Jhep06(2017)087

JHEP06(2017)087 Springer June 9, 2017 May 27, 2017 June 16, 2017 : : March 15, 2017 : : and a , Revised Accepted Published Received , Tomer Volansky a,c Published for SISSA by https://doi.org/10.1007/JHEP06(2017)087 [email protected] , Kohsaku Tobioka, b [email protected] , . 3 1608.02123 Rouven Essig, The Authors. a b c Dark matter, Dark Matter and Double Beta Decay (experiments)

We consider the absorption by bound electrons of dark matter in the form of , [email protected] Department of Particle PhysicsRehovot and 7610001, Astrophysics, Israel Weizmann Institute ofE-mail: Science, [email protected] [email protected] Raymond and Beverly SacklerTel-Aviv School 69978, of Israel Physics andC.N. Astronomy, Tel-Aviv Yang University, Institute forStony Theoretical Physics, Brook, Stony NY Brook 11794-3800, University, U.S.A. b c a Open Access Article funded by SCOAP photons from the sun.sensitivity For to all dark-sector cases, particles. direct-detection experiments can have unprecedented Keywords: ArXiv ePrint: like particles, thedirect-detection same constraints current but does direction not boundcooling detection new bounds. data parameter space improves However, beyond projected knownusing on stellar sensitivities germanium previously of can known the gopossible upcoming beyond hints SuperCDMS from these SNOLAB the and white even dwarf probe luminosity parameter function. space We consistent find similar with results for dark new bounds based on datadisfavor from previously allowed XENON100 parameter and space. CDMSlite. Moreover,SuperCDMS we We at derive find sensitivity SNOLAB these projections for experiments for silicon to experiments and with germanium scintillating targets, targets (cesium as iodide, wellThe sodium as projected iodide, for and various sensitivity gallium possible arsenide). can probe large new regions of parameter space. For axion- Abstract: dark photons and axion-like particles,and next-generation as direct well detection as experiments. ofcan Experiments dark sensitive detect photons to such from electron recoils particles thephoton Sun, with dark in masses matter, current between we a update few a eV previous to bound more based than on 10 keV. XENON10 For data dark and derive Itay M. Bloch, Tien-Tien Yu Searching for dark absorption withexperiments direct detection JHEP06(2017)087 ]. ]. 2 11 15 , 14 absorbed 14 ]. ]. However, it is entirely 1 13 – 3 6 – 1 – 5 5 4 7 4 9 14 3 is the axion decay constant and indicates the scale at which the 7 a 4 f 1 ] symmetry is broken. More generally, the spontaneous breaking of any 16 production 0 A , where a /f A µ The axion was originally introduced as a solution to the strong CP problem [ Many DM candidates exist, with Weakly Interacting Massive Particles (WIMPs) being 4.1 Signal region 4.2 Current experiments 4.3 Future experiments 2.1 ALPs as2.2 dark matter ALPs from the Sun 3.1 Dark photons3.2 as dark matter Dark photons from the Sun aJ µ detection experiments. For other types of searches see e.g.This [ pseudoscalar may∂ couple in aPeccei-Quinn model-dependent [ manner to the SM axial current, the most studied. Numerousof direct-detection WIMPs experiments (and probe forplausible other the that DM DM elastic is candidates) scattering composedin off of a ordinary a material, (pseudo)scalar matter thereby oraxions, depositing [ a axion-like its vector particles full boson (ALPs), kinetic thatThis and and can paper dark be rest-mass focuses photons energy. on the can DM search have in of this such the DM property, form candidates see with of e.g. existing and [ upcoming direct- Significant experimental evidence and theoreticalModel considerations suggest (SM) that of the particle Standard for physics the is existence incomplete. of darkof In matter the particular, (DM). most there Determining important is the problems identity compelling in of evidence particle the physics DM today. particle is one 1 Introduction 5 Results A Rates for ALPs and darkB photons in Solar various materials 4 Analysis of current and future experiments 3 Dark photons Contents 1 Introduction 2 Axion-like particles JHEP06(2017)087 ]), itself 42 s may , 0 0 A ] and on A 41 ], EDEL- ] sets the 38 20 40 ]. Numerous 18 , 17 ], DAMIC [ ], CDMS [ 40 19 (20) electrons [ ]. In this case, relic ]. We revisit the latter limit O 34 35 – 32 ]. DM scattering off electrons is one 36 ]. Significant ongoing experimental effort ] allows them to probe the lowest electron ]. We derive new direct-detection bounds 28 37 (eV) and having a reduced background. A – 35 ], in the future. Moreover, while beyond the ]. Here we show that other existing data can O 24 50 23 – 2 – is a massive vector boson that can couple weakly 0 A DM masses. ]. An intriguing possibility, however, is that the 0 ]. Not only does this probe sub-GeV DM scattering, but 31 . The A 0 – (GeV), requiring sensitivity to nuclear recoil energies above 36 ], and KIMS [ A O 29 22 ]. Below we study the prospects of such experiments to detect or s. Superconducting targets may probe even lower masses, either by 0 ] or DM absorption [ 47 ]. We show that this data improves constraints on sub-keV ALPs and A – 49 39 , , see e.g. [ 0 43 , 48 A 36 ], XENON100 [ (few eV). The sensitivity gained by developing ultra-sensitive detectors able to 21 O Future experiments are expected to achieve improved sensitivity to even lower DM XENON10’s sensitivity to single electrons [ We focus on the sensitivity gain achieved when lowering the threshold of direct- Another simple DM candidate, present in many extensions of the SM, is the dark DM. We also show that a CDMSlite dataset sensitive to DM as light as the xenon ionization energy of 12.1 eV [ (keV). However, many viable DM candidates have masses well below the GeV-scale, 0 0 scintillators, or two-dimensional targetsscattering has in been [ studied inconstrain the ALPs and context ofDM sub-GeV scattering DM [ scope of this paper, chemical-bond breaking could be used to probe nuclear recoils down strongest constraints for some masses by lowering thekey threshold to down this to improvementgaps is of the useprobe of one semiconductors or a or few scintillators, electrons which in have semiconductors band (e.g. SuperCDMS [ used to place a constraintA on DM as light asbelow. a More few MeV recently, the scattering XENON100or off electrons more experiment [ electrons published [ a searchA for events with four such technique suggested ina [ lower ionization threshold(nonrelativistic) translates DM. directly into a lower mass threshold forrecoil absorbing energies, but without distinguishing signal from background events. This data was detection experiments. Traditionally,WIMPs these with masses experiments above haveO been optimized towhich can probe only be probed with new techniques [ searches for an is sufficiently stable to playbe the absorbed role by of the ordinarystudies DM matter particle of in [ this direct-detection possibility experiments,that just were are like presented more an in constraining ALP. [ than Initial existing limits, and provide projected sensitivities. WEISS [ improve on these boundsfuture and experiments could provide go projections beyond for the strong future stellar experiments. constraints. photon, which We we find denote that as to ordinary matter through kinetic mixing [ with a similar interaction.a target This material, interactiontrons, rather allows known the than as the axion scattering axioelectric ordirect-detection off effect, experiments ALP has it. have been to conducted originally be The suggestedthe searches in absorbed assuming galactic case [ that in DM of the or absorption ALP is constitutes in produced bound in the elec- Sun, including CoGeNT [ global symmetry combined with a small explicit breaking can lead to low-mass ALPs JHEP06(2017)087 , ]. is a 53 17 , (2.2) (2.1) n 2 . More- a f , where a and v ]. We infer that a AE m 18 σ can be absorbed in , a , and decay constant, n , a 17 aee , g m 2 3 / 2 a e . v 5 1 3 . The absorption spectrum is ¯ eγ a Handbook of Optical Constants − a v 1 aee ig 2 e 2 E m + 2 a ] and the EM 2 a 2 aee m g 56 πα . We show existing bounds and projections in , 1 2 4 a , may be related to the photoelectric absorption keV energies, no gain is achieved by experiments – 3 – 55 3 4 − /f ∼ ) AE e a σ E µ m ( ], for energies above 30 eV. Below 30 eV, we use the (50%) exist between different theoretical predictions a∂ O PE 61 = 2 µ σ ]. ∂ 1 2 ' 60 aee – g a = v ) 57 a E L ( AE σ 300 eV. The main sources of theory uncertainties arise from approxi- ) from Henke et al. [ parameter space. ∼ E ], while superfluid helium could probe nuclear recoils down to keV [ , as ( a are the ALP’s energy and velocity, respectively [ ]. Discrepancies of m PE PE a 52 , σ v 60 σ – 51 57 ) below [ and versus E ( E ]. In analogy to the photoelectric effect, axions may be absorbed by bound electrons, aee PE We take The ALP absorption cross section, The ALP interaction with electrons is responsible for the “axioelectric” effect [ Finally, axions, ALPs, and dark photons may exist without constituting a significant g σ 54 and the two are related by , . More generally, however, ALPs may be described by independent a a of Solids for mating the correlation betweenare different electrons. favored by We experimental usemeasurements data the compiled [ Henke in calculations, [ which where the rate of absorptionthe of ALP non-relativistic number ALP density) DMthus has very on negligible narrow, an helping dependence electron to on ( differentiate signal from background. cross section, the 18 ionizing them.therefore Direct offer detection an experiments opportunity to search, search in for ALPs part, via for their coupling ionized to electrons electrons. and In the absence off additional couplings, the model dependence in The original “QCD” axion hasf a strict relation betweenover, its ALPs mass, have model-dependent couplinginterested to here gluons, in photons, possible and interactions SM with fermions. electrons, defined We minimally are by are dominantly produced in the Sunlowering with their threshold. Instead,low energies, we so focus that on lower dark thresholds could photons, potentially which probe are beyond produced existing also constraints. 2 at Axion-like particles These would probe different couplings from the models consideredfraction here. of the DM energyand density. can If sufficiently again light, befrom they existing absorbed would experiments be in and produced direct-detection provide in projections the experiments. for Sun upcoming We experiments. will Since discuss ALPs constraints to 10 MeV [ JHEP06(2017)087 ], aee 39 g that (3.1) (2.3) (keV) ] only D O 22 100 ton- & ]. Limits on eV for it to be cold , 18 , . , 17 0 µ PE bn σ A µ 0 A 0 ]. However, the solar ALP flux a 2 A ], although exposures m 22 keV m 65 ]. At low energies, this mixing is 1 2 . 3 25 + , 2 aee A g cm 0 µν 24 1 / ]. The more recent S2-only analysis [ F − 22 µν F day 1 – 4 – 4 GeV 2 . − − eV. Non-thermal production through defects may kg eV. = 0 µ 0 µν . (keV) energies. 19 F 20 O DM 10 ρ µν . 0 × F 9 . 1 4 and the SM photon. The relevant interactions are 0 = 1 A L ⊃ − ALPs R ] and is largest at ]). By tuning the initial misalignment angle or through late-time entropy 64 ]. Future xenon-based experiments can improve on these limits due to their 63 , 22 62 is a hypothetical massive vector boson of a broken (dark) gauge group U(1) 0 A Solar ALPs can be detected in direct-detection experiments [ ALPs could obtain the correct relic density in a wider mass range, via the misalignment The may kinetically mix withdominantly between the the SM hypercharge [ energies. Since thisexperiments, paper we is do focused not on present the discussing solar the ALP potential limits. gain from3 low-threshold Dark photons found in [ large exposures and low expectedyears backgrounds (see are e.g. required [ toexperimental probe threshold beyond without white-dwarf a coolingprovides a significant limits). negligible gain increase Conversely, in in lowering sensitivity due exposure the to over the rapidly XENON100 falling solar [ flux below scintillation) trigger with awhich 2 searched keV for threshold events with [ antal ionization-only threshold (S2) and signal, has is adrops a much rapidly larger lower at experimen- dataset low than energies,due that while to used the the S2-only in lower analysis threshold. [ includes Therefore, more the background S2-only events dataset produces a weaker bound than Independent of their reliccalculated density, ALPs in [ may be produced in the Sun.versus The the flux ALP has mass been havethe been strongest published of by which several is direct the detection XENON100 experiments, collaboration among analysis that used an S1 (primary for a local DM energy density of 2.2 ALPs from the Sun DM. Hot axions also require masses mechanism, or by thermalALPs or without non-thermal assuming production. aelectrons It specific is is production thus mechanism. interesting to The constrain ALP absorption rate on Axions and ALPs may playor the through the role misalignment of mechanism and DM.see the The decay e.g. QCD of [ cosmological axion defects isdumping, (for produced a axion review either DM thermally hasallow masses for heavier axions; quite generally though, its mass must be 2.1 ALPs as dark matter JHEP06(2017)087 in 0 (3.6) (3.4) (3.5) (3.2) (3.3) A to electrons. We ]. The detection of e DM can be modeled decay lifetime can be . is the SM photon field 0 0 67 , A is broken spontaneously A . µν T,L µ 66 ) , D are the transverse (T) and F 0 100 eV, the rate for xenon , ) A , 0 fi ] . A Lν i DM, the absorption rates are DM detection, but important m T,L PE 0 0 µ 0 m em σ A = A Lµ A eJ = to constitute all the DM. Various m [ , E L 0 ( E L ]. , mass, and A ( T,L 0 T PE 0 + Π σ PE Π 68 A 2 A , 2 σ 0.2–2.0 (1.0–1.15, 1.0–1.8). T ν i 2 ω − s from the Sun [ in the detector frame is 0 66 0 m Im Π 0 ∼ × A 2 A A ' T µ i 0 ]. The absorption of is the 2 T,L m 0 A 0 DM 34 T – 5 – A A − m DM, but here the in-medium effects of the – ρ v ]. The resulting absorption rate is given by (for = 0 m ) 2 0 32 ' A = Π A ) = i f m 100 eV, although for detect T,L ν em = → Γ & ,J 0 i below twice the electron mass, the absorption in a medium is 0 A 0 µ 0 em A + E A J A ( m h 0 m 2 A 0 T,L e σ can have two origins: a mass, Stückelberg which predicts no addi- A ( Rate per atom 0 and absorption cross-section in terms of A M 0 ) m 10% for 3 A . from the Sun. For the latter, we only consider a mass. Stückelberg 0 s is analogous to that of A denote the initial and final electron state and Π 0 A f is the dark photon velocity [ 0 4 GeV/cm . is the kinetic-mixing parameter, A s, so we discuss them in the next subsection. For 0 v and A i = 0 The matrix element for We include in-medium effects. These are especially important for the detection of DM which encode thetransverse correlation and function longitudinal modes inside of the a solar medium. The absorption rate of the Here longitudinal (L) in-medium polarization functions defined by these solar the Sun may significantlycase, affect and production summarize the and effect detection. as described We in focus [ on the Stückelberg affected only by (germanium, silicon) is changed by a factor of 3.2 Dark photons fromDirect detection the experiments Sun are sensitive to solar can then write the where ρ For sufficiently small longer than the age ofproduction the mechanisms Universe, exist, allowing see foras e.g. the the [ absorption of a massive non-relativistic particle with coupling strength. The mass tional degrees of freedom, orby a an Higgs mechanism, extra where Higgs the field.for U(1) detecting This distinction is irrelevant for 3.1 Dark photons as dark matter where JHEP06(2017)087 ]. 35 (3.7) (3.8) (3.9) (3.11) (3.10) m. The 15 − 10 , above 30 eV and × 1 , one has f ] in figure 3 of [ 82 . refr , s using existing data 0 refr ) n m is Sun’s radius. We detect L n A ] has 8 Γ DM absorption depends 2 refr . ) = 2 L 56 0 n 10 , 2 2 Φ c . A dω ) e − d × is the wavelength of a photon ) ,V L , A m 2 T + ( 96 )(1 ], and how we derive projections . / if prod T,L 2 c/ω 2 | dωdV Γ 40 ~ e ~q + d π = 6 detect T A 1 2 − | Γ

f ( 2 + (Im Π = 2 0 T πr R A ω 2 4 A 4 Φ λ dω ) n ] The database [ d , m L dr , 2 = ( A A

T 56 , X L R 2 0 Br – 6 – Π 55 0 λ Z 2 A 0 Re Π π 2 r , 2 m ) 1 − ], and CDMSlite [ πd 0 − − ω 4 39 2 refr 2 A 2 n m = ω ( = 1 − for energies below 30 eV, we use Re[ q = are given in [ T,L (1 refr 2 Xe dω 2 1 Φ n , VT f ω 4-momentum, with 1 d 2 T,L f 0 = = is the classical electron radius, A T 0 r Π ], XENON100 [ events dω 37 dN ) is the , and ω are the detector’s ﬁducial volume and exposure time, respectively. The ratio ω, ~q = 1 AU is the Earth-Sun distance and denotes the density of atoms of type = (

V,T d A q n eV DM masses. The low-mass reach of an experiment for ALP DM or The flux of solar dark photons is given by above 10 eV. To obtain ∼ 2 on the type of12.1 eV, material while used semiconductor- as orlower a scintillator-based by target. experiments about have an Xenon-based a orderto of band targets magnitude, gap, have allowing which a such is experiments low-mass to reach lower sensitivity of down 4 Analysis of current andIn future this experiments section, wefrom describe XENON10 how [ wefor derive possible bounds future on experiments. ALPs and where of the ionization ratespectrum to has the a absorption sharp rate, riselongitudinal Br, at mode. is the unity mass for threshold the because energies of the of resonant interest. production The of the consider the resonant production ofdominant the component transverse and of longitudinal the modes, flux. which gives The the spectrum of the total number of events is where Here with energy atomic scattering factors f where For an isotropic and non-magnetic material with a refractive index where the effective mixing angle is JHEP06(2017)087 0 0 A A m 1 eV) . 12 > 2 photoelectrons (PE), . 6 )). Note that the atomic 80 electrons, without taking 2.2 0 . ≤ 27 ]. ∼ 38 30 eV), where the bound is in reality − 15 ]. In the latter two, the signal was required to ∼ – 7 – 35 DM [ ]. We also show (in blue) a hypothetical DM ALP/ (the ‘primary’ electron) is ejected from the atom, and 0 (top), we reproduce the spectrum of events (orange 0 37 A 1 A ]. Each electron produces signal, we use a slightly simpler procedure, since the signal ], and 0 38 A 66 [ number of observed S2 events with 0 A ]. Previous work used these data to derive conservative bounds on sub- ], the data has already been converted from the number of PEs to the total 37 37 the XENON10 experiment uses xenon as the target material and presented ], solar 38 2 electrons. For single electrons, the efficiency is only about 0.5, and we require the We estimate below, either directly from the experimental data or from theoretical resolution. In [ number of electrons.histogram) In shown in figure figure 2signal, of [ with the(100 normalization eV chosen and 1100 at eV). the The pink 90% and C.L. magenta limit, gaussian lines at show two the different signal shape masses that ≥ signal event rate to be lessThe than number of 23.4 secondary events/kg/day ionization [ electronsmodel is it challenging to as calculate discussed precisely,which in but we [ are the actual signal seen by the XENON10 detector and defines the detector GeV DM [ be less than the into account spectral information.stringent Here bounds, we except use nearslightly the weaker. threshold spectral We ( information take the to signal place efficiency more times acceptance to be 0.92 for events with XENON10: results using 15 kg-days ofsingle data electron [ with an S2 (ionization signal) trigger threshold set to a 4.2 Current experiments We consider the following existing datasets: • the signal to beThe less energy than range the we dataand can at by use the 90% is band C.L. limiteddata gap in for by for the NaI the the resulting does ionization other (smeared) not threshold materials energy extend in (see below range. xenon 30 below eV, ( eq. and ( so we do not go below 30 eV. expectations, the variance and detectorand resolution smear (adding the them theoretical in spectruma quadrature accordingly. single if To derive needed), bin a90% containing conservative limit, C.L.. 95% we of choose Foris the the distributed solar signal over and aupwards) demand wider that that energy contains it 95% range: of is we the less first signal, than then calculate the smear the the data energy first range at and (from last bins, and require electrons produced fluctuates fromcan event be to predicted event.or in through a Their measurements. given variance Fordominates experiment, and a over average either the highly number detector by energetic resolution. primary modeling electron, the this secondary variance interactions usually To extract optimal limits, wethe need detector, to which take depends intoelectron not account that the only absorbs spectral on an shape the ALPits of detector or resulting the energy kinetic signal resolution. energy in (total Inwhich minus particular, binding) can an is lead converted to to ionizing several additional atoms, additional (‘secondary’) electrons. The number of secondary 4.1 Signal region JHEP06(2017)087 0 s 3 0 . A �� 0 �� A ). Top 9 . �� right �� ]( signal in blue =�� 39 0 �� A �·��=�� 3, with a width of 6 . 0 =�� 7 . �� ) and XENON100 [ , we show examples of solar � �·��=�� 2 left ]. The data listing the number of PE ]( � ) masses. The blue histogram shows the � 0 39

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�� A �� / ]. To derive a bound, we take the data from 40 – 8 – (bottom), where we bin the data in 1 PE bins. 1 �� ]. �� 69 =�� ·��=�� ]. Our signal calculation includes the acceptance and trigger efficiencies the XENON100 collaboration presented S2-only data with events down �� ] and apply all efficiencies and cuts (note that figure 3 is not corrected for the SuperCDMS collaboration reported results with a threshold of 56 eV 39 40 ]. As for XENON10 above, we show a hypothetical DM ALP/ �� =�� . Ionization (S2-only) data from XENON10 [ 39 �� ·��=�� ⨯�/� �� =19.7PE) on the top axis. Blue gaussian lines on each plot show two examples of the expected

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� � � � � � � from a low-threshold “CDMSlite” runfigure in 3 [ of [ the trigger efficiency).the We treat data the from energy tableresolution range I. and 56 eV–140 The fluctuations eV in total as the resolution a number single of of bin, the secondary taking signal electrons) (combining can the be experimental inferred from show, for the samelimit two DM when masses, varying the theas signal secondary discussed shape ionization above. that model. produces Thedata We the will bound derive worst be the on and presented bound sub-GeV best in DM on [ scattering solar CDMSlite: off electrons based on this for each event is reproducedThe mean in number figure of PEPE/electron generated by [ one electron isfrom 19 [ at two different masses (150 eV and 570 eV). The pink and magenta gaussian lines again varying the secondaryspectra. ionization model. Since the signalionization In spans modeling figure a should be wider small, energy and range, we theXENON100: do uncertainty not in include the the secondary to uncertainty. 80 PE, corresponding to about 4 electrons, in [ produces the worst and best limit, respectively, for the same two DM masses when � �� / • • signal shape in pink andtwo magenta DM that produces, masses respectively, when thegive varying worst the and the 90% best secondary C.L. limit upper ionization for bound the model. same times efficiency Numbers on next the to number the of blue signal events curves for those masses. plot shows the datathe number as of the photoelectrons (PE)(1e number on of the observed bottom electrons,observed axis and signal while the shape bottom corresponding forsignal plot number two of distribution shows different electrons the in DMsecondary data terms (ALP ionization as or of model produces the different number signal shapes of and electrons thus different produced limits. in We show the the detector. Varying the Figure 1 JHEP06(2017)087 ]. ) of 70 g (4.1) = 1 eV E , which 0 − A DM m DM m ) from the Sun 0 m A = g E ) and the longitudinal �� − e solid E , �� c e /ε �� =18.24 eV (30.68 eV, 101 eV) for ) σ g -decay (a flat background on a log- few kg-years, these are only relevant E β ��+�� . − e the next-generation SuperCDMS experi- and 200 eV. The spectrum of the E �� ( , �� b ω[��] 1 eV. . 100 , – 9 – . The kinetic energy ( g 50 = 1 + , E i �� ) e = 1 �� 0 E ( A 10 eV). Q m =�� h �� . � ]. Our projections assume the following backgrounds: 1 � 1 eV to a few keV), various x-ray lines produced by cosmogenic �� ∼ ω �� we use a preliminary estimate by the SuperCDMS collaboration in [ � � ) are shown for dashed . The normalized spectra of the total number of events for dark photons ( We assume that an electron inmust germanium be absorbs larger a than DM particlethis the of primary band mass electron gap is convertednumber into of additional electron-hole electron-hole pairs pairs. created The is mean total This estimate includes backgrounds fromlog tritium plot between activation, and solar neutrinos (for exposuresat of electron recoil energies Germanium: – ization signal as the previousachieve CDMSlite sensitivity versions. down Ultra-sensitive toband phonon single gap detectors electrons, may (0.67 eV allowing for thefor Ge, germanium threshold 1.1 (silicon) eV to [ for be Si). given by The the projected exposures are 20 (10) kg-years SuperCDMS SNOLAB HVment Ge will and be Si: deployedlarge at bias SNOLAB. A voltage high-voltage to (HV) achieve version the will same attempt Luke-Neganov-phonons to amplification use of a an ion- the mass ranges [56 eV, 160 eV] ([160 eV, 1.3 keV], [1.3 keV, 10.37 keV]). the observed electron capture peaks. Thus we adopt but assume zero detectorthat dark mimic counts, a i.e. signal. no spontaneous creation• of electron-hole pairs 4.3 Future experiments Future experiments are expectedDM to masses. have lower To thresholds, derive allowing projections, them we to take probe into lower account expected physics backgrounds, in a xenon detector.mode The alone combined ( transverse andcase longitudinal modes is cut ( off by the xenon ionization energy, 12 Figure 2 JHEP06(2017)087 , i F Q and h (4.3) (4.2) / e ε 2 Q σ -emitter. β ≡ ]. While ), and signal g F (1 keV) as an 10 keV, which 72 E , ee ], measurements . σ 71 71 down to the nearest y 13 [ . = 10 eV, although the t , and the fluctuations in σ t = 0 σ ]. We list F rounds . . i c , and use the values of i 74 ) y , ) g = 1 keV [eV] e e b 19.4 21.7 47.8 50.0 23.4 V e ε E e E 73 E ( ), band gap energy ( E ( [ e Q ε Q 1 1 + h h at ) in various semiconductors (Si, Ge) and = 100 F F ee i − b 4.2 + σ ) + V e b b t t = 10 eV, although the precise value is again E V V σ ( e σ e t q q σ Q h [eV] – 10 – q r 1.1 5.9 6.4 0.67 1.52 g e ' E ε = ee DM σ ee m σ ]. We take [eV] 2.9 3.6 4.2 = 1 is the electron’s charge. For DM absorption, where 17.7 19.2 e 75 200 eV would be desirable. We take ε e q Si is a relatively large contaminant and a low-energy ∼ 32 , the signal shape is dominated by the Fano factor. Q Si Ge CsI NaI GaAs , where Element b V e , this equation becomes is the variance. To calculate the width in the signal’s energy, we add in q is the bias voltage, so one electron-hole pair will produce a total phonon silicon does not have the same low-energy x-ray lines produced by cosmogenic is the mean energy per electron-hole pair and 2 Q b DM e (few) electrons are created. We set σ ε V m O ) at ionization energies of 1 keV from eq. ( at energies below for germanium (and other elements) in table ee . Mean energy to create an electron-hole pair ( = F σ g e activation. However, Together with tritium, thiswe produces take a to flat beperCDMS background 350 collaboration at events/keVee/kg/year [ based energies on preliminary estimates by the Su- precise value makes a differenceonly only at theE lowest masses above theexample band of gap the when signal widths for various elements. For large enough For germanium (and allvaries other less elements than 50% below), over almost weof two take orders in magnitude in energy [ energy of E Here, where integer. Fluctuations aroundwhere the mean are givenquadrature by the energy the resolution Fano ofthe factor, number the of phonon secondary detectors, electron-hole pairs, Silicon: – Table 1 width ( scintillators (NaI, CsI, GaAs). JHEP06(2017)087 ] , 35 68 , and g term in E t , σ e ε ]. We assume a 47 ) DM on the left 0 ] based on the low- ]. If the ALP mass A 35 84 – 82 , 3 keV, it will contribute to . 78 1 ]). for the values of ∼ masses. New experiments using 1 47 0 2 A T/ ]. The expected exposure is about 100 gram- . We find that existing constraints from 77 4 ], in the absence of a background model, (see also [ ]. However, we see that these are weaker ], using so-called “Skipper CCDs”, could allow them 23 1 23 76 – we show projections for hypothetical future ex- , ]. Prospective searches, especially SuperCDMS – 11 – 19 42 in figure 82 0 – ]. A 78 , 79 , 68 78 , 10 eV. ]. We find that this bound disfavors a gap of several hundred 35 ∼ 37 1 ]). First, we have updated the bound derived in [ ]. We make projections for three scintillating targets, sodium iodide, . For ALPs, we see that the newly derived direct detection bounds from 80 47 , 3 beyond existing constraints for sub-keV masses below 0 68 , DM, we have derived several constraints that go beyond the constraints from A 0 66 ), and use the values listed in table A (1 keV) for silicon. -decay background of 350 events/keVee/kg/year as for the silicon projection above. 4.2 β ee ]. We checked that data from KIMS [ σ only important just above the band gap. See table We show the results for the solar For Future versions of the DAMIC experiments [ 80 1 – cesium iodide, and gallium arsenide,flat although other possibilities existWe [ do not consider anyeq. x-ray ( lines activated by cosmogenics. We ignore the Scintillators (NaI, CsI, and GaAs): periments using scintillating targets withexperiments sensitivity down have to been one argued oroff more also photons. electrons to Such [ have great potential to sub-GeV DM scattering as well as possiblebounds scintillating for target experiments, can significantly improve onto existing reduce their thresholdyears, to less near than the the bandrescaled gap expected easily to of SuperCDMS get silicon exposure projections [ for for silicon. DAMIC. Our projections for SuperCDMS can be scintillator targets with sensitivity to one or a fewXENON10, photons XENON100, can and have CDMSlite similar are78 weaker reach. than the stellar coolingprovides constraints [ a weaker bound (not shown) than CDMSlite. However, the future SuperCDMS, threshold XENON10 data [ eV in mass between thedata Sun disfavor additional and parameter HB space cooling beyondSNOLAB this. bounds. HV Prospective Existing searches using CDMSlite by germanium SuperCDMS andmagnitude or XENON100 in silicon targets can probe up to more than an order of is less than thethe kinetic cooling energy of of the electrons, white which dwarf is [ 3 the anomalous energy loss in the(see Sun, also horizontal-branch (HB) [ stars, and red-giant stars [ XENON100, EDELWEISS, and KIMSthan [ stellar cooling boundsSNOLAB [ HV withcooling germanium, constraints. could Intriguingly, this improve includespossible by probing hint a part for of factor anomalous the energy of region loss consistent a in with a few white dwarf beyond stars the [ stellar 5 Results Existing constraints and projected(right) of sensitivities figure are shownXENON100 for and CDMSlite ALP partially ( improve on published bounds from CoGeNT, CDMS, • JHEP06(2017)087 ].

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�� solid colored lines �� show projected sensitivities for �� show constraints from XENON10, ]. Shaded orange region in left plot �� ], and CoGeNT [ �� (��) � � 22 ) dark matter ( �� 20 0 A -�� -�� -�� -�� -�� -�� -�� -�� -�� -��

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�� all cooling of the Sun,(HB), red which giant are stars independent (RG),bounds of white from the dwarf XENON100 stars ALP (WD), or bound [ and/or derived in horizontal [ branchis stars consistent with an ALP possibly explaining the white dwarf luminosity function. the modeling of the secondary ionization90% in C.L. xenon. sensitivities foryears) SuperCDMS targets, SNOLAB respectively. HVhypothetical using experiments either with Ge theof scintillating (20 10 targets kg-years) kg-years. CsI, or NaI, All Sidark and projections counts (10 GaAs, assume to assuming kg- a achieve an realistic sensitivity exposure background to model low-energy electron discussed recoils. in the In-medium text, eﬀects but are zero included for Figure 3 like particle (ALP) darkthe matter ALP/ ( XENON100, and CDMSlite, as derivedShaded in bands this work, as well as the DAMIC results for JHEP06(2017)087 , Yellow ]. ) for dark- 22 ], which considers 86 � �� solid colored lines �� ] based on XENON10 data [ �� (��) 66 [��] �� show projected 90% C.L. sensitivities for Super- � – 13 – �� ) and prospective sensitivities ( �� show projected sensitivities for hypothetical experiments with the -�� -�� -�� ) is the bound derived in [

�� ϵ show constraints from XENON10, XENON100, and CDMSlite, as derived shaded regions dotted line While completing this work, we became aware of [ Deep- and light-purple solid lines green solid lines ) with a mass Stückelberg from the Sun via resonant production (including in-medium 0 . Constraints ( A Colored regions , and Significant progress is being made in lowering the threshold of DM direct detection Javier Redondo for usefulEarly discussions Career or research correspondence. programFellowship. DESC0008061 R.E. T.-T.Y. and is is through supported also aEuropean by supported Sloan Research the Foundation by Council Research DoE grant (ERC)2015 DESC0008061. under - the T.V. Proposal is EU n. supported Horizon 682676 by 2020 LDMThExp), the Programme by (ERC-CoG- the PAZI foundation, by the German-Israeli related topics. Acknowledgments We thank Haipeng An, Ranny Budnik, Lauren Hsu, Maxim Pospelov, Josef Pradler, and dark absorption. We find that plannedand and scintillating possible targets, new can experiments, significantly using improve semiconducting beyond on astrophysical existing constrains, bounds. even probingphotons This well and provides ALPs. unprecedented sensitivity to low-massNote dark added. to low-energy electron recoils.Sun. Shaded gray Also regions shown show ( constraint from anomalous cooling of the experiments. In this work, we studied the implications of this progress for searching for effects). in this work. CDMS SNOLAB HV using eitherorange Ge (20 kg-years) or Siscintillating (10 targets kg-years) CsI, targets, NaI, respectively. sume and a GaAs, realistic assuming background an model exposure discussed in of the 10 text, kg-years. but zero All dark projections counts as- to achieve sensitivity Figure 4 photons ( JHEP06(2017)087 � (B.2) (B.3) (B.1) �� /��/�� , �� ) 2 ). GaAs and Ge, /ω 0 � [��] 2 A � right �� ( � m ( 0 2 p A ω = �� L ) and �� ). Inside the Sun the photon self left Re Π � 3.7 prod T,L -�� -�� -�� -�� -�� -�� Γ

dωdV

d �� ϵ 2 T,L for detecting 1 event/kg/year in a variety of = , aee – 14 – g ,V abs T,L �� )Γ �� and prod T,L dωdV Γ ω/T d � ��/��/�� − � e �� − (1 , ω 2 p � [��] ω − � �� = = and ALP models, respectively, as a function of mass. Note that these 0 T T,L A ]. We describe the relevant equations for the Stueckelberg case here. production �� 0 Re Π 66 Im Π A is the eﬀective mixing angle deﬁned in eq. ( , we show the couplings . Couplings needed for 1 event/kg/year for ALPS ( � 5 T,L The production rate is given by -�� -�� -�� -��

�� where energy is given by found in ref. [ experimental data. B Solar A detailed description of the solar dark photon production and absorption rate can be In ﬁgure materials for the calculations do not dependthese on any rates background into model. a Therefore, projection one for can easily a translate given background model or a limit for a given set of Foundation (grant No. I-1283-Budgeting 303.7/2014) Committee and and by the the Israel I-CORE Science Program Foundation of (grant the No. Planning 1937/12). A Rates for ALPs and dark photons in various materials Figure 5 and Xe and CsI have very similar behaviors due to similar refractive indices. JHEP06(2017)087 , , and (B.7) (B.8) (B.5) (B.6) 3 Phys. α , Community 300 eV. , in ω T ω > . r 0 A ) (B.4) m f L is the electron density , e = e T p . n m ω πT

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, 4 4 ) to the bremsstrahlung production mode for arXiv:0707.2063 H ) = is the plasma frequency inside the Sun, ,V [ a e, X = = e ( = ω/T arXiv:1310.8327 i f is the electron mass [ : Snowmass on the Mississippi (CSS − prod T,L res res Working group report: WIMP dark matter direct detection /m e e

dωdV = Γ ) CC-BY 4.0 (2008) 115012 (2007) 115005 d L r T m ( 2013 Φ Φ since the resonant production is absent , bremsstrahlung is the dominant e This article is distributed under the terms of the Creative Commons dω dω d d n brem (2008) 509

2 D 78 D 76 ), we obtain the corresponding flux from the resonant production, e max p ,V 3.10 ) = prod L r B 659 ( dωdV Γ ω > ω p d ω Phys. Rev. Lett. Phys. Rev. Summer Study July–6 August 2013 [ For Below the maximum plasma frequency J. Jaeckel and A. Ringwald, M. Ahlers, H. Gies, J. Jaeckel, J. Redondo and A. Ringwald, P. Cushman et al., M. Pospelov, A. Ritz and M.B. Voloshin, [3] [4] [1] [2] References Open Access. Attribution License ( any medium, provided the original author(s) and source are credited. where For H and He, wethermal take the distribution solar ( data from [ production mode, Using eq. ( inside the Sun, and for the dark photon: resonant production and bremsstrahlung. the flux is longitudinal resonant production. The resonant production rate is given as where JHEP06(2017)087 , ]. , ] , Phys. ] Phys. , (2013) , Erratum SPIRE [ IN 11 100 ][ , (2013) Phys. Rev. Radio for , Searching for Phys. Rev. Lett. ]. , JCAP ]. 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