Detecting Dark Matter with Far-Forward Emulsion and Liquid Argon Detectors at the LHC
PPITT-PACC-2101UCI-TR-2021-01
Detecting Dark Matter with Far-Forward Emulsionand Liquid Argon Detectors at the LHC
Brian Batell, ∗ Jonathan L. Feng, † and Sebastian Trojanowski
3, 4, 5, ‡ Pittsburgh Particle Physics, Astrophysics, and Cosmology Center,Department of Physics and Astronomy,University of Pittsburgh, Pittsburgh, PA 15217, USA Department of Physics and Astronomy,University of California, Irvine, CA 92697-4575, USA Astrocent, Nicolaus Copernicus Astronomical Center Polish Academy of Sciences,ul. Bartycka 18, 00-716 Warsaw, Poland Consortium for Fundamental Physics,School of Mathematics and Statistics, University of Sheffield,Hounsfield Road, Sheffield, S3 7RH, UK National Centre for Nuclear Research,Pasteura 7, 02-093 Warsaw, Poland
Abstract
New light particles may be produced in large numbers in the far-forward region at the LHC andthen decay to dark matter, which can be detected through its scattering in far-forward experiments.We consider the example of invisibly-decaying dark photons, which decay to dark matter through A (cid:48) → χχ . The dark matter may then be detected through its scattering off electrons χe − → χe − .We consider the discovery potential of detectors placed on the beam collision axis 480 m fromthe ATLAS interaction point, including an emulsion detector (FASER ν
2) and, for the first time,a Forward Liquid Argon Experiment (FLArE). For each of these detector technologies, we devisecuts that effectively separate the single e − signal from the leading neutrino- and muon-inducedbackgrounds. We find that 10- to 100-tonne detectors may detect hundreds to thousands of darkmatter events in the HL-LHC era and will sensitively probe the thermal relic region of parameterspace. These results motivate the construction of far-forward emulsion and liquid argon detectorsat the LHC, as well as a suitable location to accommodate them, such as the proposed ForwardPhysics Facility. ∗ [email protected] † [email protected] ‡ [email protected] a r X i v : . [ h e p - ph ] J a n ontents I. Introduction 3II. Light Dark Matter with a Dark Photon Mediator 4III. Detectors 6A. Emulsion Detector: FASER ν ν ν ν . Introduction Unraveling the nature of dark matter (DM) is one of the top priorities in particle physicsand cosmology today. As the search for traditional DM candidates, such as weakly inter-acting massive particles (WIMPs) and axions, resolutely marches forward, physicists areaggressively exploring new frontiers in the vast DM landscape. One particularly compellingidea is that DM is part of a light hidden sector, coupled to the Standard Model (SM) througha light mediator particle. The observed DM relic abundance can be obtained through simplethermal freeze-out in these scenarios [1–3]. This extends the standard WIMP productionmechanism to dark matter masses below the Lee-Weinberg bound [4] and provides predictivetargets in DM model parameter space in the MeV to GeV mass range [5–7]. Light DM mod-els of this kind lead to a rich phenomenology, requiring new experimental and observationalsearch strategies going beyond the traditional methods used to search for WIMPs [8–10].A promising avenue for light weakly interacting particle searches is to harness the largeand energetic far-forward flux of particles produced in proton-proton collisions at the LargeHadron Collider (LHC). In particular, the FASER detector [11–13], situated 480 m down-stream of the ATLAS interaction point (IP), will efficiently search for light long-lived particlesemerging from this forward flux and decaying visibly to SM particles [11, 14–21]. Further-more, FASER ν will initiate studies of collider-produced neutrinos and measure TeV-energyneutrino interactions in a controlled laboratory setting for the first time [22–24]. FASER andFASER ν are currently being constructed and installed to collect data during LHC Run 3,while a second stage of these experiments with much larger detectors is envisioned for theHL-LHC era. These larger detectors are unlikely to fit within the existing tunnel infras-tructure, but a dedicated Forward Physics Facility (FPF) [25], which would house these andother experiments to carry out a variety of novel SM measurements and beyond the SM(BSM) searches, is currently under study [26].In this paper we investigate the prospects to search for light MeV- to GeV-scale hiddensector DM in the far-forward region of the LHC. The basic detection strategy is very simple.Light mediator particles may be copiously produced in the forward region of LHC pp collisionsand promptly decay to light DM particles. The DM particles then travel roughly 480 m intoa detector and scatter off electrons. A similar search strategy, but for proton fixed targetexperiments, has been investigated [27–38] and successfully carried out by the MiniBooNE-DM Collaboration [39, 40]. As we will demonstrate, despite the simplicity of the signalsignature, the single scattered electron has kinematic characteristics that allow it to bedistinguished from all neutrino-induced and other SM backgrounds. This stems from thefact that the DM-electron scattering is mediated by a light force carrier and so favors O (GeV)electron recoil energies, while the background from neutrino-electron scattering is mediatedby heavy electroweak bosons and so is spread over a broad range of energies and peaks inthe several hundred GeV range. Note that DM scattering off nuclei is also potentially apromising signal, but one we will not investigate here.Although there are many different light DM scenarios that can be considered, we willfocus here on the simple and well-motivated scenario in which the mediator is a kinetically-mixed dark photon [41]. In this case, both the DM production and subsequent DM-electronscattering is mediated by the dark photon. We will consider two potential detector tech-nologies: (1) a 10-tonne-scale emulsion detector, FASER ν
2, which is essentially an upgradedand enlarged version of the FASER ν experiment, and, for the first time, (2) a Forward3iquid Argon Experiment, which we denote by the acronym FLArE, composed of a 10- or100-tonne-scale liquid argon time projection chamber (LArTPC) of the type being employedin several modern neutrino experiments. We will show that these detector types offer thepotential to detect hundreds to thousands of DM events and to discover DM in a large re-gion of parameter space in which the correct DM abundance is obtained through thermalfreeze-out.The possibility of detecting DM in the forward region has been discussed for theSND@LHC experiment [42], an 850 kg emulsion detector proposed to be placed 480 mfrom the ATLAS IP just off the beam collision axis during Run 3. For the simple modelconsidered and the luminosity expected at Run 3, no parameter space beyond currentbounds could be probed [42], but, of course, other models could be considered. In thisstudy, rather than consider such models, we focus on two minimal models, but explore thepotential of larger detectors placed on-axis during HL-LHC running. In addition, we discussmuon-induced backgrounds in detail and, as noted above, analyze the physics potential offar-forward LArTPC detectors for the first time.This paper is organized as follows. In Sec. II we describe the dark photon-mediated DMmodels to be studied in this work. In Sec. III we discuss the basic detector designs we willconsider, and in Sec. IV we provide an overview of our modeling of the DM signal. Ourestimates of the neutrino- and muon-induced backgrounds are detailed in Secs. V and VI,respectively. We present the results of the analysis in Sec. VII and our conclusions andoutlook in Sec. VIII. II. Light Dark Matter with a Dark Photon Mediator
In this section we introduce two simple, predictive benchmark models of sub-GeV DMthat can be explored in the far-forward region at the LHC. The models we study are basedon a broken U (1) D gauge symmetry, with a massive dark photon A (cid:48) µ serving as a mediatorbetween the SM and DM χ . The dark photon Lagrangian is given by L ⊃ − F (cid:48) µν F (cid:48) µν + 12 m A (cid:48) A (cid:48) µ A (cid:48) µ + (cid:15) θ W F (cid:48) µν B µν , (1)where m A (cid:48) is the dark photon mass, (cid:15) is the kinetic mixing parameter, θ W is the weak mixingangle, and B µν is the hypercharge field strength. In the regime m A (cid:48) (cid:28) m Z of interest here,the A (cid:48) primarily mixes with the SM photon, leading to a coupling of the dark photon to theelectromagnetic current with strength suppressed by (cid:15) . In the physical basis, the dominantinteractions of the dark photon are then given by L ⊃ A (cid:48) µ ( (cid:15) e J µEM + g D J µD ) , (2)where J µEM is the SM electromagnetic current, J µD is the U (1) D current, and g D ≡ √ πα D is the U (1) D gauge coupling.It remains to specify the precise nature of the DM particle χ . In this work, we will study4wo cases: (1) complex scalar DM and (2) Majorana fermion DM, with Lagrangians L ⊃ | ∂ µ χ | − m χ | χ | (complex scalar DM)12 χiγ µ ∂ µ χ − m χ χχ (Majorana fermion DM) , (3)where m χ is the DM mass. The U (1) D current in each model is J µD = iχ ∗ ↔ ∂ µ χ (complex scalar DM)12 χγ µ γ χ (Majorana fermion DM) . (4)In both models the correct DM relic abundance can be achieved through thermal freeze-out. In particular, in the regime m A (cid:48) > m χ , DM annihilates directly to SM fermionsthrough s -channel dark photon exchange, χχ → A (cid:48) ( ∗ ) → f ¯ f . In the limit m A (cid:48) (cid:29) m χ , theannihilation cross section has the same parametric form in both models, σv ∝ α v (cid:15) α D m χ m A (cid:48) = α v ym χ , (5)where α is the SM electromagnetic fine structure constant, and we have introduced thedimensionless parameter y ≡ (cid:15) α D ( m χ /m A (cid:48) ) , following Ref. [5]. A notable feature of theannihilation cross section of Eq. (5) is the velocity suppression characteristic of P -wave an-nihilation. These models therefore evade in a simple way the otherwise stringent constraintsfrom DM annihilation at the epoch of recombination, which can lead to distortions in thecosmic microwave background temperature anisotropies [43, 44].Regions of parameter space where the correct DM relic density is obtained by thermalfreeze-out are important targets for experimental searches. These can be conveniently vi-sualized in the ( m χ , y ) plane and compared with existing experimental bounds and futuresensitivity projections. We will use the results of Ref. [45] for the DM relic abundance pre-dictions, derived by evolving the full Boltzmann equation including exact thermal averagingof the annihilation cross section. To present thermal targets and experimental sensitivitiesin the ( m χ , y ) plane, we will adopt the common choices of α D = 0 . m A (cid:48) = 3 m χ . Thesechoices are fairly conservative, in the sense that they do not inflate the potential of probingthermal targets at particle experiments. However, it is important to keep in mind that theparametric scaling of the annihilation cross section in Eq. (5) is sharply violated in the res-onance region, where m A (cid:48) − m χ (cid:28) m A (cid:48) . In this region, the annihilation rate is resonantlyenhanced, and so smaller couplings are required to achieve the correct relic density, makingit more challenging to experimentally probe thermal targets [46–48].Although the particle nature and couplings of complex scalar and Majorana fermion DMmodels are distinct (see Eq. (4)), the two models yield quantitatively similar predictionsfor reaction rates involving relativistic energies. This includes DM produced in the hotearly universe, as well as DM production at accelerators and its subsequent re-scatteringin downstream detectors. On the other hand, for non-relativistic processes, such as haloDM scattering in direct detection experiments, the two models lead to dramatic quantitativedifferences in event rates. For Majorana fermion DM, direct detection rates are suppressed by5any orders of magnitude due to the inherent momentum dependence of the scattering, andDM direct detection is challenging for all existing and proposed experiments. (See, however,the recent study of Ref. [49].) In contrast, for complex scalar DM that scatters elastically,large event rates are expected in next generation sub-GeV direct detection experiments,complementing accelerator probes, including far-forward production at the LHC. We note,however, that even in the scalar DM case, one can introduce a mass splitting so that thescattering proceeds inelastically [50]. Provided the fractional mass splitting is in the range O (10 − − − ), this effectively suppresses scattering rates in direct detection experimentswhile leaving the cosmology and accelerator probes unaltered. These features will be clearlyillustrated when we present our results in Sec. VII.We note that other viable models with a dark photon mediator can be constructed; seee.g., Ref. [45] for a detailed discussion of model variations. In particular, certain modelsalso lead to visible long-lived particle signatures, e.g., the visible decay of the dark photonmediator for the case m χ > m A (cid:48) , or the decay of the excited DM state χ → χ e + e − ininelastic scenarios. Such long-lived particle signatures can also be explored at the LHC withthe FASER experiment [11, 51, 52]. III. Detectors
As already mentioned in Sec. I, our analysis will focus on two distinct detector designssensitive to the signal of DM-electron scattering. Both types of detectors have been suc-cessfully employed in past experiments and will be used in future searches. Here, we brieflypresent the basic details of the detectors we will consider.
A. Emulsion Detector: FASER ν We first consider an emulsion detector similar to, but larger than, the FASER ν detectorcurrently under construction [22, 23]. FASER ν is a 1.1-tonne neutrino detector, composed oftungsten sheets for the target material, interleaved with emulsion films capable of detectingcharged tracks with high spatial resolution. This detector design will be tested in the far-forward region of the LHC during Run 3.For the HL-LHC era, a larger 10-tonne scale emulsion detector, referred to as FASER ν
2, iscurrently envisioned [53]. For our study, we will assume a rectangular detector with locationand size given byFASER ν L = 480 m , ∆ = 2 m , S T = (0 . × . , (6)where L is the distance from the IP to the front of the detector, and ∆ and S T are thelongitudinal and transverse dimensions of the tungsten target. We assume that the detectoris centered on the beam collision axis.Tungsten-emulsion detectors have significant virtues. They are remarkably compact, asa result of tungsten’s high density of 19 . / cm , and the excellent spatial and angularresolutions of emulsion detectors make them very precise tools for reconstructing individualinteraction vertices in the detector [54]. In particular, a particle track spatial resolutiondown to 50 nm can be achieved, while, depending on the track length in the emulsion, the6ngular resolution can be much better than 1 mrad. The expected energy resolution for ∼ GeV electromagnetic showers is 30 −
40% and improves for higher energy showers; see,e.g., the discussion in Ref. [55] for showers initiated by two photons. We will assume thattracks down to momenta of 300 MeV can be detected, and that the emulsion is exchangedperiodically so that the track density remains manageable and suitable high speed scanningfacilities are available.The main disadvantage of emulsion detectors for this DM search is the lack of timing,which makes it difficult to reject muon-induced background, as we discuss in Sec. VI. Toremedy this, it is necessary to augment the emulsion-tungsten detector with interleavedelectronic tracker layers, which would provide event time information. A similar detectorconcept was successfully employed in the OPERA experiment [56], and analogous designshave been proposed for SND@SHiP [57] and SND@LHC [42]. The role of such tracker layersin mitigating potential muon-induced backgrounds will be discussed further in Sec. VI.
B. Forward Liquid Argon Experiment: FLArE
Although the emulsion detector technology allows for a compact detector with the ex-cellent energy resolution and vertex reconstruction capabilities required for the DM search,other experimental approaches are possible, especially if more space is available in a futureForward Physics Facility during the HL-LHC era [25].Liquid argon has proven to be a very efficient active detector material and has beensuccessfully used in numerous DM direct detection searches and neutrino experiments. Inparticular, LArTPCs provide precise spatial and calorimetric resolution, excellent particleidentification capabilities, and detailed neutrino event reconstruction. Well-known examplesinclude the short-baseline neutrino program at Fermilab [58] and the far detector of the futureDeep Underground Neutrino Experiment (DUNE) [59]. Current and planned detectors ofthis type have masses as large as ∼ tonnes. LArTPC detectors can therefore offer bothlarge event statistics and excellent background rejection capabilities.With this motivation, we will investigate the feasibility of detecting DM in a LArTPCdetector in the far-forward region of the LHC. We will refer to this proposal as the ForwardLiquid Argon Experiment (FLArE). Fittingly, as we discuss in detail below, the first indica-tion of a DM signal event in FLArE is the flare of scintillation light produced by the electronrecoil, followed by the ionization electron signal.Since liquid argon is about 14 times less dense than tungsten, a LArTPC detector mustbe much larger if a similar active material mass is desired. In the models considered here,the DM is produced in light dark photon decay and so is highly collimated. At a distance of480 m from the IP, the flux is largely confined to a region of a few tens of cm around the beamcollision axis. The optimal detector therefore has a cross sectional area of approximately thissize. Note, however, that in other BSM scenarios in which DM particles are produced withbroader angular distributions, for example, from the decay of heavier mesons, increasing thetransverse size of the detector could also be beneficial.Motivated by these considerations, we will consider two liquid argon detectors:FLArE–10 (10 tonnes) : L = 480 m , ∆ = 7 m , S T = (1 m × , (7)FLArE–100 (100 tonnes) : L = 480 m , ∆ = 30 m , S T = (1 . × . , (8)7here, as above, L is the distance from the IP to the front of the detector, ∆ and S T are thelongitudinal and transverse dimensions of the detector, and we assume that the detector iscentered on the beam collision axis. These detectors would require enlarging the availablespace in the far-forward region of the LHC, which, however, has already been envisioned inthe proposed Forward Physics Facility [25].LArTPC detectors can detect very soft charged tracks down to momenta of 30 MeV,a significant improvement over emulsion detectors. In addition, as noted above, emulsiondetectors suffer for this analysis from the lack of timing, which makes it difficult to rejectmuon-induced backgrounds. In contrast, the expected time resolution of LArTPC detec-tors is at the level of O (ms) due to the finite drift time of ionization electrons in liquidargon [60]. Further improvement can be achieved by using an additional light collection sys-tem in tandem with the TPC. Such a design has already been employed in the MicroBooNEexperiment [60]. This is used in the initial step of the background rejection procedure,which is based on the measurement of the light collected in consecutive O (10 ns) long timeticks [61]. The combined event time and spatial information can be utilized to efficientlyseparate the DM signal from the muon-induced backgrounds, as we discuss in more detail inSec. VI.We note that further redundancy could be provided by a dedicated muon-tagger positionedeither in front of or behind the LArTPC. In a similar fashion to the MicroBooNE CosmicRay Tagger [63], such a system could measure the crossing time and position of the passingmuons, which could then be compared with similar information obtained with the TPC andlight detection system. Notably, the time and position information of the through-goingmuons can also be obtained with the use of other experiments placed in the Forward PhysicsFacility along the beam collision axis, e.g., by employing the tracking system of the proposedFASER 2 experiment.
IV. Signal
In the previous sections, we introduced the models and detectors we will consider. Herewe discuss in detail how we simulate the signal, the characteristics of the single electronsignature, and suitable cuts to distinguish signal from background.
A. Signal Simulation
For the models discussed in Sec. II, at the LHC, DM is primarily produced throughthe decays of on-shell dark photons. The parent dark photons with m A (cid:48) (cid:46) η mesons, as well as throughproton bremsstrahlung.In our modeling, we employ the CRMC simulation package [64] and the
EPOS-LHC
MonteCarlo (MC) generator [65] to obtain the forward spectrum of light mesons produced in14 TeV proton-proton collision energy. As a cross check, we have also used the meson While MicroBooNE has photomultiplier tubes (PMTs) behind the wire planes, a future LArTPC couldemploy another PMT array on the other side of the detector, which could potentially significantly improvethe event time resolution and location determination [62]. IG. 1. The DM-electron elastic scattering signal process. spectra obtained with
Pythia 8 [66] and found good agreement. A MC simulation thengenerates the rare decays π , η → γA (cid:48) , the subsequent prompt dark photon decays A (cid:48) → χχ , the propagation of the DM particles to the detector, and the interactions of the DMparticles in the detector, χe − → χe − . To model A (cid:48) production from proton bremsstrahlung, pp → ppA (cid:48) , we use the Fermi-Weizsacker-Williams approximation, following the discussionin Refs. [11, 35, 67].An additional flux of light DM particles in the forward direction is generated when high-energy photons and neutral hadrons hit the neutral particle absorber TAXN located about130 m away from the pp IP. These then generate electromagnetic (EM) showers and hadroniccascades, which can then produce DM particles in the TAXN. Similar recent discussions ofDM production in electron- and proton-induced EM showers in the target for selected beam-dump and neutrino experiments can be found in Refs. [68, 69].We have made preliminary estimates of the TAXN-produced DM flux for the FASER ν e + e − → A (cid:48) , and from A (cid:48) productionthrough electron bremsstrahlung, but even these production modes are subdominant in oursimulations. This is due to the relatively high electron recoil energies of interest for oursignal regions, E e (cid:38)
300 MeV, and the small angular size of FASER ν
2, which covers only asmall fraction of the total angular spread of the EM showers in the TAXN. We note, how-ever, that for the larger LArTPC detectors with a lower electron recoil energy threshold,DM production in the TAXN could play a non-negligible role, especially for low DM masses m χ (cid:46)
10 MeV. We leave a detailed analysis of this effect for future studies.
B. Signal Characteristics
The signature of our interest is a single-electron-initiated EM shower in the detector thatresults from χe − → χe − scattering, as shown in Fig. 1. For the complex scalar and Majoranafermion DM models, the differential scattering cross sections are dσdE e = 4 π(cid:15) αα D m e E − (2 m e E + m χ )( E e − m e )( E − m χ )( m A (cid:48) + 2 m e E e − m e ) (complex scalar DM) , (9) dσdE e = 4 π(cid:15) αα D m e ( E − m χ )+[ m χ − m e (2 E − E e +2 m e )]( E e − m e )( E − m χ )( m A (cid:48) + 2 m e E e − m e ) (Majorana DM) , (10)9 IG. 2. The electron recoil energy spectra for the background neutrino-electron scattering events(blue histogram) and for the DM signal events. The latter have been obtained for two benchmarkscenarios with the DM mass and the kinetic mixing parameter equal to ( m χ , (cid:15) ) = (25 MeV , − )(yellow) and (5 MeV , × − ) (red). In both the DM scenarios we set the dark photon mass to m A (cid:48) = 3 m χ and the dark coupling constant to α D = 0 .
5. The number of events in the bins isnormalized to the FLArE–100 detector and the HL-LHC phase with 3 ab − of integrated luminosityand 14 TeV proton-proton collision energy. where E e is the electron recoil energy and E is the energy of the incoming DM particle.For large DM energies E (cid:29) E e , m χ and electron recoil energies satisfying E e (cid:29) m e , thescattering cross sections in these two scenarios become very similar, and they are both wellapproximated by dσdE e ≈ π (cid:15) α α D m e ( m A (cid:48) + 2 m e E e ) (approximate formula for large E, E e ) . (11)For further details regarding these differential cross sections, see Appendix A.Despite the suppression by the small kinetic mixing (cid:15) , the presence of the small darkphoton mediator mass in the denominator of Eq. (11) can increase the DM scattering ratesto a level that is comparable to or larger than those of SM neutrinos. This is especiallyrelevant for small electron recoil energies. We illustrate this in Fig. 2 by comparing the E e spectrum of the dominant neutrino-electron scattering background to the E e spectrum of theDM signal in FLArE–100. As can be seen, in the case of the neutrino-induced events, theelectron recoil energy is peaked at high (TeV) energies and the number of events decreasesfor low values of E e . This is a result of the parent neutrino energy spectrum, which is peakedat a few hundred GeV, and the increase of the neutrino scattering cross section with neutrinoenergy. In addition, given the relatively large mass of the mediator W and Z bosons, for afixed incident neutrino energy E ν , the relevant differential cross section depends only mildlyon E e .On the other hand, the low dark photon mediator mass yields a DM scattering crosssection that is largely independent of the incident DM energy. Also, the differential crosssection is peaked towards small energy transfer to the recoiled electron such that 2 m e E e (cid:46) m A (cid:48) , which minimizes the denominator in Eq. (11). The signal event rate can therefore10lectron recoil energy 300 MeV < E e <
20 GeVElectron recoil angle 10 mrad < θ e <
20 mrad for E e >
10 GeV10 mrad < θ e <
30 mrad for 3 GeV < E e ≤
10 GeV10 mrad < θ e for E e ≤ p >
300 MeV
TABLE I. Analysis cuts used in the background analysis in Secs. V and VI for the emulsion detectorFASER ν be greatly enhanced for detectors with low energy thresholds, which becomes increasinglyimportant with the decreasing dark photon mass. This can also be seen in Fig. 2, where,keeping in mind m A (cid:48) = 3 m χ , the electron recoil energy spectrum for the benchmark scenariowith m χ = 5 MeV is shifted towards lower E e in comparison with the similar spectrumobtained for m χ = 25 MeV. As we illustrate below in Sec. VII, this allows the LArTPCdetectors to probe smaller couplings than the emulsion detector in the regime with m χ (cid:46) O (10 MeV).An additional handle to distinguish the signal from the neutrino-induced background isthe electron recoil angle, θ e , which can be written ascos θ e ≈ E χ/ν E e − m T ( E χ/ν − E e ) (cid:113) E χ/ν − m χ/ν (cid:112) E e − m e , (12)where E χ/ν is the incident energy of the DM particle or neutrino, and m T is the targetmass. The target mass is equal to m e for the signal and the νe − → νe − background,but it is the nucleon mass for neutrino-induced backgrounds from quasi-elastic processes, ν ( p/n ) → e ( n/p ). For the typical case, where E χ (cid:29) m χ and E e (cid:29) m e , E e θ e ≈ m T (1 − x ),where x = E e /E χ/ν is the energy transfer to the electron.As discussed above, for the signal, the scattering rate is greatly enhanced for low values of E e and x . This implies that θ e is typically larger for the DM signal than for the νe − → νe − background. For the DM signal, for x (cid:46) . E e ∼ O (10 GeV), the typical recoil angleis θ e ≈ (cid:112) m e /E e ∼
10 mrad.On the other hand, for neutrino scatterings off nucleons, the typical recoil angle θ e is muchlarger than in the case of the DM signal, given the much increased target mass. This helpsto differentiate between the DM signal and these background events, which may be furthersuppressed by requiring no additional charged tracks in the detector. These considerationsare especially relevant for deep inelastic neutrino scattering events, as discussed in Sec. V. C. Analysis Cuts for FASER ν The kinematic features of the signal suggest simple cuts on both E e and θ e that canefficiently discriminate between the DM signal and the neutrino-induced backgrounds. InTable I, we show the cuts for FASER ν < E e <
20 GeVElectron recoil angle θ e <
30 mrad for E e > θ e cut for E e ≤ p >
30 MeV
TABLE II. Analysis cuts used in the background analysis in Secs. V and VI for the LArTPCdetectors FLArE–10 and FLArE–100.
As we have discussed above, our sensitivity estimates below are obtained for a futureemulsion detector similar to, but larger than, the FASER ν detector [22, 23] that will operateduring LHC Run 3. This dictates the charged track visibility criteria in the emulsion. Inour analysis, this will be modeled by a simple cut on the charged particle momentum, p >
300 MeV. We employ this cut both when analyzing the DM signal events and theneutrino-induced backgrounds. In particular, we reject all background events characterizedby additional visible charged tracks emerging from the vertex, other than a single electron orpositron. When presenting the results in Sec. VII, we also discuss the impact of tighteningthe electron recoil energy cut on the expected sensitivity reach.
D. Analysis Cuts for FLArE
One of the main advantages of LArTPC detectors, which makes them excellent toolsfor probing interactions of medium-energy neutrinos, is their capability to detect very softcharged particles produced in interactions in the detector. The relevant energy thresholdcan be as low as 25 MeV for the protons produced in neutrino scatterings off nuclei [61],while similar energy thresholds of 30 MeV can be achieved for muons and pions [70]. (Seealso Refs. [71, 72] for recent discussions regarding new physics searches in the short-baselineneutrino detectors.) In the analysis below, we assume a 30 MeV threshold for the electronrecoil energy [70]. On the other hand, the background rejection capabilities are only mildlydegraded by the poorer angular resolution of LArTPCs relative to emulsion detectors. Weassume below that this resolution in LArTPCs is of the order of 1 ◦ (see Ref. [70]) and thatwe can cut on angles larger than 30 mrad. We summarize the cuts used in this analysisin Table II. To understand the sensitivity of our results to the LArTPC angular resolution,in Sec. VII, we also present results assuming no cut on θ e , but more stringent cuts on theelectron recoil energy, 30 MeV < E e < γ → e + e − pair production. This can be done with high accuracy through the so-called“ dE/dx discrimination method,” i.e., by measuring the ionization at the beginning of theelectromagnetic shower [73]. When discussing the muon-induced backgrounds in Sec. VI, wewill assume that 85% of these muon-induced e + e − background events can be distinguishedfrom single e − signal events [61]. 12 IG. 3. Neutrino-electron elastic scattering background processes: ( a ) NC ν i e − → ν i e − , ( b ) CC ν e e − → ν e e − , ( c ) NC ν i e − → ν i e − , and ( d ) CC ν e e − → ν e e − . V. Neutrino-Induced Backgrounds
The signature of DM-electron scattering can most straightforwardly be mimicked by theinteractions of SM neutrinos; see Ref. [74] for a review. These can either be due to ν scatterings off electrons characterized by the same event topology, or in much more abundantneutrino scatterings off nuclei that can occasionally resemble χe − → χe − signal events. Wenow estimate the expected event rates of these background processes and analyze how theycan be reduced by employing simple kinematic cuts on the electron recoil energy and angle,as discussed in Sec. IV. To this end, we simulate neutrino scattering events in the detectorwith the GENIE
MC package [75, 76].
A. Neutrino Flux and Spectrum
The uncertainties in our background estimates are primarily related to the uncertainties inthe modeling of the far-forward neutrino flux and energy spectrum at the LHC. In the future,the relevant simulations will greatly benefit from the neutrino data collected by FASER ν during LHC Run 3. In our analysis below we rely on the results obtained by the CERNSources, Targets, and Interactions (STI) Group [77], which utilized the FLUKA [78, 79]model of the forward LHC optics and infrastructure. Notably, a similar FLUKA studyof the muon flux going through the FASER location [80] has been found to be in goodagreement with initial measurements obtained during Run 2 [13]. In our estimates, we takeinto account the full HL-LHC integrated luminosity of L = 3 ab − and the FASER ν B. Neutrino-Electron Backgrounds
The most important neutrino-induced backgrounds are neutrinos scattering with electronsin the detector, νe − → νe − , as depicted in Fig. 3. One expects O (10 ) such events in theFASER ν events inFLArE–100. These events are topologically identical to the signal, and so must be reducedwith kinematic cuts.The most important such processes are associated with neutral current (NC) scatterings13 e − → νe − events after cutsDetector (see Tables I and II)FASER ν . . . E e < . TABLE III. The expected number of neutrino-electron scattering events during HL-LHC for theemulsion detector FASER ν E e < of muon neutrinos and similar interactions of electron neutrinos. Despite the lower fluxof ν e s going through the detector, the corresponding scattering cross section has both NCand charged current (CC) contributions and is thus enhanced in comparison to the ν µ NCscattering cross section. On the other hand, tau neutrinos contribute negligibly to theexpected backgrounds. We present the relevant estimates in Table III for all of the detectordesigns we consider.In the case of FASER ν
2, we also show in Table IV a detailed breakdown of the numberof events for different neutrino flavors after imposing successive cuts in the analysis. As canbe seen, more than 90% of the νe − → νe − background events can be rejected by applyingthe upper limit on the electron recoil energy, E e <
20 GeV. In contrast, the impact of sucha low-recoil-energy cut on the DM signal events is typically much less severe, given the lightmediator mass, as discussed in Sec. IV. A small additional suppression of the backgroundevents comes from imposing the lower limit on the electron recoil angle, θ e (cid:38)
10 mrad, whichslightly increases the signal to background ratio (
S/B ). The total number of expected suchbackground events after cuts in FASER ν B ν - e ≈ C. Neutrino-Nuclei Backgrounds
The total number of neutrino-nuclei scattering events significantly exceeds that of neu-trino scatterings off electrons. Even when the electron recoil energy range is limited, as isdictated by the cuts used in our analysis, a few thousand of such events are still expectedduring the HL-LHC phase for the 10-tonne detectors under study. These are mostly dueto electron neutrino CC deep inelastic scattering (CCDIS), but there are also importantcontributions from CC quasi-elastic (CCQE) and resonant (CCRES) interactions; see Fig. 4.We now discuss these backgrounds, first for the emulsion detector FASER ν
2, and then for14 e − → νe − FASER ν E e >
300 MeV 300 MeV < E e <
20 GeV(emulsion detector) no cut on θ e θ e cut (see Table I) ν e
160 4 . . ν e
60 4 . . ν µ
70 6 . . ν µ
44 5 2 . ν τ .
05 0 . ν τ .
04 0 . TOTAL
336 20 . . TABLE IV. The expected number of neutrino-electron scattering events during HL-LHC for theemulsion detector FASER ν a ) neutrino CCQE scattering ν e n → e − p , ( b ) anti-neutrino CCQE scattering ν e p → e + n , and representative ( c ) CCRES and ( d ) CCDIS reactions. the LArTPC detectors FLArE.The CCQE scattering processes, ν e n → e − p and ¯ ν e p → e + n , are characterized by a high-energy electron in the final state and soft activity from the nuclear recoil. Hence, if theoutgoing electron satisfies the cuts, such events can easily resemble DM-electron scatterings.This is especially true for events with a neutron in the final state, as it does not leave a trackin the emulsion and can travel a distance of the order of the hadronic interaction length intungsten, λ had,W ≈
10 cm [81], before interacting. Events with a final-state proton can alsomimic χe − → χe − scatterings if the emitted proton is too soft or if it is reabsorbed beforeleaving the nucleus due to final state interactions (FSI).In CCQE scattering events, most of the neutrino energy is transferred to the outgoingelectron. Therefore, this background contribution is associated with lower energy neutrinos, E ν (cid:46)
20 GeV, given our cut on the electron recoil energy. As shown in Table V, we expectabout 10 such background events during the entire run of FASER ν
2. However, these eventsare typically associated with a larger electron recoil angle θ e and can be effectively rejectedby selecting events with low recoil angle. Last, but not least, the cut on the additionalenergetic charged tracks emerging from the vertex further suppresses this background. Thissuppression is more pronounced for ν e scattering events with protons in the final state. Boththe neutrino and anti-neutrino CCQE scatterings lead to less than one expected backgroundevent. 15 CQE
300 MeV < E e <
20 GeVFASER ν θ e θ e cut (see Table I)(emulsion detector) no other ch. tracks with p >
300 MeV ν e .
45 0 . ν e .
25 0 . Total
14 0 . . TABLE V. The expected number of CCQE background events during HL-LHC for the emulsiondetector FASER ν CCRES
300 MeV < E e <
20 GeVFASER ν θ e θ e cut (see Table I)(emulsion detector) no other ch. tracks with p >
300 MeV ν e
22 0 . . ν e
14 0 . . Total
36 1 . . TABLE VI. The expected number of CCRES background events during HL-LHC for the emulsiondetector FASER ν CCDIS
300 MeV < E e <
20 GeVFASER ν θ e θ e cut (see Table I)(emulsion detector) no other ch. tracks with p >
300 MeV ν e .
3k 40 0 . ν e .
2k 30 0 . Total .
5k 70 . TABLE VII. The expected number of CCDIS background events during HL-LHC for FASER ν Another source of background is resonant pion production in neutrino scatterings offnucleons (CCRES). After summing over all intermediate nuclear resonances, the inclusiveCCRES scattering cross section can exceed that of the CCQE scatterings in the energy rangerelevant for our analysis. Fortunately, most of these events can again be disentangled fromthe DM signal based on the electron recoil angle. In addition, if the final state charged pionsescape the nucleus, such events can be efficiently rejected by observing their charged tracksin the emulsion. This results in B CCRES ≈ . E ν ∼
100 GeV can produceoutgoing electrons with E e <
20 GeV. On the other hand, the large momentum transfer tonuclei in CCDIS scatterings generally leads to additional energetic charged tracks emergingfrom the vertex. As a result, only neutrinos with energies that do not greatly exceed the20 GeV threshold can effectively mimic the DM signal events. A combination of cuts onthe additional visible charged tracks and on the electron recoil angle reduces the CCDISbackgrounds to B CCDIS (cid:46) . χe − → χe − signal by identifying the outgoing lepton. Second, neutrino-nuclei NC scattering may mimicthe signal if a photon is emitted from the interaction vertex and is subsequently reconstructedin the emulsion as a single electron that satisfies all the cuts. In addition, all other visiblecharged tracks associated with the nuclear interaction vertex must be sufficiently soft toescape identification. The low likelihood of these combined circumstances suggests that thesebackgrounds are subdominant relative to the ν e -nucleus CC backgrounds discussed above,and so not of great concern. We note, however, that photons imitating the single-electronsignature in emulsion will be discussed further in Sec. VI in the context of muon-inducedbackgrounds. D. Neutrino-Induced Background Summary
Summing over all the neutrino-induced backgrounds, we expect O (10) such backgroundevents during the entire HL-LHC run for the FASER ν θ e , and the number of backgroundevents for FLArE–100 is about 100. These backgrounds are dominated by neutrino-electronscattering, while neutrino-nuclei scatterings, although larger a priori , can be more efficientlydisentangled from the signal in the analysis.The impact of the analysis cuts is illustrated in the ( E e , θ e ) plane in Fig. 5 for FASER ν ν - e interactions generate E e that is more spread over the entire available energy range.The ν - N interactions are instead characterized by electrons with both larger energy andlarger recoil angle. Importantly, in the plots, we show only the background events for whichthere is only a single e ± charged track emerging from the vertex with p >
300 MeV. Thisgreatly reduces the number of CCDIS background events. In Fig. 5 we also show the signalregions for both the emulsion and LArTPC detectors that were defined in Sec. IV, in whichthe excess of DM scattering events over the expected neutrino-induced background can mosteasily be seen.
VI. Muon-Induced Backgrounds
Aside from neutrinos, the only other SM particles that can pass through 100 m of rock aremuons. These muons are dominantly produced either at the IP or through collisions in theTAXN neutral particle absorber. The relevant flux of muons going through a small FASER ν detector during LHC Run 3 has been predicted by the CERN STI group [80] employing theFLUKA transport code [78, 79] and was independently measured by the FASER collaborationduring Run 2 [13]. When rescaled to account for the HL-LHC luminosity and the largertransverse size of FASER ν
2, more than 10 muons are expected to traverse the detectorduring the entire run of the experiment, and this number grows by a factor of a few for17 IGNAL χ e -> χ e ’2Dbins_chiDMsignal_plot.out’ u 1:2:3 e (GeV)131030100 θ e ( m r ad ) BG ν e -> ν e ’2Dbins_nuelectron_plot.out’ u 1:2:3 e (GeV)131030100 θ e ( m r ad ) BG ν e N -> e N’ (CCQE+CCRES+CCDIS) ’2Dbins_CCQERESDIS_FINAL_plot.out’ u 1:2:3 e (GeV)1310300.1 θ e ( m r ad ) FIG. 5. Event distributions in the ( E e , θ e ) plane, along with the regions selected by the cuts, forthe emulsion detector FASER ν
2. We show these distributions for the DM signal, χe − → χe − ,for the benchmark scenario with m A (cid:48) = 3 m χ = 75 MeV, (cid:15) = 10 − and α D = 0 . p >
300 MeV emerging from the vertex, besides asingle electron or positron, are shown. The solid and dashed green lines outline the signal region forthe FASER ν the LArTPC detectors. If not removed through selection cuts or through a dedicated muonveto, muon-induced photons that convert to electron-positron pairs inside the detector canoccasionally mimic the DM signal, as illustrated in Fig. 6. Below, we briefly discuss suchbackgrounds and possible strategies to mitigate their impact on the DM search. A. Sweeper Magnet
Part of the muon-induced background can be removed by installing a sweeper magnetplaced along the beam collision axis upstream of the detector. A convenient location for18
IG. 6. Muon-induced background processes. A photon is produced via muon-bremsstrahlung andthen converts to an e + e − pair. Such an event is a background to the DM signal if the incomingmuon is not associated with the e + e − pair production, either the electron or positron has an energybelow the detection threshold energy, and the other has the correct kinematics to pass the selectioncuts. In addition to muon-bremsstrahlung, such backgrounds can arise in direct electron-positronpair production, µN → µe + e − N . such a magnet is along the beam collision axis after it has left the LHC beampipe, butbefore it enters the tunnel wall. This location is roughly 300 m from the ATLAS IP and200 m upstream of the detector. A magnet placed in this location will not interfere withtransport, which typically uses the wider path on the other side of the LHC beampipe.A muon with energy E µ that travels a distance (cid:96) through a magnetic field B orientedperpendicular to its direction and then travels an additional distance d is deflected by adistance h B ≈ ecdE µ B(cid:96) = 60 cm (cid:20)
100 GeV E µ (cid:21) (cid:20) d
200 m (cid:21) (cid:20) B · (cid:96) T · m (cid:21) (13)in the transverse plane. Permanent dipole magnets with a magnetic field of B ≈ .
57 Tand total length of 3.5 m for an integrated magnetic field strength of B · (cid:96) = 2 . · m havealready been constructed for the FASER experiment. These magnets require no services andhave very small fringe fields. It is also important that the sweeper magnet accommodatesshifts in the beam collision axis from variations in the beam crossing angle. At the HL-LHC,the beam crossing angle may vary by up to 590 µ rad, corresponding to a shift of 9 cm at adistance of 300 m from the IP. The FASER magnets have an inner diameter of 20 cm, whichis roughly of the size required to accommodate such shifts.It therefore appears quite feasible for a sweeper magnet to eliminate all muons withenergies below 100 GeV from the detector region. In fact, with a ten-fold increase in B · (cid:96) of thesweeper magnet with respect to the current FASER magnets, one could even deflect muonswith few TeV energies, drastically reducing the number of muon-induced backgrounds. Ofcourse, in a detailed study, it would be important to trace all muons through the beam opticsand be sure that, in sweeping away muons from the detector one does not simultaneouslysweep other muons into the detector. B. Single-Electron-Like Events from Muon Interactions
As mentioned above, even if a sweeper magnet is used, some of the muons could bedeflected back into the detector. Notably, the path of such deflected muons may often notbe parallel to the beam collision axis. Given the angular cuts used in the DM search, as19 ignalregion with angular cutsFASER ν N e v en t s pe r m uon E (GeV) γ e ± (signal-like) -6 -5 -4 -3 -2 -1 FIG. 7. The expected energy spectrum of muon-induced photons (green) in FASER ν θ γ with respect tothe parent muon direction satisfies the cuts introduced in Sec. IV. For the estimates, the parentmuon spectrum with E µ >
100 GeV has been used, following Refs. [22, 80]. The spectrum of singleelectrons or positrons that can mimic the DM signal after photon pair production is also shown(blue). These are events in which a muon-induced photon pair produces, and either the electron hasan energy below the detectability threshold and the positron satisfies the kinematic cuts discussed inTable I, or vice versa. The signal region in the DM search corresponds to 300 MeV < E e <
20 GeVas indicated in the plot. described in Sec. IV, this could greatly suppress such muon-induced backgrounds. On theother hand, if the sweeper magnet deflects only a portion of the high-energy muons, theremaining ones will traverse the detector with only minimal deflection angles that, in thefirst approximation, can be neglected in the analysis. It is then useful to analyze the potentialimpact of such muons on the DM search. In the rest of this section, we conservatively assumethat only muons with energies smaller than 100 GeV will be swept away, while the moreenergetic ones will pass through the detector.For such high-energy muons, the photon bremsstrahlung and e + e − pair production in-teraction lengths are of the order of a few meters for tungsten and above 100 m for liquidargon [82]. This produces a large number of photons and e + e − pairs in both types of de-tectors. For illustration, in Fig. 7 we show the expected energy spectra for FASER ν
2. Toobtain these spectra, we performed dedicated FLUKA simulations for this study, startingwith the parent muon high-energy ( E µ >
100 GeV) spectrum predicted for LHC Run 3, andrequiring that the resulting photon or e + e − pair have angles with respect to the beam axissatisfying the cuts discussed in Sec. IV. The muon-induced photons will typically produce an e + e − pair within the radiation length of the parent muon, which is equal to λ W = 0 .
35 cmand λ LAr = 14 cm in tungsten and liquid argon, respectively [81].We first focus on the emulsion detector. Given the high density of tracks in the emulsion,this distance is often too large to associate the secondary photon pair-production vertex, γN → e + e − N , with the parent muon. If sufficiently energetic, the e − and e + tracks mayalways be differentiated as two separate tracks in an emulsion detector, given its extraor-dinary resolution. However, these events are a background to the χe − → χe − signal when20ither the electron or positron has an energy below the 300 MeV threshold energy and thusevades detection, while the other has the energy and direction required to pass the cuts.The predicted spectrum of such events is shown in the green histogram of Fig. 7. As can beseen, up to 1% of muons going through the detector can lead to such events, although thisfraction drops to about 0 .
01% for increased energy threshold E e > − eN → γeN . The outgoing electron/positron might then emerge from this layer as eithertoo soft or significantly deflected, which affects the photon vertex identification. Similarprocesses can lead to background events after direct e + e − pair production, µN → µe + e − N ,which dominates the soft muon-induced e ± spectrum. In this case, however, the visiblesignal-like e ± track is produced in the close vicinity of the parent muon track, which allowsfor better background rejection.The corresponding expected number of bremsstrahlung processes per muon in the liquid-argon FLArE–10 detector is about an order of magnitude smaller than for FASER ν
2. Thisis due to the lower density and the smaller value of the radiative muon energy-loss func-tion b ( E ) in this material [82]. On the other hand, this is partly offset by both the lowerdetection energy threshold and the absence of a lower cut on the emission angle, result-ing in a substantial number of low-energy bremsstrahlung photons that could mimic theDM signature. We expect that most of these photons can be disentangled from the single-electron-initiated EM showers using the dE/dx discrimination method mentioned in Sec. IV,while still O (10%) could be misreconstructed as signal-like events. As a result, one finds lessthan 1% of muons are able to generate signal-like events in FLArE–10. A similar conclusionholds for FLArE–100.Notably, one could also consider a modified design of FLArE–100 with a larger transversesize and reduced length in comparison with Eq. (8). In this case, an additional importanteffect could come from the non-uniform distribution of muons in the transverse plane atthe location of the experiment. In particular, for off-axis locations with radial distances ofabout R ∼ C. Active Muon Veto for FASER ν In the absence of perfect muon sweeping, another strategy is to actively veto muon-induced background events. This could be achieved by using timing information about boththe through-going muon and the EM shower in the emulsion.The timing information about the EM showers in the emulsion could be obtained byinterleaving the emulsion detector with electronic tracker layers, similar to the proposeddesigns of SND@SHiP [57] and SND@LHC [42], as well as that employed in the OPERAemulsion detector [56]. A distance between the layers of order 10 −
15 radiation lengths21ill allow one to successfully observe most of the EM showers that will typically leak tothe electronic detectors. A too-large separation between the layers would mean a reducedeffective volume of the detector, as only a fraction of the showers will be registered, limitingthe prospects of the DM search.Once the candidate DM signal event in the electronic detector is identified with no time-coincident muon, further analysis would be based on proper matching between the activityin the tracker and the EM vertex in the emulsion. Such matching could suffer from thepile-up of numerous partially overlapping EM showers in the emulsion. This will have to beovercome when scanning the emulsion in search of candidate events. The detailed analysisof this issue and the development of the algorithms used to identify the EM showers inthe emulsion is left for future studies, but see Ref. [83] for a discussion about EM showerreconstruction in the OPERA experiment.
D. Active Muon Veto for FLArE
The muon-induced backgrounds can be more easily rejected in the LArTPC detectors.This is primarily due their capability to provide active time information about the events,which could be significantly enhanced by the use of the additional light collection system, asdiscussed in Sec. III. Combined with the decent spatial resolution offered by TPCs, this allowsfor efficient rejection of background events that can be associated with a time-coincidentmuon passing through the front veto and detector.To identify the DM signal, one would first employ the excellent O (10 ns) time resolution ofthe light collection system. Based on this, one can single out individual O (ms) time windowsin the TPC data that contain candidate events. Such events can then be differentiated fromall neutrino-induced backgrounds based on their detailed characteristics, as measured bythe TPC and the analysis cuts discussed in Sec. IV. Importantly, given the low number ofexpected DM and neutrino scatterings, there is a negligible probability that both types ofevents to happen in a single time window.The muon-induced background is much more common. In the case of FLArE–10, weexpect about 10 muons passing the detector in each TPC time window. This is determinedby the transverse size of the detector and the estimated muon flux of 1 Hz / cm [80]. Sincemuon-induced photons could mimic the single-electron-initiated EM showers, they wouldhave to be rejected based on the spatial information about the event. In particular, giventhe aforementioned large radiation length in liquid argon and the maximum angle of thephoton with respect to the beam-collision axis to mimic the signal, θ max = 30 mrad, reducingthe fiducial volume of the detector by several cm wide cylinders around each of the muontrajectories will be sufficient to effectively reject all such muon-induced backgrounds. Atthe same time, the DM signal detection rate will only be mildly affected by the order 10%fiducial volume reduction, which has an almost imperceptible impact on the sensitivity reachplots presented in Sec. VII.The muon-induced backgrounds could similarly be rejected in the larger FLArE–100 de-tector. Note, however, that if the design of FLArE–100 were changed with respect to Eq. (8)by increasing its transverse size and reducing its length, the outer parts of the detector couldbe effectively eliminated from the analysis due to the increased muon flux, as discussedabove. This would have to be taken into account when designing the optimized detectorgeometry. 22 II. Results
In this section we present the sensitivity of these experiments to the dark photon-mediatedDM models introduced in Sec. II during the HL-LHC phase. In deriving our sensitivityprojections, we will assume that muon-induced backgrounds can be reduced to a negligiblelevel by making use of event time information, as outlined in Sec. VI. We will, however,take into account the irreducible neutrino-induced backgrounds discussed in Sec. V. It isconceivable that by measuring neutrino scattering processes in kinematic regions outside theDM signal region, precise measurements of the neutrino fluxes and improved modeling ofneutrino scattering cross sections could be obtained during the eventual operation of theseexperiments. Such a data-driven approach may help to mitigate systematic uncertaintiesin the neutrino-induced background rates for the DM search. We will thus work under theassumption that statistical uncertainties in the single electron data sample dominate oversystematic uncertainties. We begin the discussion with our results for the emulsion detectorFASER ν
2, and then discuss our results for the LArTPCs FLArE–10 and FLArE–100.
A. Results for FASER ν In Fig. 8, we present the expected 90% confidence level (CL) exclusion bound in theDM-electron scattering search for the FASER ν α D = 0 . m A (cid:48) = 3 m χ . As discussed in Sec. II, these parameter choices are fairly conservative in termsof experimentally testing the thermal DM production hypothesis. As can be seen, in bothcases, FASER ν m χ (cid:38) O (10 MeV) and the thermalvalue of the DM relic density that coincides with the Planck observations [84]. In the regime m (cid:48) A = 3 m χ (cid:38) O (10 MeV), the DM signal rate scales approximately as y /m χ , while theDM annihilation cross section, Eq. (5), scales as y/m χ , explaining why the FASER ν m A (cid:48) , a feature also observed in Fig. 8. The spike in theexpected FASER ν m A (cid:48) = 3 m χ (cid:39) −
780 MeV is due to the A (cid:48) mixing withthe ρ and ω mesons, which is taken into account in the dark photon production in protonbremsstrahlung [35, 85]; see also Ref. [11] for a similar discussion for FASER.In the plots, the dark gray-shaded region corresponds to null searches at BaBar [89],MiniBooNE [40], and NA64 [90]. These accelerator-based constraints are more stringentthan those coming from the electron and muon anomalous magnetic moments [91, 92]. Inaddition, in the elastic scalar DM case, bounds from past DM direct detection searches atCRESST-II [93] and XENON1T [94] constrain parts of the parameter space. These bounds,however, can be avoided in the inelastic scalar DM model and are, therefore, presented withblack lines but no gray-shaded regions. We similarly show the constraints from sensitivitylimit recasts of a number of past beam-dump and neutrino experiments including BEBC [95],CHARM-II [96], E137 [97], LSND [28], and NO ν A [98] that are implemented followingRef. [99] and presented with the thin solid black line.As is clearly illustrated in the plot, the FASER ν u p e r C D M SS N O L A B
Belle-II (50 ab -1 ) N A ( * E O T ) L D M X S H i P ( S N D ) y = ε α D ( m χ / m A ) m χ ( = m A /3) (GeV)10 -13 -12 -11 -10 -9 -8 -3 -2 -1 FASER ν S N D @ L H C B D X Majorana DM α D =0.5 r e li c t a r ge t S upe r CD M S S N O L AB Belle-II (50 ab -1 ) N A ( * E O T ) L D M X SE N SE I S H i P ( S N D ) y = ε α D ( m χ / m A ) m χ ( = m A /3) (GeV)10 -13 -12 -11 -10 -9 -8 -3 -2 -1 XE N O N T ( e l . ) FASER ν CR ESS T - II S N D @ L H C B D X α D =0.5 r e li c t a r ge t (Inelastic) Scalar DM FIG. 8. Projected 90% CL exclusion bounds in the DM-electron scattering search at FASER ν α D = 0 . m A (cid:48) /m χ = 3, and Majorana DM (left) and (inelastic) scalar DM (right). The solid black lines arethe relic targets, where the DM has the correct thermal relic density. Current bounds are shownwith gray-shaded regions and thin solid black lines (see the text for details). We also show withred dotted lines the projected sensitivities of future missing energy and momentum searches atBelle-II (50 fb − ) [9], LDMX [45, 86], and NA64 (5 × electrons on target (EOT)) [87]. Browndashed lines correspond to future detectors sensitive to direct scattering signatures of DM particlesproduced in collider and beam-dump experiments: BDX [9], SND@LHC [42], and SND@SHiP [88].In the case of elastic scalar DM, the additional future reach of the SuperCDMS at SNOLAB andSENSEI DM direct detection experiments [9] are also indicated by green dash-dotted lines. LDMX [45, 86] experiments will be able to independently constrain these scenarios. Crucially,in the case of a discovery, employing such different experimental search strategies will provideimportant and complementary information about the nature of DM, with FASER ν α D . Forcomparison, we also show the expected sensitivity reach for several proposed experimentssensitive to the scattering of accelerator-produced DM, including the dedicated emulsiondetectors of the SND@LHC [42] and SND@SHiP [57, 88] experiments, as well as the BDXelectron beam dump experiment [101].Last, but not least, the elastic scalar DM scenario will be independently probed by futuredirect detection experiments. We show projections for the SuperCDMS at SNOLAB andSENSEI experiments, following Ref. [9]. As can be seen in Fig. 8, these experiments willprobe the thermal relic target for a wide range of DM masses with m χ (cid:38) a few MeV. Inthe case of a discovery, FASER ν χ s at the LHC in FASER ν ν = ε α D ( m χ / m A ) m χ ( = m A /3) (GeV) E e > 10 GeVE e > 3 GeVE e > 1 GeVE e > 0.3 GeV -13 -12 -11 -10 -9 -8 -3 -2 -1 FASER ν θ cuts, E e <20 GeV and: α D =0.5 S c a l a r r e li c t a r ge t M a j o r ana r e li c t a r ge t y = ε α D ( m χ / m A ) m χ ( = m A /3) (GeV) -13 -12 -11 -10 -9 -8 -3 -2 -1 FASER ν α D =0.5 S c a l a r r e li c t a r ge t M a j o r ana r e li c t a r ge t FIG. 9. Impact of increasing the electron recoil energy threshold (left) and of varying the detectorgeometry (right) on the FASER ν E e , which changes as indicated in the plot. In rightpanel, the total mass (volume) of the 10-tonne detector is kept constant, while its transverse sizeand length are changed. of the lower cut on the electron recoil energy does not lead to substantial changes in theneutrino-induced backgrounds, while increasing this value could help to reduce the muon-induced backgrounds. In the left panel of Fig. 9, we show the expected sensitivity reach linesfor E e >
300 MeV (default), 1 GeV, 3 GeV, and 10 GeV. In obtaining these results we keepthe other cuts the same as shown in Table I. As can be seen, even if the lower limit on E e is increased to 3 GeV, FASER ν < E e <
20 GeV, then the expectedreach is not competitive with current bounds.In the right panel of Fig. 9, we show the expected reach for a varying FASER ν S T , as indicated in the plot, while in each case both its length ∆ and theneutrino-induced backgrounds are adjusted and simulated accordingly. As can be seen, alonger, but narrower, detector is preferred to improve the sensitivity reach. Notably, thedefault geometry of the detector described in Sec. IV with S T = (50 cm ×
50 cm) transversesize and ∆ = 2 m length appears to be close to optimal. The default design may alsofacilitate a more straightforward detector construction and may more easily fit within theavailable experimental facility in comparison to the more elongated narrower design with S T = (25 cm ×
25 cm) and ∆ = 8 m.
B. Results for FLArE
In Fig. 10, we present results for the LArTPC detectors. In the left panel are the expected90% CL exclusion bounds for the Majorana DM model and both FLArE–10 and FLArE–100. As can be seen, important parts of the relic target line in this model can be probed25
1m x 1m x 7m)(1.6m x 1.6m x 30m) S u p e r C D M SS N O L A B
Belle-II (50 ab -1 ) N A ( * E O T ) L D M X S H i P ( S N D ) y = ε α D ( m χ / m A ) m χ ( = m A /3) (GeV) FLArE-10FLArE-100 -13 -12 -11 -10 -9 -8 -3 -2 -1 r e li c t a r ge t Majorana DM α D =0.5 S N D @ L H C B D X y = ε α D ( m χ / m A ) m χ ( = m A /3) (GeV) e <20GeV, θ e cutsonly 30MeV 10 in FLArE–100, assuming that the analysis employs onlythe electron recoil energy cut 30 MeV < E e < in the HL-LHC era. The larger detector FLArE–100 offers a clear improvement in theexpected sensitivity, although the difference between the two benchmark detector designsis not as significant as might be naively expected. Given the 10 times larger volume, onemight expect a factor of 3 improvement in the reach in the y parameter of FLArE–100 overFLArE–10, but this gain is somewhat diminished by the larger neutrino-induced backgroundsin FLArE–100. In addition, the flux of energetic DM particles decreases away from the beamcollision axis, and so the increased transverse size of FLArE–100 has less of an impact onthe expected sensitivity.In the right panel of Fig. 10 we show contours of the expected number of detectedDM scattering events in FLArE–100. As can be seen, up to 1000 DM scattering eventsare expected during HL-LHC in the region of parameter space not currently excluded byNA64 [90]. Also shown are the effect of more stringent cuts on the electron recoil energy,30 MeV < E e < m χ (cid:46) 10 MeV. Suchlight DM favors a low momentum exchange between χ and e − as dictated by the smallervalue of the dark photon mass, m A (cid:48) = m χ / 3. On the other hand, for larger DM masses, m χ (cid:38) 100 MeV, restricting to events with lower electron recoil energy would result in a mildreduction in sensitivity to the y parameter.We stress that, even though the reach plots presented here look similar for both theemulsion and LArTPC detectors, the final sensitivity will also be affected by the detectorcapability to reject muon-induced backgrounds. In particular, as discussed in Sec. VI, theLArTPC experiments allow for a very efficient active muon veto and, therefore, present a26articularly promising detection technique to be employed in DM searches in the far-forwardregion of the LHC. Importantly, since the LArTPC technique is by design well-suited to thestudy of neutrino interactions, such a detector could thus be considered for a future far-forward neutrino experiment during the HL-LHC phase [102]. VIII. Conclusions The hypothesis that DM is part of a light hidden sector is both theoretically compellingand experimentally fertile. We have proposed to leverage the large forward cross section in pp collisions at the LHC to produce and detect such light DM particles in the MeV to GeV massrange. In simple models based on a kinetically-mixed dark photon mediator, an intense fluxof DM particles will be produced in the far-forward direction through neutral meson decaysor proton bremsstrahlung. Given a suitable detector situated in the forward region, perhapshoused in the proposed Forward Physics Facility [25], the DM particles can then be detectedthrough their elastic scattering with electrons, and as many as hundreds to thousands ofsuch DM-electron scattering events could be detected in the cosmologically-allowed regionsof parameter space at the HL-LHC.This search strategy is complementary to approaches utilizing missing energy/momentumat colliders and electron-fixed target experiments, because the production probes thehadronic couplings of the mediator, and the produced DM is directly detected throughits scattering. Furthermore, the relativistic nature of the accelerator-produced DM rendersthe scattering insensitive to the detailed structure of the DM interactions. This is in contrastto the non-relativistic scattering in direct detection experiments, where in certain models(e.g., inelastic scalar or Majorana fermion DM) the event rates are substantially suppressed.We have studied two plausible detector designs, one based on the emulsion detector tech-nology, currently used for FASER ν , and another employing the liquid argon time projectionchamber concept, which we have named the Forward Liquid Argon Experiment (FLArE).Kinematic and topological handles can be utilized to efficiently separate the DM signal fromneutrino induced backgrounds, including neutrino-electron elastic scattering and various neu-trino charged current reactions. We have also investigated potential background processesinduced by the large flux of forward muons. Such backgrounds may pose challenges to theDM search with a nominal FASER ν -style emulsion detector, given the lack of event timeinformation and anticipated spatial pile-up. We have suggested several strategies to miti-gate these backgrounds, including a sweeper magnet to deflect the muons, the installation ofelectronic timing layers in the emulsion detector, and the use of time and spatial informationin the LArTPC detector, with the latter approach appearing to be particularly promising.Looking ahead, it would be very interesting to investigate the sensitivity of these ex-periments to the scattering of light DM with nuclei. In contrast to lower-energy, protonbeam fixed target experiments, the higher energies of the produced DM particles offer thepossibility of detecting DM-induced DIS events. It would also be worthwhile to study theprospects for testing other light DM models with different coupling patterns. For example,the LHC pp collisions may offer distinct advantages in probing DM models with hadrophiliccouplings [30, 31, 33, 103].Although the search for DM particles provides one important motivation for experimentsof this kind in the far-forward region of the LHC, it is certainly not the only one. As alreadyhighlighted in the introduction, the main goal of FASER ν and its envisioned HL-LHC succes-27or is to study TeV-energy, collider-produced neutrinos. Along with the large neutrino DISevent rates studied in Refs. [22, 23], we have found there are significant rates for other high-energy neutrino scattering processes, such as neutrino-electron elastic, CCQE, and CCRESscattering. It would be worthwhile to understand the benefits and drawbacks of various de-tector options, e.g., emulsion and LArTPC, in measuring the various neutrino interactions.Along these lines, it would be interesting to consider the merits of re-purposing existingdetectors in the far-forward region at the LHC, such as the proto-DUNE LArTPC alreadyinstalled at CERN [104, 105]. Along with the intrinsic interest in exploring high-energyneutrino interactions, precise measurements of the neutrino flux and a better theoreticaldescription of neutrino scattering in these experiments are of critical importance in the DMsearch as it relates to the neutrino-induced backgrounds. Furthermore, besides DM scatter-ing, one can envision other well-motivated BSM scenarios with exotic collider-stable particlesthat can be detected through their scattering with electrons or nuclei, such as heavy neutralleptons with non standard interactions [106].FASER and FASER ν will soon embark on a groundbreaking physics program exploitingthe large forward pp cross section at the LHC. With most of the LHC luminosity still tobe collected, now is an apt time to broadly explore the potential physics opportunitiesafforded by a diverse array of experiments situated in the far-forward region [25]. This workdemonstrates that, along with the potential for a suite of SM neutrino measurements, asuitable far-forward detector also offers the unique and exciting opportunity to search forlight DM at the HL-LHC. Acknowledgments We thank Aki Ariga, Tomoko Ariga, Josh Berger, Jamie Boyd, Milind Diwan, FelixKling, Marcin Ku´zniak, Vittorio Paolone, Yu-Dai Tsai, and Masayuki Wada for helpfulconversations. We thank Francesco Cerutti and Marta Sabate Gilarte from the CERN STIgroup for sharing with us the far-forward neutrino spectrum [77] used in our backgroundanalysis. The work of BB is supported by the U.S. Department of Energy under grant No.DE–SC0007914. The work of JLF is supported in part by U.S. National Science FoundationGrant No. PHY-1915005 and by Simons Investigator Award A. Dark Matter-Electron Scattering Here we provide a few supplementary details regarding the DM-electron elastic scatteringcross section. We consider the process χ ( p ) + e ( p ) → χ ( p ) + e ( p ) . (A1)28he kinematics in the lab frame is described by the following four-momenta: p = ( E, , , p ) , p = ( m e , , , , p = ( E χ , k χ s χ , , k χ c χ ) , p = ( E e , k e s e , , k e c e ) , (A2)where s χ,e = sin θ χ,e and c χ,e = cos θ χ,e . The 4-momentum transfer is q = p − p = p − p .The Mandelstam variables can be written in terms of the outgoing electron energy as s = m χ + m e + 2 m e E ,t = 2 m e − m e E e ,u = m χ − m e − m e E + 2 m e E e . (A3)The differential cross section with respect to the outgoing electron energy is dσdE e = |M| πm e p . (A4)In terms of the Mandelstam variables, the squared amplitudes, averaged over initial spinsand summed over final spins, for the complex scalar and Majorana DM models are |M| = 16 π (cid:15) αα D ( t − m A (cid:48) ) × [( s − u ) + 4 m χ t − t ] (complex scalar DM) , s + u − m e ( s − t + u ) − m χ +2 m e − m χ m e ] (Majorana DM) . (A5)Combining Eqs. (A3), (A4), and (A5), we obtain the formulae given in Eqs. 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