Directionality preservation of nuclear recoils in an emulsion detector for directional dark matter search
A. Alexandrov, G. De Lellis, A. Di Crescenzo, A. Golovatiuk, V. Tioukov
PPrepared for submission to JCAP
Directionality preservation ofnuclear recoils in an emulsiondetector for directional dark mattersearch
A. Alexandrov, a,b,c,d, G. De Lellis, a,b
A. Di Crescenzo, a,b
A.Golovatiuk a,b and V. Tioukov a a I.N.F.N. sezione di Napoli, I-80126 Napoli, Italy b Università degli Studi di Napoli Federico II, I-80126 Napoli, Italy c National University of Science and Technology MISIS, RUS-119049 Moscow, Russia d Lebedev Physical Institute of the Russian Academy of Sciences, RUS-119991 Moscow, Rus-siaE-mail: [email protected], [email protected],[email protected], [email protected], [email protected]
Abstract.
Nuclear emulsion is a well-known detector type proposed also for the directionaldetection of dark matter. In this paper, we study one of the most important properties ofdirection-sensitive detectors: the preservation by nuclear recoils of the direction of impingingdark matter particles. It is for the first time it is studied in details for nuclear emulsiondetectors. We use the SRIM simulation and a realistic nuclear recoil energy distributionincluding all possible recoil atom types. Moreover, for the first time we study the granularityeffect on the emulsion detector directional performance. As well as we compare nuclearemulsion with other directional detectors: in terms of direction preservation nuclear emulsionoutperforms the other detectors for WIMP masses above 100 GeV/c . Corresponding author. a r X i v : . [ a s t r o - ph . I M ] M a r ontents Directional detection of dark matter (DM) is the strategy pursued by both new and someexisting experiments in the design of next-generation detectors [1, 2]. Based on the expectedanisotropy of the signal from the DM, this strategy offers a unique opportunity to identifyinteractions of so-called Weakly Interacting Massive Particles (WIMP) reliably even in thepresence of unrecoverable background events. The main objectives of a direction-sensitivedetector are both to measure the released energy and to reconstruct the direction of motionof the recoil nucleus after a WIMP scattering. Therefore, the direction-preserving propertyof the detector becomes extremely important as it is directly connected with its performance.In order to reconstruct nuclear recoil tracks, the spatial resolution and the granularityof the detector should be smaller than the track length, which, in turn, depends on thetransferred energy and density of the target material. For example, in solids the mean tracklength of a recoil nucleus with an energy of few tens keV is of the order of few hundredsnm. At present, such spatial resolution is achievable only with nuclear emulsions used by theNEWSdm experiment [3]. Therefore, most directional-detection experiments make use of alow-pressure ( ∼ scintillator crystals was reported in ref. [6], where the simulation isnot sufficiently detailed and is misleading. Their analysis considered only one recoiling atomspecies per detector type for all WIMP masses. Moreover, if the choice of recoiling atomsmade in ref. [6] can be justified for light WIMPs, when the energy transfer to lighter atomsis more efficient, this is not the case for heavier WIMPs where the contribution from heavy– 1 –toms in emulsion becomes rapidly dominant and must be taken into account. Therefore, asit will be shown later in this paper, the analysis carried out in ref. [6] significantly under-estimates the directionality preservation property of nuclear emulsion, especially for heavyWIMPs.With this paper we fix that flaw by generating the realistic energy spectrum for all recoil-ing atom types for each WIMP mass considered. Combining all possible recoiling atom typeswith realistic energies, we provide the correct evaluation of nuclear emulsion performance asa directional-sensitive DM detector. We focus our study to WIMP masses in the range from10 to 1000 GeV/c , which is the most popular mass range according to the concept of WIMP. The nuclear emulsion [7] is composed of tiny silver bromide (AgBr) crystals immersed ina gelatine binder. The crystals act as sensors that are activated by the ionization loss ofa passing-through charged particle. The activated state of the crystals is preserved untilthe emulsion film is chemically developed. Thus, a particle track is recorded, first as asequence of activated crystals, which later, after the development, becomes a sequence ofsilver nanoparticles, called grains. These grains have the form of randomly oriented filamentswith typical dimensions equal to several tens of nanometers, depending on the emulsion type.Two new emulsion types with nanometric crystals [8] were designed on purpose, fordirectional DM search. The first type, called the Nano-Imaging Tracker (NIT), has crystalsize of about 44 nm with the average distance between crystals equal to 71 nm. The secondemulsion type is called the Ultra-NIT (UNIT) and has crystal size and average distanceequal to 25 nm and 40 nm, respectively. The average distance between crystals defines thegranularity of the emulsion detector and, hence, the minimal track length with measurabledirection.
The readout of nuclear emulsions is typically done by means of optical microscopes. Forlarge emulsion detector experiments that could contain tons of nuclear emulsion, for exampleOPERA [9, 10], special robotized microscopes are built [11, 12] and novel scanning techniquesare designed [13, 14] for automatization and acceleration of the emulsion readout.Due to the so-called diffraction limit in optics, tracks shorter than 200 nm are not ac-cessible with conventional optical microscopes. Therefore, a special super-resolution imagingtechnique and a dedicated robotized optical microscope are designed to readout from NIT andUNIT emulsions [15, 16]. The effective resolution of the existing super-resolution microscopeis about 80 nm, comparable to the granularity of the NIT emulsion. For the 3-dimensionalreconstruction of recoil tracks the NEWSdm collaboration has designed a 3D super-resolutionmicroscope [17]. The next generation of the super-resolution microscope is now under designand will have the resolution comparable to the granularity of the UNIT emulsion.
In our study we derived the event rate for WIMP recoils following the approach similar torefs. [18–20] with more explicit derivation of angular spectrum for recoiled ions. Following– 2 – igure 1 . Individual contributions from different recoiling atoms in emulsion to track lengthdistributions for WIMP masses equal to 10 (top), 15 (middle) and 1000 (bottom) GeV/c . The plotsare normalized to the expected event rate for the corresponding WIMP mass. the notations of ref. [18] the analytical expression for the spectrum can be written as: d RdE d cos θ = R N esc E r (cid:20) exp (cid:18) ( v n − v E cos θ ) v (cid:19) − exp (cid:18) − v esc v (cid:19)(cid:21) × F ( qr n ) (2.1)where v , v E and v esc are, respectively, WIMP velocity dispersion, Earth’s velocity relativeto the Halo and Galactic escape velocity, E and θ are energy and angle of the recoiled ion,respectively, and F ( qr n ) is the nuclear form-factor (defined below in eq. (2.2)). v n = v (cid:112) E/E r, q = (cid:112) M T EE = M W v / , r = 4 M W M T ( M W + M T ) N esc = erf (cid:20) v esc v (cid:21) + 2 √ π v esc v exp (cid:20) − v esc v (cid:21) where M W and M T are WIMP and target-ion masses, respectively, v n is the nuclei velocityafter the recoil and E corresponds to mean kinetic energy of the WIMP.– 3 – igure 2 . Individual contributions from different recoiling atoms in emulsion to cos θ (left column)and weighted - cos θ (right column) distributions in case of WIMP masses equal to 10 (top row), 15(center row) and 1000 (bottom row) GeV/c .The plots are normalized to the expected event rate forthe corresponding WIMP mass. We are using the parameters of the Standard Halo Model and Earth velocity from refs. [21, 22]: v = 220 km s − ; v E = 232 km s − ; v esc = 544 m s − ; ρ = 0 . GeV c − cm − Together with numerical expressions from ref. [18] and updated Dark Matter parameters: R = 2 √ π N A A ρ M W σ v = 361 M W M T (cid:16) σ − cm (cid:17) (cid:16) ρ . GeV c − cm − (cid:17) (cid:18) v km s − (cid:19) kg − d − E r = 2 v M W M T ( M W + M T ) = (cid:18) M W GeV c − (cid:19) (cid:18) v km s − (cid:19) M W M T ( M W + M T ) × . keVwhere A is the recoiled ion atomic number, N A is Avogadro number and ρ is local DarkMatter density.The cross-section with the nucleus σ and with single-nucleon σ n cross-section for spin-independent interactions are related by the following formula: σ = σ n A µ WT µ Wn – 4 –on E max (keV) Ion E max (keV)H 12.4 Zn 717.9C 145.2 Br 855.4N 168.7 Ag 1100.8O 192 I 1254.3F 224.5 W 1656.2 Table 1 . The highest energies for ions used in SRIM simulations where µ WT and µ Wn are the WIMP-target and WIMP-nucleon reduced masses.The Helm nuclear form factor approximation suggested in ref. [18]: F ( qr n ) = 3 sin( qr n ) − qr n cos( qr n )( qr n ) e − ( qs ) / (2.2) r n = c + π a − s ; c = 1 . A / − . fm ; a = 0 . fm ; s = 0 . fm.We are using eq. (2.1) to calculate spectra for ions in different detectors for the WIMPmasses between 10 GeV/c and 1000 GeV/c . For the comparison between detector types, similar datasets for the same WIMP masses weregenerated for emulsion, LPG and crystal detectors. All possible recoil atom types and therealistic energy spectrum corresponding to each detector type were considered.Detector compositions and densities for LPG and crystal detectors are taken from ref. [6]while for the emulsion they are taken from ref. [8], namely:•
LPG detector : CF + CHF + C H gas mixture with the density of1.72 · − g/cm . Atomic fraction: H(0.0927), C(0.2046), F(0.7027).• Crystal scintillators : ZnWO with the density of 7.87 g/cm . Atomic fraction:Zn(0.167), O(0.666), W(0.167).• NIT and UNIT emulsion : the density is 3.44 g/cm and atomic fraction: H(0.41),C(0.214), N(0.049), O(0.117), Br(0.101), Ag(0.105), I(0.004). We perform the simulation in two steps:• Generating ions of fixed initial energy and angle in the corresponding detector for binsin the energy-angle grid.• Using the energy and angular spectrum from eq. (2.1) to weigh the contribution of theions in specific bins to the resulting distribution.The bins for energy-angles grid are defined for each ion as energies from 0 keV to E max - maximum recoil energy produced by 1000 GeV/c WIMP, for which eq. (2.1) becomes zero,and angles from 0 to π/ . The highest energies for each recoil atom type are shown intable 1. The weigh for each energy-angle bin is calculated as a ratio of the differential recoilrate from eq. (2.1) times bin size (∆ E ∆ θ ) the full WIMP rate of a specific WIMP mass inthe corresponding detector. – 5 – igure 3 . W eighted - cos θ mean values as a function of the WIMP mass for LPG (blue diamonds),crystal (red triangles) and emulsion (green squares) detectors. The recent comparison of the simulation with the experimental data can be found in ref. [16],where the endpoint of the simulated recoil track length distribution for C ions with energy of60 keV showed a good agreement with the measured one.
We have simulated several datasets for WIMP masses ranging from 10 to 1000 GeV/c . Foreach dataset the recoil angle θ , its cosine and the energy-weighted cosine distribution D ,introduced in ref. [6], were calculated. Similarly to ref. [6], θ is defined as the angle betweenthe line connecting the initial and the stopping points of the track and its initial direction.The energy-weighted cos θ distribution is referred to as the "Figure of Merit" in ref. [6].However, for the current analysis we prefer to call it the " weighted - cos θ distribution D ". Forcalculation we use the same formula defined in ref. [6] and for convenience we report it alsohere: D = (cid:80) N collisions i =0 ∆ E i cos θ i (cid:80) N collisions i =0 ∆ E i = (cid:104) ∆ E cos θ (cid:105) track (cid:104) ∆ E (cid:105) track where θ i is the angle between the direction of the initial recoil and the line joining twosubsequent interaction points i and i + 1 (i.e. the direction after the i -th collision); ∆ E i is the energy deposited by the recoil between i and i + 1 ; N collisions is total number ofinteractions/collisions. Individual contribution from each recoiling atom type in emulsion to the track length, cos θ and weighted - cos θ distributions for WIMP masses ranging from 10 to 1000 GeV/c areshown in figure 1 and figure 2. The plots are normalized to the expected event rate for thecorresponding WIMP mass. As expected, the contribution from heavy Ag and Br atomsgrows rapidly with the WIMP mass and is not negligible already for WIMP masses around 10– 6 – igure 4 . Intrinsic distributions for cos θ (left column) and weighted - cos θ (right column) of LPG(blue line), crystal (red line) and emulsion (green line) detectors for WIMP masses equal to 10 (toprow), 25 (middle row) and 1000 (bottom row) GeV/c . The plots are normalized to the expectedevent rate for the corresponding WIMP mass and detector. GeV/c . For WIMPs heavier than 15 GeV/c their contribution rapidly becomes dominant.Being the heaviest atoms in the emulsion mixture, Ag and Br scatter less than C, N and Oand the emulsion performance noticeably improves as the WIMP mass grows. In this paragraph we introduce the intrinsic detector performance, i.e. the ideal performanceachievable on the basis of its nuclear composition, without accounting for the granularityof the detector. The dependency of mean values of the intrinsic weighted - cos θ on WIMPmasses ranging from 10 to 1000 GeV/c is plotted in figure 3. The comparison of intrinsic weighted - cos θ and angular distributions for WIMP masses equal 10, 25 and 1000 GeV/c isshown in figure 4. As expected, the LPG detector has the best performance at WIMP massaround 10 GeV/c . However, at higher WIMP masses both emulsion and crystal detectorsrapidly fill the gap and supersede it, as the relative contribution from heavy atoms increases.Above 25 GeV/c the intrinsic mean weighted - cos θ of the emulsion detector is about 5-7%higher than that of both the LPG and crystal detectors, making the emulsion detector anexcellent choice for the directional WIMP detection in that mass range.– 7 – igure 5 . Recoil track length (left column) and cos θ (right column) distributions in NIT emulsionfor WIMP masses equal to 10 GeV/c (top row), 39 GeV/c (middle row) and 1000 GeV/c (bottomrow). The plots are normalized to the event rate for the corresponding WIMP mass. In order to be reconstructed in emulsion the recoiling ions must encounter at least two AgBrcrystal while travelling in an emulsion detector and release inside them the amount of energysufficient for activation. We approximate the nuclear emulsion as a "crystal field": a 3Dvolume randomly filled with crystals with average center-to-center distance equal to 71 ± ± ± ± igure 6 . Recoil track length (left column) and cos θ (right column) distributions in UNIT emulsionfor WIMP masses equal to 10 GeV/c (top row), 25 GeV/c (middle row) and 1000 GeV/c (bottomrow). The plots are normalized to the event rate for the corresponding WIMP mass. that the most of recoiling ions produce latent images in only two crystals and, therefore, the weighted - cos θ distribution becomes equal to the cos θ one.The granularity effect reduces the performance of both NIT and UNIT emulsion detectorsdue to a suppression of the contribution from heavy Ag and Br atoms, whose ranges are, onaverage, shorter than those of lighter C, N and O atoms. As it can be seen from figure 7,the directionality preservation performance of the NIT emulsion is less than 5% lower thanthe intrinsic one of the LPG for WIMP masses above 100 GeV/c , while the UNIT slightlysupersedes the LPG in the same mass range. Application of emulsions with granularitiesfiner than 40 nm will further improve the directionality preservation property of emulsion bypushing it closer to the intrinsic limit. In the presented study we have analyzed the directionality preservation properties for differentdetector types: LPG, ZnWO scintillator crystals and nuclear emulsions. The developedSRIM-based simulation considers all possible recoil atom types and takes into account the– 9 – igure 7 . Realistic distribution of mean values of cos θ for NIT (orange crosses) and UNIT (violetcircles) emulsions. Also shown for comparison intrinsic distributions of mean values of weighted - cos θ for emulsion (green squares), crystal (red triangles) and LPG (blue diamonds) detectors. realistic recoil energy spectrum for WIMPs with masses in the range from 10 to 1000 GeV/c .Our simulation shows that the LPG performance is almost flat in the considered WIMP massrange. Indeed, the gas mixture contains only light atoms of similar masses and, therefore, theirrelative contribution does not change much with the WIMP mass. On the contrary, nuclearemulsion contains a large amount of heavy Ag and Br atoms. At low WIMP masses the majorcontribution into the detected signal comes from light C, N and O atoms. Naturally, beingthe lightest in the mixture they suffer from stronger scattering. However, the contributionfrom Ag and Br rapidly becomes dominant and notably improves the emulsion performance.Disregarding this fact in ref. [6] resulted in significant underestimation of emulsion capabilitiesespecially for heavy WIMPs. With the presented detailed analysis we demonstrate that interms of intrinsic directionality preservation, if granularity effects are not considered, nuclearemulsion outperforms other detector types for directional DM search in the WIMP mass rangeabove 15 GeV/c .The random crystal field model enabled consideration of the granularity effect and theestimation of realistic performances of the existing emulsion detectors. Both NIT and UNITperformances show some drop at low WIMP masses due to the suppression of the contributionfrom heavy ions. Nevertheless, they show excellent performance at higher WIMP masses,comparable to the ideal intrinsic performances of both LPG and ZnWO detectors. Takinginto account that the realistic performances of the latter detectors are expected to be worse,the UNIT emulsion appears to be the best choice for the directional detection of WIMPswith masses higher than 100 GeV/c . Production of emulsions with granularity finer than 40nm is possible and can further improve the directional preservation performance of emulsiondetectors pushing it closer to the intrinsic limit. Another important advantage of a nuclearemulsion detector is that, being solid-state, it can be easily scaled to larger masses in acompact volume without major safety implications and it requires minimum instrumentationfor long and stable operation. – 10 – cknowledgments This work is supported by a Marie Sklodowska-Curie Innovative Training Network Fellow-ship of the European Commissions Horizon 2020 Programme under contract number 765710INSIGHTS.
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