-sel that can achieve the required level of neutron-inducedbackground from that source.
3. Internal TPC neutron background
We now consider the unshieldable neutron back-grounds from readout components within the TPC. Wesimulate a 1 m sheet readout positioned centrally insidethe TPC gas volume, and the simulated rates are thenscaled up to the required 2000 m . We focus on THGEMand GEM amplification stages, with readout stages com-prising a generic future strip readout, wire-based readoutor pixel chips.There are some technologies which are neglected in thisanalysis due to the relatively high background of currentdevices, such as the micro-RWELL—which combines aGEM-like structure and printed circuit board readout— and the micromegas, see Refs. [326] and [333] respec-tively. These are of high interest for Cygnus , but wouldboth need improved material radiopurities to be incor-porated in a zero-background
Cygnus -1000. Similarly,current µ -PIC readout backgrounds exceed what is ac-ceptable for a 1000 m detector, but for illustration wedo include this readout in our simulation. Extensivework by authors here is underway to reduce µ -PIC back-grounds. We point out that even the current version ofthese higher-background readouts are still of interest fornear-term smaller-exposure detectors. We also do notsimulate readouts based on optical technology such asCCD or CMOS cameras. These would need to be placedoutside of the vessel with low-activity transparent win-dows between the cameras and the TPC volume, thusrequiring a major rethinking of the vessel design. Forthese reasons we focus only on the technologies listed inTable VI. We briefly describe each below. Technology Material Thickness Total mass(mm) (tons)Gain stages:THGEM Acrylic 1.0 2.36THGEM Copper 0.1 3.6GEM Kapton (0.05) 0.0142Readout stages:Strip Acrylic-Cu 1.05 4.16MWPC (wires) Steel 0.05 1.94 × − MWPC (frame) Acrylic 10 0.236Pixel chip Silicon 0.400 1.86Pixel chip Copper 3.9 × − × µ -PIC Polyimide 1.0 2.84TABLE VI. The simulated readouts, material components,thickness and total mass. Starting with the amplification stage, a typical GEMhas a µ m-thick Kapton layer coated with a thin, ∼ µ m copper layer on either side. We only simulate theKapton layer here as it is the main mass contributor andhas a relatively high background compared to copper. Inorder to achieve high gas gains of ∼ – , the stackingof GEMs may be required [334], doubling or even triplingthe Kapton background. A Thick GEM (THGEM) onthe other hand has a thicker Kapton or acrylic layer, usu-ally between 0.4 and 1 mm thick. We use the upper endof 1 mm for these simulations as the THGEM can thenbe made of low background acrylic at this thickness [335].We also simulate 0.1 mm of copper on either side of theacrylic because the copper layers of the THGEM are sig-nificantly thicker than that of an ordinary GEM.Turning to the readout technologies, for the strip read-out we assume a single layer of x and y copper strips ona low background acrylic substrate and use the same ra-diopurity values as those adopted for the THGEM com-ponents detailed above. Regarding the wire-based read-out (MWPC), this has two main sources of background:6the acrylic frame supporting the wires, and the wiresthemselves. The DRIFT-IId detector consists of twoMWPCs each with three planes of 552 steel wires, wherethe middle plane is made from µ m thick wire andthe two outer planes µ m thick wire [242]. DRIFT-IId uses the field between the middle plane, which isgrounded, and the two outer planes, which are set toaround − V, to provide the signal amplification. Ifused in
Cygnus however, the MWPC readout would begrounded and a GEM or THGEM would provide the am-plification stage. Therefore, with no voltage being ap-plied, the wires do not need to be µ m thick. However,to ensure greater stability at larger scales, they do needto be slightly thicker than µ m. We simulate µ mthick wires with a total steel mass of 1.94 kg (based onthe total steel wire mass of 1.94 g that makes up thetwo MWPCs in the 1 m DRIFT-IId detector). We as-sume two 1 m wire planes separated by 1 cm with a2 cm thick border as the acrylic frame. The pixel chipreadout is based on the ATLAS FE-I4 pixel chip [260],made of silicon with metal and dielectric layers. Copperand aluminum make up the bulk of the metal layers, inaddition to small amounts of tantalum, chromium and ti-tanium. Here we consider a simplified model made froma 400 µ m thick block of 98% silicon, 1% copper and 1%aluminum by mass. Finally, the µ -PIC readout as usedby NEWAGE [336] is composed of a double-sided circuitboard separated by a 1 mm-thick polyimide substrate,the latter being the main background contributor.A large-scale TPC readout would require structuralsupport, most likely made of acrylic. We do not explorethe potential design and the impact on the backgroundcontribution because the focus here is on the base mate-rials. We remark however that the inclusion of a largescale support structure would further increase the back-ground inside the vessel for all readouts and that theexact amount of support required would depend on thereadout requirements. For example, with an MWPC theforces and torques exerted due to the tension in the wiresmay mean that a more rigid support structure wouldbe required than for other readouts. The basic acrylicMWPC frame investigated in this section is not for sup-port but to simply hold the wires in position. For thesame reasons, the background contribution from readoutelectronics downstream of the primary charge sensitivedevice is not studied here. However, in general this couldbe reduced by placing the electronics outside of the vesselor by using internal shielding. For the pixel chip read-out, backgrounds from front end electronics are alreadyaccounted for, as they reside on the chip itself.For the field cage and cathode, the acrylic frame fromboth of these structures provides the dominant mass,conservatively estimated to be 86.4 tons (1000 × DRIFT-IId). However, the highest source of background is fromalumina found inside resistors that make up the resis-tive divider used to define the drift field between thecathode and readout. Around 700 resistors would berequired in a 10 m long
Cygnus vessel, based on ex- trapolation from the DRIFT-IId field cage. We assumeradiopurity levels of . ± . and < . mBq/pc for U and
Th respectively, following the levels reportedby TREX-DM [252] for their field cage SM5D resistors.These resistors have dimensions . × . × . mm [337].A block of alumina with these dimensions is simulated atthe center of the TPC gas volume and the resulting neu-tron background rate is scaled up to the required numberof resistors. Technology Material Neutron recoils U/Th limit(yr − ) (mBq kg − )Gain stages:THGEM Acrylic 0.122 ± (cid:51) THGEM Copper 2.4 ± × − (cid:51) GEM Kapton < 9 ± ± (cid:51) MWPC (wires) Steel 4 ± × − (cid:51) MWPC (frame) Acrylic 0.048 ± (cid:51) Pixel chip Silicon 25 ± ± × − (cid:51) Pixel chip Aluminum 0.29 ± (cid:51) Other: µ -PIC Polyimide <160 ±
16 0.185/0.20Resistors Ceramic < 0.35 ± (cid:51) TABLE VII. Table of neutron rates and required radiopuritiesfor the readout background. In the final right-hand column, atick indicates that the U and Th levels are indeed seen to besufficiently low for that material to reach the < yr − goal.Where this is not true we give an estimate of the maximum al-lowed U and
Th radiopurity levels (termed U/Th limit)that must be reached to obtain the < yr − goal. The predicted rates and required radiopurities for allthe generic internal TPC components studied in this sec-tion are listed in Table VII. A full readout plane requiresboth a gain stage and a readout stage, with backgroundrates from both parts contributing to the total back-ground. An example would be a THGEM gain stagecombined with a strip readout. In Table VII (and simi-larly Table IX) the first three rows refer to components ofpossible charge gain elements. For a single THGEM gainstage, values in the first two rows need to be summed.The various components for strip, wire and pixel read-outs, are given in the following rows of the table. Valuesfor the strip readout assume a 2d copper strip formaton an acrylic support. The final rows give typical valuesfor the necessary field cage resistors and an example µ -PIC readout [336]. Current values for Micromegas stripreadout [338] are similarly high.Assuming the radiopurity measurements of acrylic andsteel, made by SNO+ and LZ respectively (see TableIV), it appears that only the THGEM amplification stagecombined with either wire readout or future acrylic-basedstrip readout can likely satisfy the Cygnus backgroundcriteria without significant improvements to intrinsic ra-diopurity. Although recent µ -PIC design developments7have allowed for a significant decrease in their alpha emis-sion [331], a better understanding of the polyimide ra-diopurity will be required to estimate the true neutron-induced recoil rate more accurately. This is also the casefor the GEM amplification stage and the pixel chip read-out, where the activity levels of Kapton and silicon re-spectively are still only upper limits. For all these cases,further study could possibly reveal a lower neutron back-ground, but if the true levels are close to the upper lim-its alternative materials would need to be found. Fi-nally, readouts aside, the field cage fortunately has a neu-tron background within limit, based on using the TREX-DM resistor values. New resistive sheet technology [339],may also provide an alternative to conventional field cagestructures in the future and possibly contribute a totallower background. Note also that in this study no al-lowance has been made for additional internal detectorsupport structures.These results are useful benchmark values. Ultimatelyhowever an important developmental step for Cygnus will be to perform extensive material screening to resolvethese uncertainties further and to develop new ways to in-stall the readout planes that minimize material use. Thebackground from all readouts could be lowered by usingmore radiopure materials or by attempting to improvethe radiopurity of the same materials. This is particu-larly relevant to the µ -PIC readout and GEM amplifi-cation. For instance, better-refined glass polyimides arebeing developed for the µ -PIC, and a Kapton replace-ment for the GEM made from high purity G10 insulatoris already being investigated by some of the authors. Thebackground for pixel chips could also be reduced if chargefocusing [321] becomes a possibility, as this would reducethe number of units required to fill the readout plane.
4. Muon-induced neutrons and active vetoing
Neutrons produced by muon interactions in andaround the detector are another source of background.To compute the energy spectrum, flux and angular distri-bution of incoming muons we use the MUSUN code [325].The simulation takes into account the angular profile andthe composition of the rock overburden for the trans-portation of cosmic-ray muons. The muon energies, posi-tions, and momenta are then put through Geant4, whichtransports them through m of rock before reaching thedetector. More than 200 million muons are generated atthe surface of the rock volume. Those reaching the rock-cavern boundary are then normalized to the measuredmuon flux at Boulby: (4 . ± . × − cm − s − [340](with a vertical rock overburden of ± m.w.e.).Over a period of (2 . ± . × s, no events are recordedwithin the fiducial volume, providing us an upper limiton the rate of muon-induced neutron nuclear recoils of2.75 yr − . More extensive simulations will be requiredto see if the actual rate might be lower. If not, these re-maining few events could be identified and tagged using Recoil energy [keV] E l ec tr o n r ec o il r a t e [ k e V − y r − ] Total U Th K Copper vessel
Wall thickness: 30 cm
FIG. 29. Gamma-induced electron recoil background contri-bution observed in the 20 Torr SF gas volume, originatingfrom a 30 cm thick copper vessel. We see clearly that eachnuclide has an essentially flat recoil spectrum that lies below < ∼ keV − yr − . either an active muon veto, such as a plastic scintillator,or by looking for coincident electromagnetic events in thegas. This could be made possible by installing PMTs inthe water shielding described earlier. B. Gamma backgrounds
The challenges in performing electron/nuclear re-coil discrimination below 10 keV ee were discussed inSec. IV H. The electron rejection rises exponentially withenergy, and is expected to exceed 10 between 1 and 10keV ee , even after diffusion. The exact threshold wherethis occurs will be readout-dependent, and must be deter-mined in the future. We focus therefore on the gamma-electron recoils in this range, aiming to find vessel andreadout materials with intrinsic radiopurity levels thatcan allow the detected background rate to be limited to < ∼ keV − yr − .Using Geant4, we homogeneously populate the rock,vessel, and sheets of readout materials with U, Th,and K, assuming secular equilibrium. The 75 cm watershield is also included for these simulations (see Sec. V A).The corresponding gamma fluxes are then computed fol-lowing the simulation of the decay chains of each isotope.For materials with relatively small thicknesses, such asthe readouts, the homogeneous distribution of the iso-topes allows for the simultaneous simulation of the bulkand surface background. For each isotope, the electron8recoil rate due to gammas was computed as, R γ = N r N tot M a . (16)Again N r is the observed number of recoils and N tot isthe total number of decays simulated for the isotope inquestion. As before, a is the material radioactivity perunit mass for that isotope and M is the total materialmass. The recoil spectrum is flat to a good approxi-mation over the 1–10 keV range because the majority ofgamma recoils are due to Compton scattering. Figure 29,shows an example of this: the recoil energy spectrum forgammas originating from a 30 cm copper vessel and scat-tering within the fiducial volume. This example is alsobelow our electron recoil target rate, as we discuss next.
1. Rock, vessel and shielding gammas
As in our discussion of the rock neutron background,we assume the measured contamination levels of thesalt rock at Boulby, now with the inclusion of ± ppm K [326]. For rock gammas, an even smaller cm depth is all that contributes to the background,beyond which the rock is self-shielding. Since we foundthat 75 cm of water shielding was needed to shield therock neutrons, we now include this also in our rate cal-culation.The rock and vessel gamma-induced electron recoilrates for each material and thickness are listed in Ta-ble VIII. As before for the neutron results (see Table VII)in the right-hand columns a tick indicates where we findthe levels sufficiently low for that material to reach the < keV − yr − goal for the listed isotope. Where thisis not true we give an estimate of the maximum allowedradiopurity levels (termed U/Th/K limit) that must bereached to obtain this goal.For metal vessel materials, rock gamma recoils are re-duced by ∼ ∼ × keV − yr − at20 cm, ∼ × at 30 cm, and ∼ at 30 cm for steel,titanium, and copper, respectively. This effect does notoccur in acrylic. Indeed, Table VIII shows that acrylicis not comparatively effective as gamma shielding andas such would not be an appropriate vessel material, atleast not by itself. The only way the saturated gammaflux from the metals can be addressed further is if the radioactivity levels are lowered from what we are assum-ing here. Since some of the values from Table IV are infact only upper limits, further screening tests may revealcertain materials to be within limit in addition to thosealready shown. For example, with 30 cm thickness, cop-per gives a rate only slightly above keV − yr − anda U activity of around one half of the upper limit as-sumed here would be acceptable. A purely copper vesselcould be a viable option but as we discussed in Sec. V A 2if a steel or titanium frame were needed in addition to theinternal acrylic shield then every material would need areduction in radioactivity, if actual rates are close to thelimits seen.
2. Internal TPC gamma background
Next, we consider the gamma background due to thesame readout systems and field cage resistors listed inSec. V A 3. For the latter, we assume the same radiop-urity levels of
U and
Th from before, but we nowalso include the 0.17 ± − of K [252].Table IX shows the gamma-induced electron recoilrates, given here in the same manner as Table VII, splitbetween gain stage and readout components. We can seeclearly that the K radioactivity levels of acrylic causesthe dominant gamma background for the THGEM andwire readout, both of which produce a background rateonly slightly above limit. Cutting the current K activ-ity of acrylic in half would bring the wire frame gammabackground to within keV − yr − . Similarly, a factorof four would be needed for a THGEM gain stage and forthe generic strip readout. For a single GEM gain stagehowever one would need an order of magnitude reduc-tion; as with acrylic, the K activity of Kapton is thedominant factor here. Additionally, based on the mostcurrent measurements of micromegas readouts [338] andof µ -PIC readouts [331], we confirm that current typi-cal radioactivity levels are, respectively, a factor of 10 and 10 away from matching the activity produced bythe 1 mm thick acrylic, as used here for the conceptualstrip readout example. For the polyimide in the µ -PICreadout, further screening is underway to better under-stand its radiopurity levels. In the pixel chip, silicon isthe main source of gammas, since they only contain asmall quantity of copper and aluminum. Again, sincethe silicon radiopurity is an upper limit, true levels couldbe lower, and more sensitive tests are required. Also,charge focusing [321]—as mentioned earlier—could helpto reduce the number of pixels needed and therefore thebackground. Finally, the gamma background caused bythe field cage resistor chain is twice the tolerable limitand a reduction in the U activity of ceramic by a fac-tor of four is needed. Again, resistive sheets [339] shouldbe evaluated as a potential resistor replacement.In summary, the general conclusion for the gamma-induced backgrounds internal to the TPC is that someexisting technologies are already close to meeting the de-9
Material Width Rock γ recoils Vessel γ recoils Total γ recoils U limit
Th Limit K Limit(cm) (keV − yr − ) (keV − yr − ) (keV − yr − ) (mBq kg − ) (mBq kg − ) (mBq kg − )Steel 5 3.8 ± × ± × ± × ± × ± × ± × ± × ± × ± × ± × ± × ± × ± × < 2.9 ± × < 1.0 ± × ± × <4.13 ± × < 4.2 ± × ± × < 4.17 ± × ± × ± × < 5.11 ± × < 5.6 ± × ± × < 1.57 ± × ± × (cid:51) (cid:51)
10 4.0 ± × < 1.60 ± × ± × (cid:51) (cid:51)
20 9.5 ± × < 1.58 ± × < 2.53 ± × (cid:51) (cid:51)
30 5.1 ± × < 1.58 ± × < 1.6 ± × (cid:51) (cid:51) Acrylic 5 2.5 ± × ± × ± × ± × ± × ± × × − × − ± × ± × ± × × − × − ± × ± × ± × × − × − target volume, for vessel wall materials of varying thicknesses, and therequired radiopurities to obtain a rate of 10 keV − yr − .Readout Material (width) γ recoils U limit Th limit K limit(keV − yr − ) (mBq kg − ) (mBq kg − ) (mBq kg − )Gain stages:THGEM Acrylic (1 mm) 3.3 ± × (cid:51) (cid:51) ×
2) < 1.5 ± × (cid:51) (cid:51) (cid:51) GEM Kapton (50 microns) 1.57 ± × (cid:51) (cid:51) ± × (cid:51) (cid:51) µ m) 1.8 ± (cid:51) (cid:51) (cid:51) Acrylic (2 cm × ± × (cid:51) (cid:51) µ m) < 2.55 ± × µ m) < 24 ± (cid:51) (cid:51) (cid:51) Aluminum (4.5 µ m) < 937 ± (cid:51) (cid:51) (cid:51) Other: µ -PIC Polyimide (1 mm) < 1.3 ± × ± × (cid:51) (cid:51) TABLE IX. Readout gamma recoil rates in 20 Torr SF for different readout materials and the U, Th, and K radiopurityrequired to achieve 10 recoils keV − yr − (as well as the materials which already satisfy this requirement). sign goal of keV − yr − . This appears particularlytrue for the THGEM-wire combination and generic stripreadout. Most other technologies and materials will re-quire further screening and/or further reductions in back-ground levels before they can be shown to be viable for Cygnus . C. Radon and radon progeny backgrounds
Radon gas emanating from materials is a further sourceof background for rare-event experiments. In particu- lar, the low energy ( ∼ keV) of radon progeny recoils(RPRs) can mimic WIMP interactions [16]. Being a no-ble gas, Rn has a low chemical reactivity making itparticularly difficult to filter. Moreover, its 3.8 day half-life allows enough time for the radon gas to spread fromthe materials in which it is produced, resulting in a ratherwidespread source of background.Alpha particles from radon decays are relatively easyto identify. For a back-to-back TPC (such as that shownin Fig. 1 of Sec. I), events that trigger on both the leftand right readout planes of the detector can be spottedvia their coincidence in time. The only events with tracks0 − . − . . . . Time relative to trigger [ms] − A m p li t ud e [ m V ] Minority carriers region Main peak region
D P S
FIG. 30. Amplitude as a function of time of the main signalpeak as well as several minority peaks from the DRIFT-IIdgas mixture, adapted with permission from Battat et al. [241].The minority peaks are labelled D, P and S by convention. long enough to achieve this are alpha particles originatingfrom an RPR event fully contained within the fiducializedgas volume. These types of events can be used to esti-mate the level of radon present in the detector [16, 253].However, not all RPR events originate within the fidu-cial volume as the positively charged radon daughter nu-clei drift towards the central cathode and become stuckwithin the material. A recoil event caused by the decay ofRPRs can prove difficult to reject as the associated alphaparticle may not be identified if it remains trapped. Onemethod of reducing the number of trapped particles is tohave smaller cathode widths, thus increasing the trans-parency. This approach was successfully implementedin DRIFT with the use of a submicron thick cathode.This helped to reduce the RPR rate from approximately130 events per day to less than one [341]. In DRIFT-IId, RPRs originating from the cathode surface withouta detected alpha track are vetoed by defining the fidu-cial region such that any recorded signal within 2 cm ofthe cathode is rejected [242]. A similar technique is alsoused by MIMAC [253] where an analysis cut based on the z positions of events is used to reject RPRs originatingfrom the cathode. Ideally, a similar z -cut to veto RPRswould be used in Cygnus .Many techniques for dealing with RPRs rely on fidu-cialization: the ability to fully locate in three dimen-sions the source of ionization within the TPC gas vol-ume. This is of vital importance for rare event searchTPCs as it allows for background events from mate-rial surfaces to be distinguished from potential signalevents occurring within the target volume. Fiducializa-tion in the TPC readout plane ( x, y ) can be done at thereconstruction stage for the more segmented readouts. For less segmented readouts one can use a surroundingveto area that triggers when events enter from outsideof the fiducial volume. Fiducializing parallel to the driftfield ( z ) presents more of a challenge as no active vetocan be placed in front of either the cathode or readout.However, z -fiducialization has been achieved in previouswork [264, 298, 301]. DRIFT-IId uses a gas mixture ofCS , CF and O at a ratio of 30:10:1 Torr to producedistinct groups of “minority carriers” within the gas thatdrift at different speeds. The signal then has a main peakadjacent to three minority peaks as shown in Fig. 30.The separation in time between these peaks is propor-tional to the drift distance traveled and therefore the z position at which the primary event occurred. Refer-ence [299] showed that the same fiducialization method ispossible with SF due to the presence of an SF − minoritypeak; so we believe fiducialization should be achievable in Cygnus . There are other options available, such as usingtiming differences between the signals at the cathode andinduced signals at the anode as in MIMAC [342], or bymeasuring diffusion of drift charge transverse to the recoilaxis as demonstrated by D [264, 301]. Several of thesetechniques may also be combined to further improve per-formance. Note that fiducialization via minority carriersis only possible with negative ion drift gases, as proposedhere, so that we expect the best fiducialization in suchgases. D. Cosmogenic activation
When materials are present at the surface they aresubject to a much higher flux of cosmic rays than whenunderground. If materials spend a significant time aboveground cosmic ray interactions can activate differentlong-lived isotopes, which when part of the detector be-come an additional source of background. As rare eventsearches increase in both size and sensitivity, this cos-mogenic activation is going to have an increasing influ-ence on the ultimate background rate. See for exampleRef. [343] for further details.The activity of a cosmogenically activated isotope isexpressed as, a = R [1 − e − λt exp ] e − λt cool , (17)where R is the production rate, λ is the decay constant, t exp is the time the material spent exposed to the cosmicray flux and t cool is the ‘cooling off’ time the materialspent underground.Activation can occur in all materials, but we use copperhere as an example since it is our best candidate vesselmaterial so far. Reference [344] showed that cosmic rayinteractions with copper at sea level can produce mul-tiple unstable isotopes. The longest-lived is Co whichoriginates from Co contamination and has a half-life of5.26 years. The measurement from Ref. [344] was takenafter a relatively long t exp = 345 days compared to themuch shorter t cool = 14 . days. The saturation activity1for Co was 340 ± µ Bq kg − . Taking the upper end ofthis measurement, we estimate that the rate of gamma-induced electron recoils for a 5 cm thick copper vessel willbe < . ± . × keV − yr − in the – keV energyregion. This rate is ∼ U, Th, and K radioactivity in the samethickness of copper (see Sec. V B 1), assuming the upperlimits are the actual radiopurity values.Since the measurement and simulation of the cos-mogenic activation in copper have shown good agree-ment [344], for a more detailed study we can make use ofthe simulation tool ACTIVIA [345]. This enables us topredict the minimum amount of time a material shouldspend above ground and cooling off underground in orderto limit activation.For SF , the longest-lived isotope of fluorine, F (witha half-life of 109.77 minutes), is still too short-lived toproduce a lasting background contribution. Nearly allisotopes of sulfur have half-lives on the scale of secondsto minutes with the exception of S, which has a half-lifeof 87.5 days. We simulate 90 days of surface time withACTIVIA, during which the gas is exposed to cosmicrays sampled from an energy spectrum ranging between – MeV. After this we assume a 180 day cooling-off period underground, during which time the gas is notexposed to cosmic rays. This resulted in a S productionrate of R = 0 . kg − day − , giving a decay rate of 2.61mBq/kg. A 1000 m vessel filled with SF at 20 Torrwill hold ∼ kg of gas, of which ∼
35 kg is sulfur,so the total decay rate for the detector is 91.35 mBq.We simulate S decays in Geant4, originating fromthe center of the 20 Torr SF gas volume. Only threegamma induced electron recoil events between – keVwere observed in the simulation time of ∼ . days. Weestimate therefore a rate of ± yr − , too small to bea significant electron recoil background.In general the amount of cosmogenic activation is re-duced by limiting t exp and extending t cool . In additionone should limit the amount of time the material spendsas air-shipment and therefore subject to a higher cosmicray flux. One might also want to electroform the metalliccomponents underground, at the construction site, wherepossible. E. Backgrounds at atmospheric pressure
A 1000 m vessel filled with low-pressure target gaswould need to withstand outside pressures of ∼
760 Torr,requiring larger amounts of structural support than a ves-sel filled with atmospheric pressure gas. Sections V A 2and V B 1 found that a steel or titanium support struc-ture would increase the total vessel background. There-fore, running at atmospheric pressure rather than at 20Torr SF would be advantageous. An addition of 740Torr He allows for TPC operations at atmospheric pres-sure, while increasing the density only by a factor of ∼ alone (see Table I). Adapting our previous simulation to this 740:20 Torrmixture, we find that an increase in density correspondsto an increase in both the gamma and neutron back-ground by around the same factor of ∼
2. The resultspresented thus far throughout Sec. V can scale straight-forwardly between low pressure and atmospheric pressureby this factor. In addition, the results can be scaled togive an approximation of the background rates at otherratios of He:SF . For example, a ratio of 755:5 Torr wouldincur a density increase and, therefore, a background rateincrease of around 25 percent compared to pure SF at20 Torr.A major advantage of atmospheric pressure operationis not only the reduction in vessel support needed, butalso that the vessel itself could be built with a lower av-erage thickness. A 1000 m Cygnus vessel operating at760 Torr would need an average thickness of around 30,12, 10 or 8 mm of acrylic, copper, steel or titanium re-spectively [346]. Due to the strength of titanium it mayeven be possible to construct a vessel with as little as6 mm average thickness. The acrylic estimate does notinclude additional structural support which would alsoneed to be taken into consideration, but the copper, steeland titanium thicknesses are averaged over both the ves-sel walls and structural support. We employ the simula-tion described in Secs. V A 2 and V B 1 to re-estimate theneutron and gamma recoil rate due to vessel materials forthe new 740:20 Torr He:SF gas mixture. Table X liststhese estimates. Note that the rock and water shieldingare not included now, but expected background changesdue to these will be commented on below. Material Thickness Gamma recoil rate Neutron recoil rate(mm) (yr − ) (yr − )Acrylic 30 3.57 ± × ± ± × < 0.12 ± ± × ± ± × < 4.0 ± ± × < 2.4 ± gas mixture scenario. We can compare the 740:20 Torr mixture results ofTable X with the 20 Torr SF results at the thinnest pre-viously simulated vessel thickness, 5 cm, shown in TableVIII. While the gamma recoil rates are similar, the neu-tron rates from the metallic vessel walls are all lower withthe atmospheric pressure. However our general conclu-sion from before—that the steel and titanium vessel neu-tron background exceed the design target—still persistsat atmospheric pressure.It seems that the increase in background due to theincreased gas density is approximately compensated by adecrease in background due to the reduction in requiredvessel material. So at the very least we have shown thatthe vessel background does not increase for the atmo-2spheric gas mixture. However the rock-gamma shieldingefficiency would suffer with a thinner vessel. If an ad-ditional copper shield were to be implemented then thistoo would contribute to the total background, requiringpotentially a thickened water shielding to counterbalanceand keep the total background acceptable.We have seen that for a fixed detector, backgroundrates are proportional to gas density. Hence can alreadyconclude that a 755:5 Torr He:SF target gas, which hasonly 25% higher mass density than 20 Torr SF , is al-ready close to acceptable from a background point ofview, provided we do not change the vessel design. Itseems quite likely, that with thinner vessel material thatcan be considered for atmospheric pressure, backgroundscan be reduced further, probably below the 20 Torr SF scenario that has been studied in detail here. We there-fore are cautiously optimistic, but also note that detailed,dedicated simulations of complete atmospheric pressurescenarios should be carried out in future work with highpriority. F. Conclusions
In this section we have discussed in detail the intrinsicbackgrounds for a 1000 m Cygnus
TPC. We have takeninto account neutron and gamma backgrounds originat-ing radioisotopes in the rock, vessel and detector, as wellthose originating from cosmic ray muons, radon emis-sions and cosmogenic activation. Following Sec. IV C, wehave aimed to determine the feasibility of limiting elec-tron recoils to a rate of 10 recoils keV − yr − in theenergy range 1–10 keV ee , and nuclear recoils to a rate of < yr − between 1–100 keV. These numbers are compat-ible with zero electron background after offline electronrejection and limit nuclear recoils from neutrons to lessthan a sixth of the solar neutrino signal. The feasibil-ity of achieving the electron background limit is essentialas it will ultimately control the threshold of the experi-ment and the sensitivity to low WIMP masses, whereasmeeting the nuclear recoil rate target is important foroptimizing sensitivity to WIMPs and solar neutrinos.While we have assumed a fill gas of SF at 20 Torrin much of our discussion, we have also shown how theresults scale to atmospheric pressure He:SF mixtures,which appear most desirable for Cygnus . From a back-ground perspective, SF is advantageous due to its mi-nority carriers which enable z -fiducialization. A vesselrunning at atmospheric pressure also requires less struc-tural support and thinner walls than a vessel running atnear-vacuum pressure and therefore produces less intrin-sic background.Summarizing the results we can state first that toshield rock neutrons the vessel would need to be sur-rounded by cm of water shielding to bring the nu-clear recoil rate, above 1 keV r , down to less than oneevent per year. Next, for the vessel material itself, wedetermined that 20–30 cm of copper is optimum. The electron recoils from the rock gamma background are al-ready shielded to within our limit using this thickness,whereas the neutron and gamma backgrounds from thevessel fall only slightly above it. If it can be demon-strated in further screening tests that copper’s Uradioactivity is around half the upper limit used here( < . mBq kg − [328]) then it will be an attractivecandidate for the Cygnus
TPC. Although such a ves-sel would likely need a steel support frame—introducinga further background—conceptual designs are feasible inwhich the frame is embedded in the copper, thereby pro-viding the necessary additional shielding. Ideally thisvessel would spend only a short time above and belowground, by limiting air-shipment of materials, procuringthe materials and, if possible, electroforming, as close tothe site as possible; all in the aim of reducing furthercosmogenic activation.In simulating the various readout technologies and am-plification stages we conclude that while some readout-generated backgrounds can be kept within the limit, fur-ther R&D is clearly still needed to establish the optimumchoice for
Cygnus from a background standpoint. Afew issues that would need to be addressed include: (1)for strip micromegas, GEMs and µ -PIC, a better under-standing of the radiopurity, as well as an investigationinto the use of lower background material alternativessuch as acrylic; (2) for the pixel chip readout, measure-ments of the radioactivity levels of silicon, combined withan investigation of charge focusing to reduce the requirednumber of chips; and (3) an improved field cage designusing a smaller number of resistors, which ideally wouldcontain lower levels of U than the ceramic resistors weassumed here. Resistive sheets [339] should be evaluatedas a potential resistor replacement.The issue of the readout background may also be par-tially addressed on the analysis side. For instance, im-proving the electron/nuclear recoil discrimination by afactor of 10-100 would both widen the available choicesof readout material, while also permitting background-free operation with a lower energy threshold. This maybe possible by using a larger set of recoil discriminationparameters than already discussed in Sec. IV C, and/orby decreasing the drift distance to limit diffusion.As long as the total neutron recoil background remainssubdominant to solar neutrinos, then the WIMP crosssection sensitivities from Sec. IV I would be largely unaf-fected. We reiterate that the most important impact onour final physics reach at this stage comes from the elec-tron discrimination threshold. Hence the electron back-ground and electron discrimination should take priorityin future work. Ultimately, while we conclude that whilethere is more work still needed to prove that
Cygnus can sustain completely background-free operation, we donot yet consider there to be any immediate showstoppers,and have identified steps that should be taken to addressour unresolved issues.3
VI. UNDERGROUND SITES ANDENGINEERING
We displayed the locations of several candidate under-ground sites that are currently under consideration for
Cygnus in Fig. 2. This section provides a summaryof the significant logistical and engineering requirementsthat must be considered for these sites to host directionaldark matter detectors. Principal of these for gas TPCsare space requirements and the need to provide handlingof the gas target underground. Both of these factors de-pend on the choice of gas and operating pressure, so wecenter the discussion around a first stage
Cygnus
TPCof order 10 m operating at one atmosphere. A. Site requirements
While a TPC with 1000 m fiducial volume is ratherlarge in total volume, a corresponding advantage of theconcept is that there is no particular restriction on theshape of that volume. For instance, one could consideran elongated ‘worm-like’ sectional design where one di-mension is substantially longer than the other two. Thisis not only feasible but actually has certain advantagesfor operations and maintenance. Cygnus is thereforewell-suited to sites where long tunnels and restrictions onavailable height are normal, e.g. mine sites like Stawell,Australia or Boulby, UK. The relative simplicity of theservices needed—in particular that there are no cryogen-ics involved—is also is an advantage here. Additionally,the experiment can be built as separate detectors, eitherin one site, or in multiple sites. This also allows cross-correlation of data at different latitudes which could aidin the control of systematics. Such geometric featureswill not necessarily be required for a first 10 m stagebut will become important in 1000 m designs aiming togo below the neutrino floor.Due to finite door, elevator, and cavern sizes, certainsites will have more stringent constraints than others onthe maximum size of an object able to be brought in, e.g. × m at Boulby. This would need to be accountedfor in the vessel design. A baseline single × × m detector could be engineered in sites such as Gran Sasso,where there is available head-room and good access. Adifferent, segment-based design could be used for a de-tector of the same total volume distributed in differ-ent sites, as well as for an elongated version of, say, × × m that would conceivably fit in an existingfacility at Boulby.The site overburden requirement is not foreseen to beas important a consideration here since the candidatesites are all > km in depth. The muon-induced neutronevent rate at this depth (calculated in Sec. V A 4) can berejected with a combination of an active external muonveto and the inherent charged particle tracking capabilityof TPCs, depending on the adopted TPC readout tech-nology. The need for an external veto would have only a modest impact on the overall dimensions of the experi-ment, probably a < m increase in linear dimension forthe case of plastic scintillator with support structure. B. Engineering requirements
One of the most important engineering constraints forgas TPCs is that they typically need to be operated atlow pressure, requiring a vacuum vessel. We have pro-posed here however that the addition of helium—suchthat the experiment operates at atmospheric pressure—alleviates this constraint whilst simultaneously gainingthe experiment access to low WIMP masses and a largerrate of solar and reactor neutrinos. The impact on direc-tional readout sensitivity and the intrinsic backgroundwere discussed in Secs. IV and V respectively, and theresults were promising. From an engineering perspectivehowever, it is possible that the TPC would still need sig-nificant certification as a pressure vessel if contaminationis an issue. Purification is conventionally achieved viaoutgassing under vacuum, so it would need to be proventhat flushing gas through the vessel prior to operationcan sufficiently reduce contamination. If possible thiswould obviate the need for the vessel to be of vacuumstandard, greatly reducing the mass of steel, titanium orcopper needed. This option is under investigation. Wenote that the NID gas CS is known to be highly tolerantof impurities so that the DRIFT experiment operates wellwith up to 1% gas impurity, but SF needs more studyin this regard.Figure 31 shows an example design for an 8 m Cygnus vessel based on a steel construction. An alter-native is to use a cylindrical design to reduce the massby a factor of about two, but at the cost of additionalcomplexity in the detector and shielding.For the design of Fig. 31, it is feasible to obtain therequired ∼ < background neutron per year, how-ever the intrinsic gamma background would still be toohigh (see Table VIII). An alternative would be copper,as proposed for NEXT-100 [347] whose screening processproved ultra low-background levels of < . mBq/kg U, < . mBq/kg Th, and . mBq/kg K. Althoughit may not be possible to build a large-scale pure cop-per vessel, a hybrid design in which copper is used forthe main vessel panels with steel or titanium supportstructures could be engineered instead. Ultimately, weenvisage that the scale and engineering requirements fora 10 m Cygnus vessel are unlikely to be challenging forany of the possible underground sites.In addition to the O (10 m ) vessel, external neutronand gamma shielding would likely contribute an addi-tional ∼ FIG. 31. Design for a first stage 8 m steel vessel (courtesy of D. Warner, Colorado State University).FIG. 32. DRIFT-IId interlocking acrylic block shielding sur-rounding the detector and containing water, located at Boulbyunderground laboratory. pensive, it would have a potential advantage in that itcould be instrumented with photomultipliers to providea Cherenkov muon veto as well.While there is no need for complex cryogenics engineer-ing in Cygnus , consideration is still needed with regardsto the engineering aspects of the gas supply. In mostcurrent generation directional detectors the target gas isflowed and disposed of through filters to the atmosphere.However, for
Cygnus , recirculation will be needed, bothfor cost and environmental reasons: SF is a powerfulgreenhouse gas. Recirculation also provides a potentialmeans for the reduction of radon and water from the tar-get. Purification of SF is well known in industry [348] so Time [hours] R a d o n c o n ce n tr a t i o n i nS F [ B q m − ] Filter off Filter on Cold trap
FIG. 33. Experimental results for the radon in SF as a func-tion of time when using a 5 Å molecular sieve. The blackpoints show the radon concentration prior to being divertedthrough the sieve. Then dark blue points show the reductionwhen the filter is turned on. The filter is then cooled withdry ice resulting in a further reduction, shown in light blue. therefore is not seen as a major impediment here. Mean-while, recent experiments by the Sheffield group have in-vestigated active radon removal in SF [349]. Figure 33shows the results from an experiment in which SF wascirculated through a vessel with a known level of radonadded via a sealed radon source. When the gas is di-verted through a 5Å molecular sieve, the radon is seen toreduce. When the filter is cooled with dry ice a further re-duction is seen. The final up-turn in this data is believed5to be due to the gradual temperature increase of the dryice over time. An earlier test also checked that the SF itself was not absorbed by the filter. These experimentsshow for the first time that active radon removal in SF is possible.Summarizing this brief overview of the Cygnus siteand engineering issues we conclude that, while the re-quired vessels do present challenges, they are surmount-able. One of the major benefits of the
Cygnus exper-iment is the significant flexibility in the approach to itsshape and modularization. This opens up prospects forconstruction in sections underground and at multiple lo-cations so that various constraints imposed by each sitecan be met. It is clear that building
Cygnus at the suf-ficient scale to reach below the neutrino floor is a chal-lenge. Nevertheless, it is worth noting that a 1000 m vessel represents approximately 1/50th of the cryogenic internal vessel volume proposed for DUNE [199] at Sand-ford Underground Laboratory, for which rock excavationis now underway. VII. SUMMARY AND RECOMMENDATIONS
We have outlined the physics case, technology choices,and design of the first large-scale directional nuclear re-coil observatory. We name the project
Cygnus after theconstellation from which the wind of dark matter origi-nates.While previous work on the subject of directional de-tection (summarized in Ref. [14]) was often based on ide-alized theoretical concepts, here we have calculated thesensitivity of a directional detector, incorporating exper-imental realities. These include energy-dependent per-formance parameters such as detection efficiency, energyresolution, head/tail recognition, and angular resolution;as well as background considerations such as radioactiveimpurities in the vessel, readout and environment, andthe ability to discriminate between nuclear and electronrecoils. This article is therefore the first to bridge the gapbetween the theoretical and experimental literature. Ourprincipal conclusion is that, despite some remaining tech-nical challenges, a
Cygnus nuclear recoil observatory isindeed feasible in line with the sensitivities displayed inFig. 3.A ton-scale ‘
Cygnus -1000’ detector, with a fiducialtarget volume of 1000 m , filled with a He:SF gas mix-ture at room temperature and atmospheric pressure, andwith 1–3 keV r event detection thresholds, would have anon-directional sensitivity to WIMP-nucleon cross sec-tions extending significantly beyond existing limits. ForSI interactions this sensitivity could extend into presentlyunexplored sub-10 GeV c − parameter space, whereas forSD interactions, even a 10 m -scale experiment wouldbe sufficient to compete with generation-two (G2) detec-tors currently under construction, such as LZ and Super-CDMS.As we discussed in Sec. II, the physics motivation for Cygnus is substantial, prior to, or even in the absenceof, a positive detection of DM. Even for the worst-casescenario of an 8 keV r nuclear recoil threshold, Cygnus -1000 would observe around 13 CE ν NS events over sixyears from B and hep solar neutrinos. This would be asignificant achievement, given that CE ν NS will not be-come an appreciable signal in conventional direct detec-tion experiments until LZ or XenonNT have taken data.For a threshold of 1 keV r this number increases to 37which would already be enough to begin to characterizethe neutrino spectrum.In addition to solar neutrinos, supernovae occuring atdistances closer than 3 kpc would be sufficient to pro-duce a measurable number of highly energetic nuclearrecoil events in Cygnus -1000. For even larger volumes,the possibilities open up for the detection of geologicaland reactor neutrinos. Another interesting signal, butone that is not explored in detail here, are the signalsfrom neutrino electron scattering events (see Fig. 4). Alarge number of high energy electron recoils would be ex-pected in
Cygnus -1000, primarily from the lower energycomponents of the flux like pp or Be neutrinos.
Cygnus could have a lower threshold for electron events than evenBorexino, so the prospects to contribute to the physicsof solar neutrinos may even extend beyond what we havediscussed here. Just as the excellent nuclear/electron re-coil discrimination permits the identification of a WIMPsignal, this same capability also implies excellent poten-tial background rejection if solar neutrino-electron recoilsare the signal of interest. An investigation of both so-lar and geoneutrino-electron recoils in directional exper-iments is therefore worthy of a detailed follow-up study.We expect
Cygnus to be capable of full 3d event re-construction, good directional sensitivity and excellentelectron/nuclear recoil discrimination even at energieswell below 10 keV r . This will require a highly segmentedcharge readout and the limiting of the diffusion of ioniza-tion in the target gas. High electron rejection will enablethe detector to operate free of internal background, withthe capability of distinguishing WIMP-nucleus scatteringfrom CE ν NS or unexpected nuclear recoil backgrounds.For example, with a high-resolution pixel or strip read-out, on average 4-5 detected 100-GeV c − WIMP-fluorinerecoils above 50 keV r are sufficient to rule out an isotropicrecoil distribution at 90% C.L. For a 10-GeV c − WIMP,less than 20 detected helium-recoil events above 6 keV r or3-4 events above 20 keV r would suffice to rule out aneutrino-induced nuclear recoil distribution at 90% C.L.This would constitute the first step in firmly establishingthe galactic origin of a tentative dark matter signal.We estimate that the most cost-effective way to achievethe desired high readout segmentation, low diffusion,and good directional performance at low recoil energies,is via strip readout technologies and negative ion drift. Cygnus -1000 would then require 2000 m of strip read-out planes. Thanks to LHC technology development,large strip micromegas planes from CERN that wouldmeet our technical requirements are already available at6a cost of order $12,500 /m . If a radiopure version ofthese detector as well as preamps with integration timeappropriate for NID are developed, then Cygnus -1000could be constructed relatively soon and at quite rea-sonable cost. Assuming 20 million readout channels atan electronics cost of US $1/channel for mass production,the total charge readout cost of
Cygnus -1000 would thenamount to US $45 million. Downstream DAQ, gas ves-sels and shielding would add to the cost, but due to theability of
Cygnus to operate with low noise at roomtemperature and atmospheric pressure, these costs willbe kept reasonable.We do not anticipate
Cygnus to be a monolithic ex-periment like most detectors currently in operation. The target volume would be best achieved using mul-tiple smaller detectors (see Fig. 1), say of × × m ,potentially located at multiple underground sites (seeFig. 2). As well as simply facilitating our the sensitiv-ity goals while maintaining low pressure operation, themodularity and distribution of the experiment would al-low for the control of systematics by comparison betweendetectors, and importantly, leaves room for future expan-sion at each site. Utilizing multiple detectors would allowalso the use of multiple target gases and pressures, butthe currently favored scenario is to include a negative-iondrift gas, preferably SF mixed with helium, to arrive atatmospheric total pressure. This mixture has multipleadvantages: it improves the directionality of all recoilspecies, permits z -fiducialization via minority carriers,and extends the sensitivity to both low WIMP massesand neutrinos. Atmospheric pressure also avoids the needfor a vacuum vessel.While a low-density gas such as 755:5 torr He:SF isessential to maintain low-mass WIMP and neutrino sen-sitivity with directionality, the planned segmentation of Cygnus naturally enables operation of parts of the de-tector with a higher-density "search mode" gas. If thefinal
Cygnus design does not require a vacuum vessel,then for example half the fiducial volume could run with760 of SF gas, which would boost the exposure by afactor of 150. If we choose a vacuum-capable gas vesseldesign, then this would be capable of withstanding a 1atmosphere pressure differential. In that case the searchmode could utilize 1520 torr of SF for a factor 300 boostin exposure. The beauty of Cygnus is that the exactpartitioning of the target volume into low-density andsearch mode running can be optimized and varied even af-ter construction, and be responsive to new developmentsin the field. This flexibility may prove particularly im-portant for larger volume detectors, e.g. a Cygnus -100k,which will required a substantial investment of time andfunding.The new simulations presented here, validated in partby experiment, suggest that electron rejection is feasi-ble down to 1 keV ee in the atmospheric pressure He:SF mixture. The discrimination power depends on the so-phistication of the readout but rises exponentially withenergy. With a simple discriminant the expected electron rejection factor to exceed at 5 keV ee for fluorine, and10 keV ee for helium. Our first investigations with deeplearning neutral networks suggest this can be improvedupon by several orders of magnitude[319]. Machine learn-ing efforts by the MIMAC collaboration [350] similarlysuggest great improvements are possible. The optimiza-tion of the electron rejection, and finding the optimaltradeoff of intrinsic background versus the sophisticationof readout is the subject of future work.To limit the background from the Cygnus vessel, weenvisage a skeletal design based on titanium, copperand acrylic, surrounded by an inner layered structure ofgamma shielding, incorporating copper and steel. Shield-ing from neutron backgrounds can be achieved by usingwater blocks outside the inner shield (see Fig. 32), and aconventional muon veto depending on site depth. Someimprovement in copper radiopurity will be needed for theshielding but a back-up to this would be to use entirelywater shielding.
Final recommendations
To clarify the route forward, we have five main recom-mendations: First, the strawman design discussed hereshould be advanced to a properly optimized technical de-sign. We expect that the low-mass reach of a fully opti-mized strip readout detector will exceed the physics reachestimated here, as we found that our strawman design isdiffusion-limited. Second, all energy-dependent perfor-mance metrics introduced here, such as the recoil effi-ciency, angular resolution, head-tail efficiency, and elec-tron rejection, must be demonstrated experimentally ina small prototype with full drift length and high readoutresolution: a ‘
Cygnus
HD1 Demonstrator’. Third, theintrinsic radioactivities of the components of the stripreadout must be reduced to where they are consistentwith the measured electron rejection capabilities. Fourth,inexpensive, scaleable readout electronics for large-areastrip readout planes should be designed. Lastly, the ex-pected physics sensitivity of
Cygnus should be morebroadly investigated. For example, we expect that the3d ionization measurements should be uniquely capa-ble of detecting and identifying non-conventional DM-nucleon scattering final states; and as mentioned above,the prospects for novel physics based on electron recoilsshould also be investigated, such as in the context of neu-trinos or axion-like particles.Independently of this main development path, we alsorecommend the pursuit of alternative design approaches,based on electron drift. Electron drift gases will allowmuch higher avalanche gains than NID gases, but at thecost of increased diffusion. For electron drift, fiducializa-tion would be performed via measurements of diffusion,rather than via observation of minority carriers. Thehigher gain could be a good match for optical readout,and hence the CYGNO experiment in Italy [278] will pur-sue that option. Another interesting configuration is a7pixel or strip readout detector with electron drift andlow threshold. This is being pursued by US CYGNUScollaborators. We leave the evaluation of these optionsfor future work.
VIII. CONCLUSION
An exciting physics program will be possible with theanticipated network of
Cygnus detectors, as illustratedin Fig. 34. The initial 1 m Cygnus
HD1 demonstrator,or a slight scale-up, could be used to demonstrate di-rectional sensitivity to CE ν NS with reactor or spallationsources. This would guarantee sensitivity to a directionalsolar neutrino signal in the subsequent detectors. Then,for every factor ten increase in exposure, interesting newmeasurements are possible.
Cygnus -1000 would detectbetween 13 and 37 CE ν NS events over six years, depend-ing on the exact energy threshold for background freeoperation. An ambitious
Cygnus -100k detector, withvolume similar to that of DUNE [199], would have non-directional WIMP sensitivity in excess of any proposedexperiment, and would, in addition, allow us to utilizedirectionality to penetrate deep into the neutrino floor.Finally, if a dark matter signal is observed, this wouldmark the beginning of a new era in physics. The com-munity would seek to firmly establish the galactic originof the signal, which is only possible by observing someform of direction-dependence. After that, a worldwideeffort would ensure to map the local velocity distribution and explore the particle phenomenology of dark matter.A large directional detector such as
Cygnus -100k wouldbe essential to enable this.
ACKNOWLEDGMENTS
SEV acknowledges support from the U.S. Departmentof Energy (DOE) via Award Numbers DE-SC0018034and DE-SC0010504. CAJO is supported by the Uni-versity of Sydney and the Australian Research Coun-cil. EB is supported by the European Research Coun-cil (ERC) under the European Union Horizon 2020 pro-gramme (grant agreement No. 818744) KS is supportedby the U.S. Department of Energy and the National Sci-ence Foundation. WL, NJCS, CE, ACE and FMM wouldlike to thank STFC for continued support under grantST/S000747/1 KM is supported by the Japanese Min-istry of Education, Culture, Sports, Science and Tech-nology, a Grant-in-Aid for Scientific Research, ICRRJoint-Usage, Japan Society for the Promotion of Science(JSPS) KAKENHI Grant Numbers 16H02189, 26104005,26104009, 19H05806 and the JSPS Bilateral Collabora-tions (Joint Research Projects and Seminars) programand Program for Advancing Strategic International Net-works to Accelerate the Circulation of Talented Re-searchers, JSPS, Japan (R2607). Computing resourceswere provided by the University of Chicago ResearchComputing Center. [1] G. Bertone and D. Hooper, Rev. Mod. Phys. , 045002(2018), arXiv:1605.04909 [astro-ph.CO].[2] M. Battaglieri et al. , in U.S. Cosmic Visions: New Ideasin Dark Matter College Park, MD, USA, March 23-25,2017 (2017) arXiv:1707.04591 [hep-ph].[3] G. Angloher et al. (CRESST), Eur. Phys. J. C , 25(2016), arXiv:1509.01515 [astro-ph.CO].[4] R. Agnese et al. (SuperCDMS), Phys. Rev. D ,022002 (2018), arXiv:1707.01632 [astro-ph.CO].[5] L. Hehn et al. (EDELWEISS), Eur. Phys. J. C , 548(2016), arXiv:1607.03367 [astro-ph.CO].[6] C. Amole et al. (PICO), Phys. Rev. Lett. , 231302(2015), arXiv:1503.00008 [astro-ph.CO].[7] C. Amole et al. (PICO), Phys. Rev. D , 052014(2016), arXiv:1510.07754 [hep-ex].[8] P. Agnes et al. (DarkSide), Phys. Rev. D , 081101(2016), arXiv:1510.00702 [astro-ph.CO].[9] A. Tan et al. (PandaX-II), Phys. Rev. Lett. , 121303(2016), arXiv:1607.07400 [hep-ex].[10] D. S. Akerib et al. (LUX), Phys. Rev. Lett. , 021303(2017), arXiv:1608.07648 [astro-ph.CO].[11] E. Aprile et al. (XENON), Phys. Rev. Lett. , 181301(2017), arXiv:1705.06655 [astro-ph.CO].[12] G. Adhikari et al. (COSINE-100), Phys. Rev. Lett. ,031302 (2019), arXiv:1903.10098 [astro-ph.IM].[13] S. Ahlen et al. , Int. J. Mod. Phys. A , 1 (2010),arXiv:0911.0323 [astro-ph.CO]. [14] F. Mayet et al. , Phys. Rept. , 1 (2016),arXiv:1602.03781 [astro-ph.CO].[15] J. B. R. Battat et al. , Phys. Rept. , 1 (2016),arXiv:1610.02396 [physics.ins-det].[16] J. B. R. Battat et al. , J. Instrum. , P11004 (2014),arXiv:1407.3938 [physics.ins-det].[17] D. Santos, J. Billard, G. Bosson, J. Bouly, O. Bourrion, et al. , EAS Publ. Ser. , 25 (2012), arXiv:1111.1566[astro-ph.IM].[18] S. Vahsen, H. Feng, M. Garcia-Sciveres, I. Jaegle,J. Kadyk, et al. , EAS Publ. Ser. , 43 (2012),arXiv:1110.3401 [astro-ph.IM].[19] C. Deaconu, in UCLA 11th Symposium on Sources andDetection of Dark Matter and Dark Energy in the Uni-verse (2014).[20] K. Miuchi et al. , Phys. Lett. B , 11 (2010),arXiv:1002.1794 [astro-ph.CO].[21] T. Marrodán Undagoitia and L. Rauch, J. Phys. G ,013001 (2016), arXiv:1509.08767 [physics.ins-det].[22] M. Schumann, J. Phys. G , 103003 (2019),arXiv:1903.03026 [astro-ph.CO].[23] G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mam-brini, M. Pierre, S. Profumo, and F. S. Queiroz, Eur.Phys. J. C , 203 (2018), arXiv:1703.07364 [hep-ph].[24] R. Bernabei et al. , Eur. Phys. J. C , 2648 (2013),arXiv:1308.5109 [astro-ph.GA]. ° WIMP mass [GeV] ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° S I W I M P - p r o t o n c r o sss ec t i o n [ c m ] ∫ - fl o o r ( F ) m m m m k m k m k m [ S e a r c h m o d e ] n e u t r i n o ( F ) Cygnus -N m £ C YGNUS -1 m Background-free operation down to 0.25 keV r Improve upon WIMP limits for <2 GeV C YGNUS -10 m Background-free operation down to 0.5 keV r Best SD-proton limits across all masses C YGNUS -10k m Best SI limits across all masses Detect core-collapse supernova at 8 kpc C YGNUS -100k m C YGNUS -1000 m Sensitive to reactor neutrinos O (10) Solar neutrinos per year C YGNUS -100 m 〜 FIG. 34. Summary of the projected SI WIMP 90% CL exclusion limits as a function of the total fiducial volume of the networkof detectors comprising the
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