JHEP02(2020)134 Springer February 6, 2020 January 14, 2020 February 24, 2020 September 8, 2019 : : : : Revised Accepted Received Published Published for SISSA by https://doi.org/10.1007/JHEP02(2020)134 b,a [email protected] , spectra in unstable isotopes. To confirm the possibility β and Robert McGehee decays in isotopes which are stable in vacuum as well as shifts [email protected] c , β . 3 1908.10861 Gilly Elor The Authors. c Beyond Standard Model, Effective Field Theories a,b

Absorption of fermionic dark matter leads to a range of distinct and novel , [email protected] Berkeley, CA 94720, U.S.A. Department of Physics, UniversitySeattle, of WA Washington, 98195, U.S.A. E-mail: Theory Group, Lawrence Berkeley NationalBerkeley, Laboratory, CA 94720, U.S.A. Berkeley Center for Theoretical Physics, University of California, b c a Open Access Article funded by SCOAP ArXiv ePrint: signals is necessarily unstable leadingNevertheless, to stringent we bounds find from a indirectlong detection large lived searches. viable and parameter detectable in space current in and which future dark experiments. Keywords: matter is sufficiently different nuclear recoil energy spectrum fromchannel that leads of elastic to scattering. induced Theof charged current the kinematic endpointof of observing these signalsexample higher in dimensional light operators of thattheir other lead phenomenology. constraints, to Most fermionic prominently, we dark absorption introduce matter signals UV which and exhibits study completions fermionic of absorption Abstract: signatures at dark matter direct detectionsignals and from neutrino fermionic experiments. absorption by We nuclear study targets,Fermi the operators: which possible we divide neutral into and two charged classesabsorbed current. of by four In a the target neutral nucleus current and signal, a dark neutrino matter is is emitted. This results in a characteristically Jeff A. Dror, Absorption of fermionic dark matter by nuclear targets JHEP02(2020)134 – 1 ]. On 16 – 4 We organize 1 ]. 41 ] — a scenario in which the dark matter 40 28 15 24 – 1 – 10 29 decays β ]. 36 19 – endpoint shifts 23 7 17 β 4 3 decays decay − + 1 β β ]). With this direction in mind, we recently considered the absorption of 27 39 – 37 ] for recent work on MeV sterile neutrino dark matter elastically scattering off electrons. 42 Another strategy for progress is to explore novel dark matter direct detection signals See [ 4.1 Induced 4.2 Induced 2.1 Neutral current 2.2 Charged current 1 ]. As such, both theoretical and experimental programs have moved beyond the WIMP mass energy is available to theonly target its (in contrast velocity-suppressed to kinetic thebuild well on energy studied this elastic may foundation scenario by betargets, where exploring imparted). and leaving cataloging the all In such consideration absorption our of signals present off electron nuclear work, targets we to future work [ In tandem, new proposals hopedark matter to candidates probe [ regions of parameter space interesting for(see lighter e.g., [ a fermionic dark matter particle in a detector [ 3 paradigm. Onand the production theoretical mechanisms side, have motivatedthe explorations dark experimental of matter side, masses alternative belowexperiments progress dark a are has GeV matter needed [ been candidates to made search on for signals the with size rates frontier consistent — with where current ton-scale bounds. 1 Introduction Despite increasing sensitivities, dark matter directyield detection null experiments results have continued for to the long sought after weakly interacting massive particle (WIMP) [ A Neutral current rate at higherB order Relevant current experiments 5 Charged current: 6 Discussion 3 Neutral current nuclear recoils 4 Charged current: induced Contents 1 Introduction 2 UV completions JHEP02(2020)134 − + is β β χ , the (1.2) (1.1) ,  ]. The e A p ], where j p Γ j n Γ p ] [¯ decays do not e ] [¯ i ν β Γ i χ Γ χ decay energy threshold of ] and [¯ decays n β j β Γ n , ] [¯ ) and atomic mass number ν ∗ , i ( Γ Z X X χ 1 Z A A ∓ decays for all isotopes within a detector. + Z decay rates suffer relative to those of + β + + ν (—) β  or e → − – 2 – β → X ], where it was concluded that immense quantities by the nucleus as well as Pauli blocking effects of Z A X 39 + Z A + e from the decay of the excited daughter nucleus, and decay targets in current dark matter direct detection + χ γ (—) − χ β (—) mass is still converted into kinetic energy for the recoiling χ contains all possible Lorentz structures. Since dark matter must is a Standard Model (SM) neutrino. This signal is generated by } ν 400 keV. This kind of signal has been considered in the context of µν , σ ∼ 5 γ µ , γ µ , γ decay of the final nucleus, if it is unstable. Due to these multiple signals and 5 (and potentially photon) energy, dedicated searches for induced ) denotes a possible excited state of the nucleus (which range from below an β X is the nuclear target with atomic number ∗ , γ Z A  1 e { In principle, one can look for induced Another set of fermionic absorption signals are induced We begin by considering signals from absorption of fermionic dark matter from “neutral 5 keV) is needed to probe the parameter space consistent with indirect detection bounds . = 2 i Indeed, we find manyand induced neutrino experiments. However, induced due to the Coulomb repulsionthe of outgoing the neutron. As such, we will primarily be interested in signals from induced masses larger than sterile neutrino dark matter detection [ of Dysprosium (which is∼ rare but has anfrom sterile anomalously neutrino decay. small In thisfind paper, that we current study alternative experiments dark can matter candidates, easily and observe signals consistent with other constraints. recoil of the daughteranother nucleus, a large rely on the nuclearprocesses recoils themselves have being kinematic above thresholds a allowing given them to experimental only threshold. probe dark However, matter these MeV to 10s ofcurrent” processes MeV are above generated theinduced by ground dimension-6 decay state operators can depending of occur(or the on in meta-stable) form the isotopes [¯ isotopes isotope). that existthese can are Such in be stable “charged macroscopic employed to or quantities look unstable in for in multiple current correlated the experiments signals: vacuum. and the energetic so Stable ejected future experiments best suited to detect these processes. where ( that the outgoingertheless, neutrino a carries fraction away of mostnucleus, the of resulting in the a darksorption distinct rates matter can signal. (mass) enjoy a energy.the Like coherent neutral spin-independent enhancement current Nev- WIMP for in larger detail scattering, by nuclei. the surveying In ab- current this experiments work, and we discussing study the types of where the dark matter, and dimension-6 neutral current operatorsΓ of the formbe [¯ lighter than the nucleons to avoid rapid decays, energy momentum conservation ensures fermionic absorption. current” processes of the form these signals by the corresponding types of higher dimensional operators which lead to JHEP02(2020)134 with ]. We β may be with the 46 , χ χ 45 ] for Super- or 37 χ decay spectra. Despite β and so, requiring dark matter to be ]. Previous studies have focused on and introduce a mixing of decay thresholds, they may be used to χ χ β 44 m , 43 – 3 – decays are worth consideration since they allow + β is put into a right handed doublet with the electron instead of the neutrino. decays of stable isotopes and their projected reach. χ β 1 does not place any restrictions on the model parameter space that is of interest . 0 decaying isotopes, such as PTOLEMY [ ∼ − This paper is organized as follows. For the neutral current and charged current Importantly, dark matter candidates which allow either the neutral or charged current For unstable isotopes, it is more challenging to accumulate macroscopic targets in 2 β h χ matter stability. In general, a varietycan of thermal accommodate (and the non-thermal) production observedΩ mechanisms dark matter relic abundance.to Therefore, fermionic accommodating absorptionmechanisms signals. from the current As work. such, we omit a detailed discussion of production 2 UV completions In this section, we present twosignals UV presented completions in that this realize work. thecosmological neutral After and and presenting charged the collider current models, constraints, we with discuss a in detail particular the emphasis various on implications for dark tions in section 2.dependent Additionally, section dark 2 matter contains decay athrough 5, detailed modes we discussion that comprehensively of consider constrain the allgets possible our UV at signals model- current parameter from and absorption space. futureexperiments. by nuclear direct We In tar- detection, conclude sections in neutrino, section and 3 6. neutrino-less double beta decay models where In all cases, the decayssufficiently depend long-lived on leads large us powers to of consider masses well belowdimension-6 the operators GeV scale. which yield these unique signals, we present simple UV comple- using telescope observations. Sincedependent, these we indirect treat detection all boundsdimension-6 of fermionic are the absorption inherently operators. dominant model- decays Forgauged the in baryon-number neutral with concrete current, additional we UV coupling present completions(Dirac) a to neutrino. model of of the For the above charged current, we present a modification of left-right symmetric sterile neutrinos where it’s challengingpropose to to compete test with light currentnecessary decay dark bounds to matter [ probe using parameter this space signal consistent and with overview other the constraints. fermion types absorption of experiments signals are inevitably unstable and their decays can be searched for detectors. Nevertheless, since they have nodetect induced arbitrarily light dark matter.energies To find beyond these the signals, kinematic onethese can endpoint practical look of challenges, for there the outgoing are targeton proposals isotope’s with other primary physics goals which rely Kamiokande. Nonetheless, induced complementary isotope targets innecessary experiments to to probe search the forpresent same the today. operators asymmetric In and dark this might work, matterfor be we induced scenario, survey where the only current experiments which can be used to look decays off of Hydrogen targets in neutrino experiments, as considered in [ JHEP02(2020)134 a χ φ 0 Q Z (2.5) (2.3) (2.4) (2.1) (2.2) decay νγ .... → + . , χ invariant mass c . µ arising from the 0 0 2 Z 0 π + h µ Z 16 0 ! . / 2 Z c , with all of the quarks 2 ν χ χ . -induced 0 m eg

W + h + R ∼ ν P  µν R yields the following dimension- ! F P 0 χ . χ µ µ Z . 0 µν m Z 2 χ χγ ¯ χγ i  2 ) ¯ m q φ p 0 0 h µ µ + + i y µ ¯ 2 qγ pγ 0 φ i h

Z φ q + ¯
y h . Furthermore, a mixing is induced between X ! 2 ¯ n 2 χ given by: i χ χ µ – 4 – y µ φ ¯ ν R Q h θ q nγ 1 3 ¯ 2 χγ (¯ 0 y χ = 2 2 Z R χ θ Q g + R c m θ ) = 2 χ 0 R . + s θ c 2 Z ) which gains a vacuum expectation value (giving the q . m s 0 , which has a natural value µ 2 χ m  L ⊃ q g ¯ qγ + h χ ν Q q R X ) is an operator typically considered in elastic scattering. Now 1 3 ¯ gauge coupling, we have taken the dark matter to have charge χP L ⊃ 0

2.2 yφ χ with a mixing angle, g under the U(1) + ( R mixes with the SM neutrinos through a Yukawa interaction of a scalar, , and we have set the quark charge to unity without loss of generality. We ν 0 χ and the SM quarks are charged under a new U(1) L ⊃ χ ¯ χχ Q χ χ and m is the U(1) χ χ ⊃ R g P We now discuss the phenomenology of this model. The direct detection signal is Note that eq. ( ≡ mass L R the case of sterile neutrinos). primarily governed by the effective operator: Since the mixing israte only is between heavily suppressed the while right maintaining handed a fields, large the direct detection signal (in contrast to After diagonalization, there isone one massive massless state state withχ (identified mass with the SM neutrino) and mass contribution). For simplicity, wematter consider and a model approximately with masslessterm lepton is Dirac number given charged neutrinos by: dark such that the U(1) suppose that (with charge under the U(1) also include a kineticrunning mixing, of quarks within6 the operator: loop. Integrating out the where Simple models that generateduction the of neutral current additional operator U(1)between can symmetries the be broken dark built above through matterwhere the the candidate only weak intro- and scale, a andcharged equally neutrino. a (i.e., mass-mixing gauging For baryon simplicity, number): consider a scenario 2.1 Neutral current JHEP02(2020)134 s. s. 0 0 Z Z (2.7) (2.6) + ) induced ν e induced by + . left ν e − ! ( loop analogous e 0 1 8 Z + W , W m νe 2 9 χ W ) and charged current 11  m ) π → R π − − θ left propagators. A curious e e c χ (4 R R R - Model θ Z 0

mixing can lead to various W W s 2 Z R χ O ν or g m W 0 χ − can be massless, these potential Z χ χ χ χ eQ = 0 +  3 π 5 χ νγγ m → 512 χ ν ν Γ  3 – 5 – 31 − ν in the neutral current model ( 0 induce 1 photon or 2 photon decay channels up to ) via mixing with , Z χ ! ). Consider first those decays in figure 2.5 0 12 Z left 16 log 2 m γ ( 13 χ χ  13 does not 1 ) m + − π = - Model e e (4 0 − e

Z e + O the dominantly constraining decay mode is νe γ γ → e model is it χ   m 0 Γ ν ν 2 Z 0 0 = 0 + Z Z do not couple to the SM photon after diagonalization), while the 2 photon & depicted in figure 0 ). νγ χ ). Including neutrino mass insertions induces decays through a χ π → . Most constraining decays for m χ m right χ χ Γ . For As alluded to above, dark matter is unstable as the χ m enters the effective operator indecay eq. channels ( can be made arbitrarily small. We assumekinetic this mixing here with for decay simplicity. rate given by The leading contribution to theAll 2 of photon channel these comes contributions from( are a negligible 2-loop diagram for with theto 2 dark those matter of masses sterile ofon neutrinos the interest but flavor to structure suppressed between us by the here an right and additional left mixing handed neutrinos. angle and Since the dependent neutrino that insertions: For the 1 photon channel, the dominant decay is through a 3-loop diagram with 3 these additional insertions — the singleby photon gauge channel invariance through (this kinetic is mixinga equivalent is to forbidden new the U(1) usual statementchannel that is particles forbidden charged by under chargehigher conjugation orders, (also we known find as the Furry’s theorem). decay Considering of dark matter to 1, or 2 photons up to neutrino mass this model. decays of by 1-loop kinetic mixingfeature without of additional this insertions of model ( There will also beinterest an here, elastic scattering as mode itelastic but produces scattering it a is will smaller challenging generally energy to be deposit. see weaker for Consequently, than searches the a looking masses dedicated of for fermion absorption search in Figure 1 JHEP02(2020)134 (2.8) (2.9) νγγγ → χ is always less decays induced and L through kinetic ν Z − e . + 2 νγγγ νe . ! 2 → R → ! ] (one can also circumvent θ well above the weak scale, c 2 χ χ 0 47 ] for a recent summary). For 0 R α 3 θ Z 2 Z R we use bounds from the non- s 51 0 ]. θ 2 χ m m c 2 Z g 50 R , which proceeds through a large 2 χ m θ ν ννν 4 e s Q 3 )  m depends on the initial DM production

→ χ → g 3 R χ χ 360 π ν 5 χ χ relative to that in a SM Q m R 128 (8 ν

– 6 – 11) 13 χ − m 7 ] while for − decay mode by choosing a scalar which does not carry 49 10 ν being dark matter. For 3 ' χ → = (16 log 2 χ νγγγ → ννν χ mixing angle: Γ → χ R Γ χ . Therefore, ensuring a stable dark matter candidate leads us to consider χ ]): − m can decay invisibly to neutrinos, 48 R [ ν χ . Thus, though the energy density in 3 − , the dominant constraints arise from flavor changing meson and 0 operator that can cancel these decays modes to some level. As we show, this 10 MeV. Z ν ∼ In addition to constraints from indirect detection, there are bounds on this UV com- Another possible tension could be that the production of dark matter results in too The particular decay rates computed here clearly depend sensitively on the particular & MadGraph χ pletion that do notthe depend dominant constraints on arise from mono-jetlighter searches (see [ by a Wess-Zumino-Witten term present in theories which gauge an anomalous combination great an energyproduced density via in UV the freeze-in,for right-handed we the neutrinos. find NC that operators,than for Assuming the the energy that lightest density dark dark in mechanism, matter matter in masses is general, we itradiation consider does energy not density. have to be in tension with measurements of the early away decays by introducingthe a 3 UV kineticwill mixing be necessary parameter in andm all a the UV detectable contribution parameter to space of neutral current absorption for model chosen. As a strikingto example, completely note eliminate that the ina the case coupling of to a two scalar neutrinos.the mediator its signal In possible an regions effort observable to in not experiments, let the we specifics allow of for the the model possibility overshadow of fine-tuning lighter dark matter candidates. Theon limits the on dark dark matter matterdecays mass decay we rates and recast depends particular sensitively constraintsobservation decay from of channel. [ an anomalous For changeof in the the Cosmic Microwave equation Background of until state present of day the [ Universe from the era All the decays ariselarge from powers of irrelevant operators, and as such the rates are proportional to In addition, power of the mixing in conjunction with thekinetic Euler-Heisenberg mixing Lagrangian [ by attachinginvolves parametric external suppressions photons by meson toThe masses a decay and rate we loop is estimate of estimated itof as to quarks (computing be however the subdominant). phase this space diagram factor numerically with the aid For lower dark matter masses the dominant visible decay is JHEP02(2020)134 ) × R ] for 2 R 56 ≡ (2.13) (2.14) (2.10) (2.11) (2.12) 3 ] 0). This , 55 ¯ 2 , 2 . . EM L U(1) , i charged as ( H h ! −−→ i.e., a singlet under all gauge β . doublet scalar, Φ charged as H 0 Y s L ! R χ β 0 c ) under SU(2) 0 u in alternative structures (see e.g. [ U(1) L

. × 2 ≡ 2 3 L/R v R 1 operator could have a scale a little below the L √ . √ T χ 3 R in this set-up is identified with the right µ = + = 0) and is assumed to complete the lepton T , i 3 i ¯ χ L χγ 2 SU(2) + q T Φ H , µ h h i 1 X + – 7 – qγ Φ h −−→ , , = X X ! Y ! = 0 0 2 + + 1 Q φ is formed out of a linear combination of SU(2) h φ h U(1) ]. Since the scale of the effective operators we consider 0 1

− 2 Y × h h charged as ( 54 R

χ Φ = R = P H SU(2) ≡ ]. Constraints also come from looking for heavy anomaly-canceling × R χ L 53 , 52 and left handed fermions in doublets ( SU(2) R 2), gets a vev; charges: / 1 X , The lepton number carrying dark matter In principle, this conclusion may be too hasty since, while the fermion absorptionMore operator generally, the scale fermions we may be charged under SU(2) 2 only couples to baryons we estimate there are no additional strong constraints. 2 3 , 0 1 consider will always beweak above scale. the weak Nevertheless, scale, sinceZ the we work ¯ in a regime where it isa at review). most comparable to the weak scale and prefer a particularAdditionally, one there will as be they an inertsymmetries. do left handed As not component is affectfermions typical the for (we fermionic left will right absorption considerunder symmetric SU(2) phenomenology. only models one we place generation the here) SM into right-handed right handed doublets ( handed component right handed doublets. Wepartners do for not the need to SMMany introduce neutrinos, known gauge but mechanisms singlet may may right-handed be do neutrino so used to to realize generate a SM standard neutrino seesaw masses mechanism. and we do not where the EM charge is given by, U(1) The second stage ofcorresponds to: breaking can be accomplished with a The initial breaking can( be accomplished when an SU(2) In this stage of breaking U(1) UV completions which result in a chargedunder current electromagnetism. signal typically Such require a new situation statesone is charged a example prediction of of which an we extended electroweak explore sector, here. A simple extended breaking pattern is [ fermions directly in collidershere [ are above thebeam weak scale, dump, or we supernovae do which not are expect often significant crucial2.2 constraints when from discussing star light Charged cooling, dark current matter. of SM charges [ JHEP02(2020)134 R ≡ is a and ˜ H (2.18) (2.19) (2.20) (2.21) (2.15) (2.16) (2.17) L W χ and H such that the v ν y . In this sense this ]. L .  58 χ u , χ y After integrating out the . . u . 4 ¯ χχ, 2 + h.c.) ]. / u + h.c. at tree level given by, 1 2 χ ) 57  χ R √ 2 χ R y χ + h.c. . g ) + h.c. R W  νP d µ R (¯ + P χ R µ W v 2 2 ⊃ R R P µ ν g µ and P ¯ eγ √ ( y µ W 1 2 .  uγ β c + W ¯ n eγ 2 . = + ¯ s ) ¯  `` 2 5 e R d v 2 v + h R ` Z is a free parameter. R λγ R √ y P – 8 – g P ! contributes negligibly to the breaking of SU(2) χ µ µ L e decay. To minimize this mixing we work in limit χ + g m H ¯ χγ (1 + uγ 1 4

χ ¯ (¯  dd (1) and hence there is a mixing angle between as follows: µ u , M R 2 1 v 2 O R d ¯ Rµ pγ R g √ y  ˜ is χ P 2 2 R 2 1 W W HR states as well as the additional inert R L ⊃ − , and are given by g β Φ¯ ¯ + 2 L i 2 R W 2 M R 2 R = χ g s √ Φ g χ y h ¯ M uu R 4 v and 2 W u L ⊃ √ = 0 as in the inert doublet model [ L ⊃ y M L ⊃ β from forming a Dirac fermion. We assume L ⊃ 0028 is the axial to vector coupling from data [ s . ¯ LHR R ), which leads to 0 L ⊃ χ R  gauge boson masses primarily arise in the usual way, from the kinetic 2 W R and /m = 1 and 2694 L . 2 W 0, which can be achieved if ν β 1 c m ( → ' of the form O β 2 λ is not needed, but is included since no symmetry forbids it. However, we do assume that it is suffi- 2 σ s of ν ∗ boson we get the quark level interactions: Unlike standard studies, instead of considering right handed neutrinos in the lepton Recall that we place the quarks into right handed multiplets, while the dark matter The SU(2) completes the lepton right handed doublets. This leads to the following term allowed y 4 H R R R 2 ciently small to prevent significant decays to 3 left-handed neutrinos through the SM 4-neutrino coupling. where W In terms of the nucleons this gives the interaction: preventing SM neutrino is effectively massless and doublets we have introduced model explicitly breaks thesinglet true it forms left-right a symmetric Yukawa coupling nature with of the the Φ setup. and the Since right handed doublet, Additionally, fermion masses areσ generated from Yukawa interactions with such that χ by all the symmetries: For a generic scalar potential W that term once Φ develops a vev In addition, there is a mass mixing between the JHEP02(2020)134 (2.26) (2.23) (2.25) (2.22) (2.24) , and at low , u 2 . ! c . u QCD . m + h 2 Λ ., − ! c π . ν R ). The safest possibility is log µ 2 W j . The decay rates (ignoring ∂ µ L 2 χ M + h W j i process however we note that d 1 R right µν M + 2 m W R µ L,ν g to minimize the mixing between R ( eχ u j 2 W M ν W ! R 1 m R ∂ 2 π → 2 R M g f ¯ 2 π 2 g d u ) 2 R R,µ 2 L QCD + u boson which vanishes at m j g π g Λ 8 One loop radiative corrections induce a µ 2 L + µ (4 g ∂ W 5 W

log ! L 3 2 e 3 g 2 2 W W π h 5 χ π d m – 9 – π M 7 χ M m as dark matter. The most powerful direct search 2 m 1 f R 512 R 256 u m χ 2 2 W W m  ⊃ M 2 11) R M 2 g and the SM 2 31 24 π i ) − 2 L f 2 π Σ mixing worse, charging more SM generations would introduce new, π g R 2 − R µ m R g (4 W 8 D 2 L W †

g - log 4

W Σ)  µ L ⊃ is heavy such that it is never produced on-shell. In this case, there D = = (16 log 2 ( L ⊃ R h ν ν − − ) contains additional factors of inverse mediator when compared to W e e ) will in general be less constraining than decays in the neutral current Tr + + 2 loop) π e e 4 f ) , and so we focus on this case. − 2.25 → → 2.25 π R ) we can extract the mixing with the pions: ( χ (1 χ ). π Γ Γ W are the left and right gauge currents (defined without the couplings). Below /f a 2.9 σ a µ L,R and )–( j iπ e 2.7 As in the case of the neutral current, one can look directly for the operators we consider We now consider possible decays as shown in figure W In addition to making the ≡ 5 searches being inapplicable (as they rely on a final stateaccompanying neutrino). dark-sector Nevertheless, states there forthey are the would heavier not SM produceand leptons. charged a current If signals heavy they at leptononly comprise experiments emitted come as a from would processes fraction the be with fraction of kinematically a of dark forbidden. dark “first matter, generation” matter Thus, dark absorbed matter. the charged current signals would here without requiring the presencearise of from collider physics fromon searches the for limit heavy where chargedare states. limits For using simplicity the we energy-enhancedthis focus nature process of does the not interfere with any Standard Model rate resulting in most collider Note that eq. ( model as eq.eq. ( ( which of the two termsthe dominates interference will depend terms) on are: the mass of (Σ Integrating out the pions induces a coupling between the left and right handed currents: where the QCD scale thereat is leading an order additional using contribution chiral from perturbation the theory. running which Starting we with estimate the chiral Lagrangian to only charge the firstthe generation under the newlog-divergent SU(2) mixing between energies, is approximately JHEP02(2020)134 . , . ], 0 2
' 2 Z 4 − 60 F − (3.2) (3.1) Λ /m G ( R θ O c F operators ]. 5 TeV) R . G θ χ 68 3 s (4 2 χ 10 g . χ & R Q 2 W 2 ν ≡ M 2 masses below 60 MeV 4 Λ / ), while for χ / 2 2 conserved vector current experiments is R g − ν ], which can interfere with β Λ ν . j , F is sensitive to the interference Γ ) G e ~q ( ν ] [¯ O n + h.c. i ] for earlier work). Such transitions ν Γ 5 TeV, which is weaker than present p ) + N( R 66 . [¯ ν – 1 P 2 ~p µ ( − ν 61 & ν χγ ) ¯ → p µ – 10 – 0) ~ with the identification 1 pγ decay channels become kinematically unavailable, + ¯ β 2.1 ] (see also [ n ) + N( µ 60 . The constraint on Λ ~v ] (what became known as the χ χ nγ )[ (¯ 67 m + ( ]. We estimate that these restrict 2 0 1 χ Λ 59 decay experiments can have assuming a similar analysis can → β + (MeV) different = 0 O P I & ], however these searches are not able to extend to is the Fermi constant). Computing these constraints for the operators of χ 69 2 m [ − decays. For any such decay, the SM prediction is hard to evaluate rendering it χ  β e GeV Outside of nuclear decays its possible to use charged pions decay searches looking for In addition to direct collider searches, one can look for deviations from the SM in 5 → — when −  by the UV model discussed in section This operator leads to the the nuclear recoil process; or supernovae since theweak scale. scale of the effective operators we3 consider here Neutral are current above nuclear the We recoils first study the nuclear recoils from the dimension-6 neutral current operator generated π due to backgrounds from muoncharged decays, current which operator. will beUV Lastly, outside completion, we our we comment range do that, of not interest as for expect for the significant the constraints neutral from current star operator cooling, beam dump, collider bounds. We also emphasizeχ that such constraints dependquickly critically weakening the on constraints. the Other massare possible of ways using to the handle the neutronconstraints nuclear using lifetime uncertainties these and techniques angular are weaker distributions than in the nuclear ones estimated decays, above however [ the term between the SMthere and new is operator no termfermion interference. which absorption is Defining withEquating the a the higher scale observed dimensional Λ, limitout operator the to we for leading this would term charged expect operator current in a we the sensitivity find of that order, if Λ such a search were carried the SM amplitudes resulting10 in a limit oninterest the here operator is cutoff an scale:estimate involved task the Λ and sensitivity beyondbe the done scope for of operators this work. involving Instead, we roughly suggested to use super-allowed (Fermi)and transitions in unit between parity isotopes ( withare vanishing spin insensitive toget the renormalized axial under part QCDhypothesis), of which [ makes the it possible operatorconstraints to and are compute the put the rates on to vector the operators contribution sub-percent of level. does the In not form, [ Λ be roughly applicable here [ known challenging to use these processscale for of precision the searches higher for dimensional new operator physics in is the well limit above that the the weak scale. Nevertheless, it was searches at 8 TeV which look for helicity-non-conserving contact interactions which should JHEP02(2020)134 , δ ~q (3.4) (3.5) (3.6) (3.7) (3.3) is the and
4 ~v Λ π . While this 4 is the energy ν , ~p /
2 χ M 2) 2 m / / , 2 for the experiments 2  is the local number ) = q v µ f , th p th χ
= E NC E n 0 R − R σ (1 + E µ ν − χ E , p ) 0 R − m of momentum − th E is the angle between R . ν − µ i E
E p ν qv 0 )Θ( ) terms, the energy-conserving R − p θ δ v 0 + R E 0 ( R + χ µ χ E E − p M O is absorbed by a target nucleus N at R m −  R E Θ( ~v 4 ' R E δ for a summary of  δ
E 4 v ) ( δ ) B 2) δ 2 R π qv 2 / 2 θ | ) 2 dσ (2 q v dE against the light N – 11 – ( 3 ν is the atomic mass number of the target nucleus, ) ~q  πvM p F (cos . The incoming dark matter is non-relativistic, so π 2 j χ |M χ A 16 d p (1 + n qv A ] of the target nucleus (normalized to 1). (2 model, we emphasize that these signals can arise from 3 . Thus, the differential cross section reduces to χ θ R T j 0 d = 70 NC m πvm N E M Z σ dE R 2 cos 2 − 16 χ = | χ  dσ ) approximates the nuclear recoil energy threshold of the ν j ρ vq dE N m R Y p χ th χ is the mass of the nucleus, T v E m dR + m 2 |M dE N | N 2 is the local dark matter energy density, gives rise to the distinctive fermionic absorption nuclear recoil spectrum. R M − N R E 3 = M − E R χ 0 E R 2 ν 2 since R E |M cm 6 E q δ m 4 / r dR dE + M  2 = = 2 χ / v m 2 χ 2 χ is the matrix element squared averaged over initial and summed over final 4 GeV . d σ m ∼ m 2 0 | is the initial (final) four-momentum of the nucleus, q is the number of nuclear targets in the experiment, = q N ) ' f T 0 R ) is the Helm form factor [ ( χ = µ i q N |M E ρ could in fact be any neutral, light fermion in the dark sector. As long as it is much lighter than p ( ν p F R The differential scattering rate per nuclear recoil energy in an experiment is related to The relevant experimental observable is the differential scattering rate per nuclear ν 6 where absorption cross section perand nucleon, dark matter, distribution, and Θ( experiment with a step functionconsidered (see here). appendix The average over the dark matter velocity distribution is trivial and yields where density of dark matter, the average is performed over the incoming dark matter’s velocity this differential cross section by its energy is roughlyfunction simplifies equal to to its mass. Dropping where where spins, of the recoiling nucleus, and recoil energy. We begin with the usual differential cross section, rest which then recoils withvector momentum structure is inspired by the operators with a morealso general be Lorentz applied. structure for which the formalism that follows can in which an incoming dark matter with velocity JHEP02(2020)134 3 10 ] from ∼ 72 /v ), we calcu- 3.7 function to first = 7 GeV, while δ . Also shown is the 2 WIMP cm m 40 − function in eq. ( = 10 ) at one particular experiment, δ T NC σ M = 7 GeV and spin-independent cross section WIMP m – 12 – reduced mass), while the fermionic absorption re- times larger than that of usual elastic recoil. This N 6 - χ 10 ∼ 2 is the /v = 7 MeV dark matter with for details). CRESST illustrates the differences in scattering , along with the CRESSTIII nuclear recoil threshold at 100 eV. The χ χN 2 A . To make an illustrative comparison, we set the spin-independent . Therefore, for a fixed dark matter mass, the nuclear recoil energy m µ cm 2 M 2 40 / − 2 χ , and show the elastic rate for a heavier WIMP, (where 2 m = 10 cm n ], in figure /M σ (see appendix 40 72 2 χN − v . Differential scattering rate per recoil energy per detector mass at CRESST [ µ ] for a recent review) since the typical recoil energy from an elastic scatter is of the 2 v 71 = 10 This scattering rate is different from the usual elastic scattering rate for dark matter NC σ taking 7 MeV for thethe fermion fermionic absorption absorption signal. peaks which Tolate obtain are the not the differential given finite scattering by heights rate the and afterorder widths expanding in of the energy-conserving times lighter than normal,sures but in higher addition thresholds to toences between make allowing fermionic competitive absorption neutrino searches. and detectors elastic Inscattering scattering order with rates rates, to we larger per highlight compare the expo- recoil theCRESST differential differ- [ energy per detectorWIMP mass cross-section ( equal to the absorption cross section per nucleon, which we set as (see [ order coil is peaked at for fermionic absorption isallows 1 direct detection experiments to probe dark matter candidates roughly 1 per nucleon figure inset zooms in on the bunched peaks corresponding to the four isotopes of Tungsten. Figure 2 fermionic absorption of a elastic scattering rate for a WIMP with mass JHEP02(2020)134 = for T χ (3.8) T M 1, as described in . = 1 eV and s and decays of 0 = 0 , lighter isotopes are th Z χ E crystals which give rise . Q /M ) 4 1 th ∝ E 10 events occur in a given , and R − 5 . E < 1 at future detectors with Hydrogen − 0 R,j χ E m = 10 Θ( 2 R ) θ q s ( j MeV. Since F by requiring 2 j . A – 13 – χ NC T,j σ as a function of m N = 18 GeV, 0 NC j Z σ X m ]. The figure demonstrates the relative ease with which NC σ 72 χ χ ρ m = R present in an experiment, we find the total event rate is j . Projected upper bound on We start by considering the regime Having discussed the novel signature of neutral current nuclear recoils from fermionic For simplicity, we projectexperiment. bounds on particularly useful in probing such light candidates. Even still, reaching such light masses absorption, we nowsignal. project Integrating the the differential sensitivities scatteringall rate of isotopes over all future recoil energies and and current summing over experiments to this background by correlating the locationsisotopes. and Even heights in of the scatteringpeaked absence rates of nature off multiple of multiple distinguishable the target peaks,signal fermionic detectors from can absorption the still noise. differential use scattering the rate to differentiate the the text. rates well because it contains multipleto target four isotopes peaks in from its absorbing CaWO resolution fermionic dark is matter less which are thanexperiments distinguishable 50 looking if eV the for [ energy fermionic absorption nuclear recoils can see the signal above the Figure 3 or Lithium targets. Bounds100 for both kg potential yr. targets Also arethe shown shown benchmark assuming in UV gray completion are with the constraints from direct searches for JHEP02(2020)134 ] ] ), Li 75 81 6 ννν ] for lime → ]( 34 , χ 85 24 1. Also shown . ), and CRESST ), PICO-60 run 1, the ), PandaX-II [ . = 0 (see [ red ), SuperCDMS [ blue χ 3 = 0 ), DAMIC [ ]( Q χ 78 Q , ] (solid green 77 88 , and navy blue sky blue ]( 2 Li to recoil with an energy − 7 84 , and , for the benchmark point chosen, 5 at current experiments, including . 1 83 χ ] (solid = 10 χ − Li above the threshold. ] (dotted m R 80 [ θ 6 1 s 8 decays in tension with indirect detection = 10 F 3 ), CRESST II [ R = 100 kg yr in figure θ ), COHERENT [ ννν s T ), LUX [ → T orange and decays of χ ), DarkSide-50 [ = 18 GeV, M ]( s 0 0 – 14 – 87 as a function of Z purple Z and navy blue m aqua ]( NC − = 18 GeV, e σ 74 0 + Z νe ] (solid m 76 ] (dashed → = 1 eV and ), PICO-60 run with C 82 χ th and we approximate the energy threshold with a step function, E ), Borexino [ /M 1 sky blue ), EDELWEISS-SURF [ ), any UV completion will have other relevant constraints. In particular ∝ ). Here we have taken R ), XENON1T [ 3.1 E red yellow dark purple ]. ] (dashed ]( ]( 79 50 ), CDMSlite Run 2 [ , 86 73 . Projected upper bound on I[ 49 3 navy blue ] (dashed Li. Since aqua 7 While the projected sensitivities only rely on the defining neutral current absorption 72 the kink occurs whenabove the the threshold, dark but matter is is still too heavy enough light to tooperator push cause in eq. ( for our UV completion, setting possibly involve absorption bywe simply collective make modes projections ratherfuture for scattering than experiments off with individual individual nuclei.proposals). nuclei of The Hydrogen kink Instead, or in the Lithiumand Lithium in line is due to the two naturally occurring isotopes, UV completion to avoidbounds rapid [ requires nuclear recoil thresholds lower thandetailed those projections of current for experiments. any We do specific not make future experiment since they are diverse and would with CF (solid NEWS-G [ III[ are the constraints fromas direct described searches in for the text. The dashed grey contours show the level of fine-tuning necessary in our Figure 4 CUORE [ (dashed JHEP02(2020)134 ] 51 ) is [ (4.1) 0 , and 2 2.7 Z ] , and − 78 ], denoted in the final , 50 = 10 ∓ 77 transitions in e in eq. ( R β θ  ]. However, the s 91 ], denoted with dashed 49 , = 18 GeV, . For sufficiently massive dark ], COHERENT [ 0 R are model-independent and en- Z 2 W 74 decays [ MeV. This dark matter is suffi- + h.c. m M NC  − 4 e σ & χ / + R χ 2 R P g νe m µ ]. Additionally, searches for such a ≡ ] are the most stringent direct constraints. ¯ → eγ MeV. 2 50 processes in neutrino physics. This processes 53  χ Λ n / . ∓ ) ) is necessary to varying degrees [ β – 15 – 5 χ . These fine-tuning contours further motivate fu- decays m 2.9 λγ ν β decay in a vacuum. Signals arising from the decays of . Similar to our discussion of the kinked Lithium line, (1 + : µ β B ¯ 2.2 pγ  2 ], PICO-500, and SuperCDMS SNOLAB [ in the figure. Additionally, fine-tuning against the IR contri- 1 Λ  90 decay in eq. ( . In fact, the recoil energies can be so large that they allow non- 0028, with we identify 1 ννν . 0 4 →  χ 2694 ], to probe viable parameter space. We summarize the relevant details of each . ], DARWIN [ 1 73 89 1 for our simple UV completion in the figure. Fine-tuning of ' . λ As discussed before, any particular UV completion of the neutral current absorp- Next, we consider heavier dark matter with = 0 χ nucleus into a proton/neutron, accompaniedstate by — the analogous emission to of the ancan familiar energetic lead induced to a variety ofmatter possible mass. correlated signals We depending now on considerisotopes the the target that nucleus scenario are and in dark stable which against dark matter induces UV model discussed in section where matter, scattering on a nucleus can result in the conversion of a neutron/proton within the naturally suppress decays bounded by indirect detection. 4 Charged current: induced We now study the signals from the dimension-6 charged current operator generated by the requirement of fine-tuning toFor evade indirect example, detection introducing bounds flavor-dependentany is fine-tuning. couplings highly Regardless, model-dependent. might the greatlycourage projected reduce both bounds searches on the for needat these for current neutral experiments current and fermionic the dark study matter of absorption UV signals completions of these operators which more grey contours labeled FT bution to the with dashed grey contoursture labeled iterations FT of currentas experiments Argo with [ larger exposures and lower thresholds, such its corresponding experiment’s recoil threshold. tion operator will haveQ additional constraints. Weneeded set to avoid indirect detection bounds on ciently heavy to causeas nuclear shown recoils in above figure detectordark thresholds matter at specialized existing experiments,CUORE experiments, [ such as Borexinocurrent [ experiment in appendix every kink in this figure corresponds to a particular isotope’s recoil energy dropping below and bounds on SM four-fermionBoth interactions direct [ andmoderate, indirect achievable bounds energy are thresholdsviable, and shown unexplored exposures as parameter of gray space light for regions isotopes in can quickly the probe figure. We see that decay is the most constraining indirect bound [ JHEP02(2020)134 χ X. m Z A (4.4) (4.3) (4.2) . An e , is sig- m χ − m decay is most A,Z are straightfor- + β > M of the isotope A,Z , . 1 M − + − decays in experiments e e .  + + + A,Z χ ) ) β ∗ ∗ M . nucleus ( ( m for detectable cross-sections. X X 1 χ A,Z A A +1 − m 10 MeV, the proton/neutron will X can undergo electron capture. M Z Z (nucleus) Z A (electron) − . → → 1 e − X X m ) Z Z A A and daughter nucleus are: ∗ ( A,Z +  + + 1 M e ¯  χ χ 2 ) / ∗ 2 ( A,Z
⇒ ⇒ – 16 – β th M β th to be the mass of the − + m ≡ e e decays in heavy isotopes where in general the number m process in the limit that − . , then the nucleus ∓ + + + − β e A,Z β th χ 5 p β n χ m M m m → → − > m p n    χ + + A,Z ' m χ χ R ]. However, dark matter decays rates scale as a large power of E : ¯ : < M 58 + − decay, we limit ourselves to isotopes with 1 β β − + β A,Z transitions will occur if the dark matter mass is above the kinematic thresh- M ) for the expressions for our charged current UV completion), and so will tend β 2.25 decay spectrum for section β The kinematics of the induced If the energy imparted upon the proton/neutron by the dark matter, i.e. Induced transitions into the ground state or lowest lying excited states of the daughter nucleus + ward to compute. The energy of the outgoing of possible new signals.standard techniques The [ inclusive cross(see eq. section ( in thisto case be may in be conflictWe computed with leave using astrophysical a constraints detailed at study of larger this regime to future work. nucleus will generically bethan produced 10 MeV in (where the an incoming excited darkupon matter scattering), state. also other begins signals For are to dark in resolveincoming the general matter possible. individual dark nucleons masses matter In particle greater particular, can withwill enough break energy apart then the the hadronize nucleus and and the ejected shower proton/neutron for energies above the QCD scale, leading to an array Note that as a result of angular momentum conservation considerations, the daughter disfavored. This motivatescontaining us Hydrogen to as a focus target. on signals ofnificantly induced less than thenot binding have energy enough of energy thenucleon nucleus to remaining escape bound to and the the nucleus, dominant leading process to two will possible be processes: from the outbound interesting for isotopes wherematter electron induced capture is kinematicallyadditional forbidden. complication occurs Thus, for forof dark neutrons is far greater thanβ the number of protons, and Pauli Blocking effects would make Throughout this work, weNote take that if These isotopes are generally not long-lived, so the scenario of induced the target material of currentof direct unstable detection and isotopes neutrino and experiments. thetheir effect We reserve of study dark matter transitions on the kinematic endpointold of given by: stable isotopes are particularly appealing as such nuclei exist in large abundances within JHEP02(2020)134 is → j χ (4.7) (4.5) (4.6) m transitions ) is the mo- accounts for β χ j ~p n ( ) holds for both e ~p 4.7 decays and make pro- β ), is low enough. A list of , 2 | 4.2 N , 10 MeV), the absorption process j |M . i . is the number of targets of a given ) ) σv χ h − + the recoiling nucleus signal will be, as j m β β T, j decay: n X ( ( N 4.4 β j transitions energy could potentially be detected, and T, j Z | | e N χ j  − ~p ~p e | Z | emission). An additional factor j j – 17 – X A  e 2 cm χ ( χ E ) requires experimental input along with the compu- m ρ 1 2 ' 2 π j 4.5 = n 64 R = Ω is the angle between the incoming dark matter and the emitted d σ d θ the amplitude is for scattering off of nucleons, . As can be seen from eq. e N decays. However, the nuclear rate will depend on which of the two , the center of mass frame is approximately the lab frame, and we drop any indices
M + 0 > m v β χ O m and below the binding energy of nucleons ( χ for is the local dark matter density, and − 7 β m χ th β ρ m We emphasize that any large exposure experiments (both neutrino and designated For We now compute the inclusive rate for dark matter induced − Note that to 7 χ dark matter direct detection)fermionic can absorption be provided re-purposed the toselect kinematic stable search threshold, (or for eq. meta-stable) induced isotopes ( in beta which decays light dark from matter could induce to this affect. mentum of the electronwhich (dark manifests matter), as and a hereinduced sum we over sum the over allowed possible transitions.processes nuclear is Note spin under-consideration, that states and eq. we ( discuss this further in what follows. where Ω is the solidelectron/positron, angle fore, computing the rate astation in of eq. the ( scattering cross section for dark mattercannot off resolve nucleons. the constituentsnuclei. of the In nucleons this andframe) regime, we as we consider may only write scattering the off differential entire cross section (in the center of mass We emphasize that the rate scales with target volume and experimental exposure. There- where isotope. Here weintegrate over have all assumed energies that andthe angles any total of number of parton level targets for the experimental thresholds and haveof several interest, correlated the signals. events are HenceThe striking for signal enough most rate that experiments for theygiven an by: should experiment easily carrying pass a experimental set cuts. of target isotopes parameterized by m with the neutral current signal, velocity independent to leadingjections order. for current experimentalthe end sensitivities. of this We section defer but discussion note that of these specific charged current signals signals to are typically well above Note that the recoil energies parallel the neutral current case with the replacement JHEP02(2020)134 ) + β 4.2 or 5 keV . . From − β B 25 MeV), . 06 MeV) . 1 transitions, with a 355 keV), 1 75 MeV), , 7 MeV) . . β , , 374 keV) 3 5 for additional possible , , , ) for the transition with 5 . This was considered Xe nucleus at a Xenon − 4.2 54 e 131 25 MeV transitions leads to a wide . 1 ) 09 MeV . −  1). Note that for Gamow Teller 76 MeV 22 MeV β . .  Xe(570 keV = Te(2 Ho + Te(430 keV = Xe(1 54 I 52 67 O(2 131 C(2 128 I 52 163 54 8 6 125 136 17 13 ∆ for a summary of various transitions , processes involving target materials with → 5 + = 0, ∆ = 0 β I Dy I 66 33 MeV), 62 MeV), 163 . 4 MeV), 3 MeV), . . 41 MeV), . Te has a particularly low threshold of 374 keV, 1 490 keV), 65 MeV) 6 . . + transitions Pauli blocking effects in heavy isotopes 1 , , , 52 16 1 17 – 18 – 125 , χ , , , + crystals and was designed to search for neutrino- β 2 19 MeV 23 MeV 42 MeV 1 MeV . . 4 MeV 3 MeV . . . . 355 keV from absorption by a 70 MeV . 8 MeV) 1 transition with the lowest threshold — (though other . ∼  Te(1 Te(3 Xe(1 Xe(2 C(18 O(16 O(2 χ H(1 6 8 8 52 52 54 54 = 12 16 18 130 126 129 1 1 134 1 transitions, m . The isotopes are grouped by their stability against  I 1 I = Cs F N A 53 n 9 A 7 A 55 I A → → → → → H ). The right hand column displaces the threshold eq. ( O Te C decay, particularly suited to probe sub-MeV dark matter masses. For the Process Isotope (Threshold ∆ 1 1 8 Xe 6 A A A B 52 = 0 and ∆ A β 54 transitions many processes exist with low threshold (see figure I − : : . Here we summarize notable isotopes that could undergo induced β 1 ground state to ground state transitions are possible leading to the sub-keV thresholds. For we see that the lowest possible dark matter mass that the induced beta decay − + ] as a way to probe sterile neutrinos. Unfortunately, the tremendous expense of  β β 1 The plethora of different isotopes that undergo induced 39 = I to observe fermionic absorption. charged current process,is we one focus transition entirely inthat on the can current Standard employ experiments. Model ∆ within an Interestingly, [ anomalously there smallbuilding threshold large of volume 2 experiments filled with Dysprosium make it a challenging direction experiments and correspondingtable target materials andsignal exposures, can probe see is appendixbased about experiment. Additionally note that making CUORE, which utilizesless TeO double transitions are also generally accessiblecorresponding — to see figure the experimental targets we consider here). range of signals at various experiments utilizing different target materials. For a list of Hydrogen. is summarized in table decay, and for each possible transitionfor we quote the the value ∆ of the threshold given by eq. ( daughter allowed by the selection∆ rule in question (∆ induced higher threshold transitions), howeverwill for generally disfavor transitions intoleads the us, lowest in lying the excited present states work, of to consider the only daughter induced nucleus. This Table 1 focus on the most(see abundant appendix isotopes of materialsthe interesting smallest for splitting the between experiments the we ground consider here state of the parent nucleus and the excited state of the JHEP02(2020)134 j = = ,A µ ) at = 0. (4.8) (4.9) p +1 GT ) j (4.10) µ ∗ I F ( 4.5 Z p I ). Fermi M 0) = 1 and generated N r ∼ χ − e 2 m q − + ( e p V f ) for low momentum → 4.1 , , where we also show n 5 πη + e χ 2 . Here the nuclear radius ). Note that here we have , − 2 ) S π 2 Z ~q
2 | α e X( ~p . A | ), may then be written as follows: − ) contains both vector and axial +1 all angular momentum transitions N Z 1 r M transitions decays 1 4.7 4.7 ) 2 √ − N e − − , the Fermi function asymptotes to a r ) + 2 e β β = e | transitions, and is given by: 2 ,E ) ~p ) m  ( S β S iη χ − + 1 e  ) is the usual Fermi function accounting for + m Z e and ( S ] for → 4.9 E – 19 – 2 e F Γ(1 + Γ( 58 0) | ~ m momentum normalized to nuclei mass i.e. p ) X( − S n = Z A / 2 e p N E ) includes a sum over all possible nuclear spin states. ) in eq. ( decays to occur given each excited state mass ) + — therefore experiments utilizing light target nuclei (such p M ~v / 4.7 ,E − Z e . For large χ 3 β / m ) = 2(1 + 1 ( + 1 e χ A αZE Z ( ), with the = Z,E ]. Note that while the technology exists to compute form factors for scattering F ( | , and agree with results from the neutrino literature namely 4.1 58 decays 2 fm e 2 F . ) ~p | e − k / e β = 1 − 2694 [ . 1 χ N k − r αZE The factor = ( = is the parton level scattering amplitude for 2 8 0) = . q η j ∼ M ,Z As discussed above, eq. ( 2 j Note that the vector and axial vector form factors are implicitly defined in ( q 8 2 A ( A the kinematic threshold for transfer f between different nuclei generated byin general the operators, literature. we are unaware of such a computation carried out parallel spins so that the nucleus1. spin must Both change Fermi to and conservefocused angular Gamow-Teller momentum transitions entirely ∆ on preserve the parity low ( are energy accessible. limit. For Aexperimental target summary materials of considered here all is possible presented in Fermi figure and Gamow-Teller transitions for the transitions will dominate (other transitions willtransitions be are suppressed transitions by in factors which of theso spin that of the the spin dark angular matterMeanwhile, and momentum for the of axial electron the and are initial axial-vector parallel and couplings, and Gamow-Teller final contribute transitions nucleus to become is possible the unchanged sum. ∆ In these transitions the dark matter and electron have anti- The Lorentz structure ofmomentum a selection given rules are charged in current effect,For operator and the therefore dictates which model what nuclear transitions considered kindvector are here of allowed. couplings. angular the operator In in the eq. case ( of a pure vector operator and light dark matter, Fermi where is given by larger for isotopes with larger Super-Kamiokande and Borexino) are(as particularly they sensitive result at in larger higher dark energy matter electrons). masses M Coloumb interactions between nucleons [ compute the differential scattering cross section in eq. ( Here by the operator in ( We now focus specifically on signals from induced and compute projected experimentalspecific limits experiments by given computing current the exposures. expected rate The eq. nucleon ( level amplitude, required to 4.1 Induced JHEP02(2020)134 ) A 4.9 (4.11) (4.12) )–( 4.7 , i
2 e m ) is the electron’s e − ), and interference 2 ) = 0. Therefore, the m e λ 2 E π − ∝ − χ χ m m , − 2 1 and ∆ | + 2 , j j  decay we consider, plotted in the p β th N m − = m = 0 transitions, while the axial term β 2 e |M )( + I π j χ m n ), axial vector ( ,Z m j 0 − m 2 A λ ) − (2 j e | M e e ∝ E , j χ ~p E | β th − – 20 – = 0 and ∆ 2 m χ πm λ 18. I m 16 − + = (
2 j ). = + 2 | 2 e decay is given by: e j p 1 m = 16 ~p i | − m A − β σv h − 2 e n E m λ ) (the smallest thresholds possible for Fermi and Gamow-Tellar (2 e + 2 4.2 E ) contains both vector ( h ) we can compute thermally averaged cross section from eqs. ( χ ) for induced m 4.11 decays, which we find to be: 4 n 4.11 Λ 4.1 − m β 4 ). All terms contribute to ∆ . Circles represent nuclear transitions in which the nuclear spin does not change, while λ = . A comprehensive summary of every induced β th 2 ∝ m With eq. ( The parton spin averaged nucleon level matrix element arising from the charged current |M| for induced where as the rateout is the independent angular of integral. solid angle Here, to leading order we able to trivially carry terms ( additionally allows for Gamow-Tellerdaughter transitions nucleus ∆ is often necessarilyFermi be or formed Gamow-Teller spin in angular an momentum excited selection state rule. — one that obeyed the Note that eq. ( as dictated bytransitions eq. is ( also quoted in table operator eq. ( Figure 5 versus crosses represent those which change byoxygen, 1. hence their Note that overlap Super-Kamiokande from and CUORE both contain JHEP02(2020)134 . 3 ) and (4.14) (4.13) 4.5 which could  e . 2 ) into eq. ( |M| 4.12 ) e are the dominant isotopes } ,E + 1 8%) . , ) Z ∗ ( ]). ( F 92 j Cs 136 (8 A ,Z , 55 j index refers to a specific transition (Fermi 2 A + j j | 4%) M − . e e χ ~p | – 21 – → . The πm j 134 (10 16 ,Z Xe j j , A 54 A n + M T,j 2%) . χ induced decays within a Xenon based detector. Stable (or N  − j , j β X β th event rate at this level i.e. we assume all events are above the χ 131 (21 χ , m − , m ρ 2 χ β ) we see that there is significant velocity-independent nuclear recoil may now be computed by plugging in eq. ( = 4%) . , m 4.4 − e R β m 126 (28 { = A Decay of unstable nucleus Recoiling nucleus at recoilneutral current energies case peaked discussed above). around aPhoton single from bin nucleus being (analogous produced to in the an excited state Emitted high energy electron As an example consider We now comment on the possible signals due to a charged current event. From the • • • • meta-stable) isotopes can undergo the charged current absorption process: where given in their natural abundance (note that neutrino-less double beta decay experiments The plethora of correlatedThe signals makes optimal it search possible strategymental to will capabilities, trigger depend and on the on several dark different the matter signals. specific mass. target being considered, experi- secondary decay will emit aphoton photon emission. which Furthermore, may the betime produced searched scales for nucleus of at itself interest experiments may to sensitive beas the to follows: unstable experiment. and In decay summary on the possible signals are summarized Even more striking, charged current processesbe result observed in at an experiments. emitted energetic Theone emitted may energetic electron then can search shower for indaughter the this nucleus detector, will electron and typically in be parallelmomentum produced with selection in the rules) an nuclear which excited recoil. will state Additionally, then (as the decay determined (typically by with angular a known lifetime). This has a higher energy detection threshold of 3.5 MeVkinematics [ in eq. ( energy, analogous to thecorrelated peaks situation between in different isotopes neutral in current the target processes. material as One discussed in can section then look for In contrast to theposed neutral on current the signal rate induced experimental there energy threshold are (with no the implicit notable exception experimental being cuts Super-Kamiokande im- which in the limit that or Gamow-Teller) of arate given isotope for of induced ansumming experimental over target the material. contributionsisotope The from could total undergo each event under isotope the and angular momentum each selection possible rules: transition a given outgoing 3-momentum in the center of mass frame (which is approximately the lab frame), JHEP02(2020)134 5 Xe to Cs is in 54 131 55 131 1 transitions for a  signals at XENON1T, 1 transitions are also − = β  I , state while that of = 0 + 3 2 GT I = (searches for high energy electrons . produces an excited state of Cesium P − for various experiments summarized I B e + 6 3 2 → transition from the ground state of + 3 2 crystals in CUORE. The various experiments, their + – 22 – 5 2 2 → + = 0 and Gamow-Teller only ∆ 3 2 I Cs also occur at relatively low threshold 490 keV. For setting = 0 transition 54 F 131 I Cs contributes with threshold 360 keV, additionally transitions to 54 131 Xe). Depending on the Xenon isotope and the transition that takes place, , where note that again (with the exception of Super-Kamiokande) these 54 136 B Xe. The ground state of this isotope is a 54 131 . The projected constraints from a dedicated search for induced state. The Fermi ∆ = 571 keV for the process to occur. To project the sensitivity of current experiments to charged current signal we require For an axial vector coupling the Gamow-Teller, ∆ + 5 2 β th at least 10 eventsin with appendix the results shownprojections in assume figure no experimentalcorrelated cuts possible which signals; is nuclear recoil, motivated energetic due to the large number of the ground state of the third excited state of limits, we sum over all relevantshows contributions from the the values various of allowed transitions. thegiven various Figure isotope ∆ atomic numberabundances. that correspond to relatively low thresholds and significant 60 keV above the Xenonm ground state. Adding the electron mass resultspossible in and a one threshold must of takethe into amplitude. account the In contribution of particular, all the such possible transitions in use enriched the resultant Cesium nucleus may or mayconsider not be in an exciteda state. As an explicit example, Figure 6 LUX, Panda-XII, EXO, and KamLAND-Zenino for for Xenon absorption conversion. by Super-Kamiokandeexposures Hydrogen, and and Borex- and physics by goals TeO are summarized in appendix JHEP02(2020)134 − β = 0 I occur crystals 6 2 , and decay of ). In particular, γ 4.5 MeV of the ground state. ∼ signals at XENON1T, LUX, Panda- decays. In this process, an incoming − β + β – 23 – 16 MeV when it becomes kinematically possible to induce . In particular, the discontinuities in the limits of figure target materials. The capabilities of Super-Kamiokande become & 5 Z for all the possible transitions in the experiments considered here χ m β th decay m we discussed constraints from colliders as well as indirect detection + β 2.2 , below which transitions become inaccessible for a given isotope. Projected O (which comprises about 99% of the oxygen in its natural abundance). ], but we leave a detailed analysis to future work), emitted 8 β th 16 93 m ∼ Xe at about an 1 MeV, absorption occurs through the significantly sub-dominate χ 54 In section As with the neutral current case, limits are sensitive to the different isotopes in a given 136 m Xe target material, while Xenon based dark matter detectors contain Xenon isotopes 54 nuclei contain a significantlythe larger outgoing fraction neutron ofstates, disfavors neutrons thereby the over resulting production protons, inbeen of Pauli larger studied blocking a thresholds. in of neutrontransitions the in Additionally, is context while the not of such lowest-lying available supernova transitions energy in neutrinos, have the a literature detailed and analysis we of leave this the to favored future work. For the considerations favor dark matter masses lighterfavor than mediator about scales 10 MeV heavier and than collider about constraints a4.2 TeV. Induced We now briefly considerdark signals matter from converts a induced proton into a neutron and a positron. For heavy isotopes whose more pronounced for decays off constraints due to darkhand. matter stability Regions excluded for due the to case these of constraints the are charged shaded out, current and UV as model expected at stability looking for neutrino-less doubleof beta dark decay, is matter also off shownand both and Borexino do the could particularly search Tellurium well for andand simply absorption in Oxygen due particular to nuclei. enjoy their an enormous Note enhancementto Hydrogen at that detectors detector large with Super-Kamiokande volume energies larger due to the Fermi function relative with XENON1T beingand more KamLAND-Zen sensitive do than betterHowever LUX than once or LUX energies Panda-XII. andoff fall At Panda-XII below high due the energies toisotopes, threshold EXO their weakening the for larger projected induced exposures. limits. CUORE, beta an decays experiment employing by TeO absorption consider the projections forXII, searches for EXO, induced andEXO KamLAND-Zen are for dedicated136 Xenon neutrino-less conversion. double Note betain that decay their experiments KamLAND-Zen natural which and abundance utilize within. enriched As expected the projected limits scale with exposure transition is not available we take the splitting toexperiment, be where 1 MeV. are summarized in figure at scale linearly with exposure of a given experiment as is expected from ( data set [ an unstable daughter nucleus.fully mapped out. For some In general,angular isotopes, however momentum for the heavier for excited elements each anFor states excited practical transition have state purposes should with not when matching exist yet the within been data on the excited state corresponding to the ∆ could in principle even be done using an existing analysis, for instance the S2 XENON1T JHEP02(2020)134 (4.15) . Relative  O of Super- e 2 5 MeV). Projected . signals from Hydrogen + β decay in the liquid H , transitions in experiments employing + + , once again, to set the limit, we assume β e + 7 β + n decay without the presence of dark matter. In → β – 24 – H 1 1 + target material of Borexino. In this way, two large χ 3 ) 3 endpoint shifts transitions induced by charged current operators, we now con- (CH 3 β β H 6 8 MeV. . , further motivating carrying out both types of searches. + 9 MeV in Borexino (which has a detection threshold of 70 keV), and the . β processes tend to have larger thresholds leading to complementarity between or we show projected limits for induced − + 6 . The projected constraints from a dedicated search for induced β β , − The kinematics, matrix element and rate can be calculated from the discussion above. β 3 MeV in Super-Kamiokande (which has a detection threshold of 3 . 5 Charged current: Having already considered sider the possible signals inthese isotopes isotopes, which light dark matter absorption with an unstable parent nucleus causes a shift limits for these to experiments arethat shown a in given figure experiment canto resolve and measure thethe energy two of types the of produced searches.in Lastly only we note that asymmetric dark matter models may result In figure Kamiokande, and the C volume experiments can nowthreshold of probe 1 low dark5 matter masses — down to the kinematic a target material consisting of Hydrogen, and consider the process; with threshold of 1 Figure 7 at Super K and Borexino. present, we simply focus on the case of induced JHEP02(2020)134 ) ]. 13 en- 4.1 = 0, ] and − 101 , seconds π Pu 94 β [ and 10 13 241 + 100 8 9 β Ac 227 ], detecting the decay. seconds and would decays and has a 98 8 − Pb – − β 10 transitions are kine- β 210 96 × β Tl 204 1 eV, thus requiring a target . Os 0 194 ∼ the spin change. The Fermi and ν I decay have smaller scattering rates In addition to dominantly decaying Sm m + 151 β 10 . Cs 2 Ra 2) or second forbidden transitions (∆ ]. Only Fermi and Gamow-Teller transitions are MeV, where induced 137 228 B detection experiments must resolve decays and has a half-life between 10  ν , 104 are of particular interest to us since they are the − 1 – 25 – . Eu Sr β 2 ], and producing light sterile neutrinos [  90 χ , 154 99 m spectrum. Since the decay is allowed in vacuum, this Sn = 0 Ni Kr B) [ 63 β I 85 126 ν ). Isotopes which seconds in table Se Tc Co 4.2 13 79 99 60 is the parity change and ∆ = 1, ∆ Si π Ar π Nb decaying isotopes more generally than the present proposals. ], so this target selection criterion is irrelevant. This motivates us 32 42 94 spectra endpoint shifts is difficult due to the lack of experiments with − and 10 decay due to the Fermi function, while those which electron-capture β − C 8 Cl Ar H − 103 β -decaying isotopes for which the dark matter capture rates would not be 3 , 14 β 36 39 ] decaying isotopes. Unfortunately, the smallest mixing angle they constrain is − β 95 102 or electron-capture decay and just focus on those which value: tritium. By contrast, the fermionic dark matter we consider is heavier: 3), where ∆ decaying isotopes: measuring the SM neutrino masses [ + Q ] which corresponds to an already-constrained Λ in the charged current operator in eq. (  β , − 94 2 [ β . Every isotope which dominantly  3 190 eV [ − Toward this end, we categorize every isotope which dominantly Detecting rare Fermi Gamow-Teller 1st forbidden 2nd forbidden & = One could also consider re-purposing sterile-neutrino search experiments which used We do not consider shorter half-lives since tritium’s half-life is roughly 4 10 9 χ I 10 × electron-capture [ 4 from direct searches. therefore be a better targetdecay than via any even shorter higher lived isotope. order forbidden Isotopes transitions. with longer half-lives than 10 forbidden transitions (∆ ∆ Gamow-Teller transition isotopes in table most long lived m to consider different half-life between 10 via Fermi or Gamow-Teller transitions, some of these isotopes predominantly undergo first ments to look for fermionicdetecting absorption. dark matter Needless in to this say,experimental the way physics experimental are goals. requirements often for quite For relaxed example,ergies relative C at to the those possible needed forwith scale a other of low SM neutrinos’ masses, large exposures of unstable targets.employ There are only a few wellCosmic motivated physics Neutrino goals Background which (C In this section we consider the possibility of using one of these existing or proposed experi- kinematic endpoint shifts canmatically probe forbidden by eq.than ( those which decay still have kinematic thresholdsnaturally (albeit smaller ones). Thus, we ignore targets which seconds, categorized by theirnot main momentum-suppressed transition for [ our charged current operators and therefore of interest toin us. the kinematic endpointis of a the threshold-less process and can occur for arbitrarily light dark matter. In particular, Table 2 JHEP02(2020)134 ]. 110 (5.3) (5.4) (5.1) (5.2) There Ra [ . 12 228  i ]. 2 e 2 e 99 m m ], and This is expected − signals, we show B[ − ν ].  109 β 11 e -decay experiments  46 e E − Eu [ E β − 154 − χ , ], χ m m 108 + 2 6 keV + 2 . Ni [ He 63 , both the vector and axial-vector 18 3 He + ], 3 , . m 2 ' e m − / ν 107 ν e + 1 ]. Regardless, we will do a proposal- − ]. Then, in the light dark matter limit, + ¯ m 391 MeV are the nuclear masses. The H . 3 → Co [ H − 111 for tritium exposures of 100 g yr, 1 kg yr, − 3 e 112 60 m + [ e He + 8 spectra and half-lives are generally small. 2 m 2 ], 3 2808 2 / m λ  − 3  e 106 β → − / – 26 – e ' He + E 3 E H  Si [ He h 3 788 2 He 3 32 in figure . → ) 3 λ e 2 + ], ) allow tritium to capture incoming dark matter via m
H ] also use tritium, they need far less than PTOLEMY’s proposed m 4 + χ p 3 ,E − Λ 105 4.1 98
2 e π H → C[ 4 3 + 1 m 14 ) from above, we find the rate for tritium to absorb fermionic λ m / Z − ( 2 χ = 2 e 4.12 F m E Q 4 ≡ Λ λ | H σ 921 MeV and e 3 . ] and Project 8 [ ~p ) and ( | + 2 96 πm decays to Helium via 4.5 4 He refer to the nuclei (and not the atoms) of those isotopes. The Q-value 2808 3 − H 3 β region to those already considered above from the induced ' N χ H χ χ 3 m ρ m H and m 3 = To project the sensitivity of future tritium-based experiments, we again require the Using eqs. ( Tritium The largest experimental proposals with targets which can undergo a Fermi or Gamow- References for each isotope are While KATRIN [ R 11 12 this low- projected bounds on amount for theiroperator measurements parameter of space the which is electron not antineutrino’s already mass ruled out and by will LHC not constraints. probe charged current in a nucleus are difficultfor to such compute, corrections, for we tritium, map we these reproduce have been the well standard studied. neutrino To capture account cross section onnumber tritium of [ absorption events to be less than 10. To connect the projected sensitivities of Unlike in heavy elements where corrections due to the Fermi-Dirac distribution of nucleons Since the tritium nuclear transitionoperators is from contribute 1 to the fermionic absorption rate. dark matter is where charged current operators in eq. ( where for this decay is has also been recentto interest in measure using coherent a neutrino-atomindependent comparable scattering analysis exposure [ of below tritiumwhich when in only projecting depends an on experiment sensitivities the exposure to of the tritium. charged current signal to verify that none had significantsince exposures the of exposures these interesting required targets. to determine Teller transition are madePTOLEMY of which tritium. hopes The to proposal be with the the first largest experiment tritium exposure to is measure the C momentum suppressed. We systematically checked the most recent JHEP02(2020)134 , χ m ]. 103 , . It is interesting 102 2.2 ] on our UV completion and the lightest possible 59 – 27 – ] with these charged current interactions. This 103 , ] on the UV completion from section 102 59 ] expects to have an exposure of at least 100 g yr. We also MeV while remaining consistent with bounds from collider 99 190 eV consistent with dwarf spheroidal galaxies [ . ∼ χ χ m m ]. Also shown is the LHC bound [ 99 . Bounds from dark matter capture events on tritium inside an experiment with a 100 The neutral current operators induce dark matter velocity-independent nuclear recoils We present the generalfind that expressions future for (lowerachieve the threshold) sensitivity dark rates to matter as experimentssearches well employing and as lighter targets indirect study can above detection. the an kinematics. MeV, Due the We to bounds decay from rates indirect scaling detection with become large powers stringent. of However, these from a set of dimension-6broadly operators classified which into do “neutral not current” and conserveUV “charged dark current” completions matter varieties. which number We lead and present simple can tofor be these dark operators matter and decays, consider as bounds well from as indirect bounds searches comingat from distinct energies searches with at relative collider spacing experiments. and peaks which result in a distinguishable signal. 6 Discussion In this work, wematter comprehensively by nuclear consider targets signals at direct from detection the and absorption neutrino experiments. of These fermionic signals dark arise and 10 kg yr.show the PTOLEMY direct [ searches bound [ that with less than 1possible kg fermionic yr of dark tritium, matterprovides a further [ future motivation experiment to could pursue start proposals probing such the as lightest PTOLEMY. Figure 8 g yr, 1 kg100 yr, or g 10 yr kg [ fermionic yr dark exposure. matter For reference, PTOLEMY has a proposed exposure of at least JHEP02(2020)134 ) at (A.1) 3.3 from the decay of ,
γ 0 qv function in eq. ( θ decays for any element, δ + cos β v − χ the more promising candidate m qv − and θ 30 MeV. In addition, we make β − β cos . δ χ m ' , we find .
 1 2 v 2 v – 28 – O 1 + yields a differential scattering rate proportional to a 
χ 0 )). At v m − 3.7 O ν p decays in Hydrogen for Borexino and Super-Kamiokande. Due + + rates in heavier isotopes makes β R + decays are prominent signals that can be seen in almost any dark E β (see eq. (  , we need to evaluate the energy-conserving β R δ 2 E spectra in isotopes that are already unstable in a vacuum. Due to the lack of , the nuclear recoil of the daughter nucleus, a prompt β  e since evaluating it at 500 keV. To probe lower masses one can instead look for shifts in the kinematic
1 There is a host of current experiments which could discover dark matter from dedicated While induced In the presence of a dark matter background, the charged current operators can induce & v decays in otherwise stable isotopes. This yields multiple possible signals: the ejected χ O delta function in represents an exciting new class ofof signals dark that could, matter. in the near future, discover the nature A Neutral current rateTo at produce higher figure order such, different experiments couldspace. probe The complementary possibility unexplored ofor regions dark charged of matter current parameter which operators interactshave with further other the motivates concrete SM many physics through proposedWIMP goals. either future paradigm neutral experiments and As which into the the quest ocean for of dark light matter dark leads matter us scenarios, away fermionic from absorption the tritium-based experiment, such as PTOLEMY.the We find lightest that such possible experiments fermionic couldwhich probe interacts dark with matter the consistent SM through with these phase charged space currentanalyses operators. packing for bounds signals from the absorption of fermionic dark matter on nuclear targets. As matter or neutrinoheavy experiment, to they induce inevitably suchm require a dark transition matter puttingendpoint the that of rough is lower sufficiently existing bound or future on experiments the with such sensitivities targets, we of focused on the projected sensitivity of a direct and indirectprojections constraints for for induced 300to keV their shear size,space, we having find the these largest experiments potential impact can for probe heavier deep masses. into unexplored parameter the excited daughter nucleus,(unique and for further every isotope decay in ifpossible an its experiment) backgrounds. could unstable. be While searchedlarge one These for suppressions may correlated simultaneously in to consider signals reduce both for every element, other than Hydrogen.matter We and project neutrino sensitivity for experiments, a finding variety of powerful current sensitivities, dark easily surpassing current indirect detection constraints can inmatter principle be and fine-tuned neutrino away. experiments Regardless, can current similarly dark probe a largeβ unexplored parameter space. energetic constraints depend on the UV completion, while our projected sensitivities do not, so JHEP02(2020)134 ] 115 (A.6) (A.2) (A.3) (A.5) ]. It’s 117 . 2 , ) (A.4) min ] and not Run 3 [ min , v ) 82 | v>v ] for a review) e − ~v  v 71 1 v ( + θ  . . ~v ) at which the energy-conserving 2

χ j v χ v ( F − | m qv 2 j f m normalizes the velocity distribution θ v − A esc . We approximate the dark matter 3 −  j v
R  d ( R 2 R 0 M v θ ν Z R χ p /v χ # ME per target mass is 2 χ ν E 2 m ME ME 2 m 2 p 2 2 esc ) j | 2 2 m e 2 χ v √ T N ~v p 2 √ √ 0 − j ) is then v +  M + πm – 29 – v + + M 2 |M ( R ~v j 16 R ( E exp M O N E R −

0 550 km/s is the galactic escape velocity. Thus, the M = " E R esc 2 πv NC v = ' E 2 0 qv √ σ r 2 θ exp χ . A few additional comments are in order for some of these ). With this, we produce the differential scattering rates χ Xe, while KamLAND-Zen is 91%. χ − χ min esc − ρ 7 m ] ρ 1 54 v v m N cos 0 136 A.3 T M = /v R N j , and ) = R E esc ~v = 6 v ( , √ dR dE f χ ], which corresponds to a proton recoil threshold of 500 keV [ R 4 T erf [ 1 m dR dE  2 M 116 3 0 √ v 240 km/s is the Earth’s approximate galactic velocity (dominated by the 2 2 220 km/s, and / 3 q ' is given by eq. ( π ' e = v = 0 ν v min p v N : The differential scattering rate at v function’s argument vanishes. This cosine’s allowed range places a minimum condition underestimate Borexino’s exposure by assuming8-hr that exposure the only 3218 had daysis an which close 8-hr to had exposure. 70 at keV Borexino’s [ leastalso electron an worth equivalent noting energy that threshold light the yield. Carbon EXO-200 recoil is threshold 80% is too high thanks to its poor relative B Relevant current experiments Here we summarize thesensitivities in relevant figures details ofexperiments. all We current give experiments projectionssince for based Run which on we 2 Run project had 2 a of CDMSlite larger [ exposure and roughly the same threshold. We conservatively where from fermionic absorption off the few target isotopes in CRESST in figure to unity, Sun’s), differential scattering rate on a single isotope where where velocity distribution with a capped Maxwell distribution (see [ on The superscript indicates thatδ this is the value for cos where JHEP02(2020)134 ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] 78 84 1 , , 73 86 92 75 72 88 76 82 81 85 87 79 74 80 113 114 Refs. 77 83 th NR E 3.3 keV [ 500 keV [ I 13.6 keV [ 8 3 F 3 3 ) Xe — [ 3 54 136 crystals 100 eV [ crystals 307 eV [ O—[ 2 (CH crystals 100 keV [ 4 4 3 2 Xe in LS — [ H 6 54 136 . Experiments without an explicit nuclear recoil 7 – 30 – , and 817 t yr C 504 kg yr 233 kg yr Liquid 150 kg yr Liquid Xe 3 keV [ 86.3 kg yr TeO 6 171,000 t yr H , 4 β 2 ν ), which permits any use, distribution and reproduction in ν β β β NS 6726 kg day CsI[Na] 6.5 keV [ 2 2 2 ν ν ν ν ν CC-BY 4.0 This article is distributed under the terms of the Creative Commons , are not used for neutral current projections. th NR E . Experiments which can probe fermionic dark matter absorption signals for which we Super-Kamiokande COHERENT CE Borexino solar KamLAND-Zen 0 EXO-200 0 CUORE 0 XENON1T DM 1.0 t yr Liquid Xe 3 keV [ CDMSlite DM 70 kg day Ge crystals 0.4 keV [ SuperCDMS DM 577 kg day Ge crystals 1.6 keV [ PICO-60 DM 1167 kg day Superheated C PICO-60 DM 3420 kg day Superheated CF PandaX-II DM/0 NEWS-G DM 9.7 kg day Neon 720 eV [ LUX DM 91.8 kg yr Liquid Xe 4 keV [ EDELWEISS DM .0334 kg day Ge 0.06 keV [ DarkSide-50 DM 6786 kg day Liquid Ar 0.6 keV [ DAMIC DM 0.6 kg day Si CCDs 0.7 keV [ CRESSTIII DM 2.39 kg day CaWO CRESSTII DM 52 kg day CaWO Experiment Goal Exposure Target DE-SC0011637. Open Access. Attribution License ( any medium, provided the original author(s) and source are credited. We thank ArturTongyan Ankowski, Lin, Carlos Ian Blanco,and Moult, Tim Jason Maxim Detwiler, Cohen, Pospelov, Volodymyr Jackthe Tretyak, and capabilities Vetri Collins, of Velan, Lorenzo dark and Simon Ubaldi mattertract Lindley Knapen, detectors. for DE-AC02-05CH11231. Winslow JD for useful GE is input discussions, is supported on in supported part by by the the U.S. DOE Department under of con- Energy Award threshold, Acknowledgments Table 3 show projected sensitivities in figures JHEP02(2020)134 , ]. , , 398 Phys. , ]. SPIRE B 662 (2016) IN Phys. Rev. Phys. Rev. ][ , , SPIRE 117 IN ]. ][ Astrophys. J. , ]. Phys. Lett. , (2014) 171301 (2018) 063524 SPIRE ]. IN ]. ]. ]. SPIRE 113 ][ IN ]. Phases of cannibal dark Semiconductor probes of light D 97 days of data from the ][ ]. SPIRE Phys. Rev. Lett. arXiv:1607.07400 7 SPIRE SPIRE SPIRE ]. . , [ IN ]. 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