Direct Detection Signals from Absorption of Fermionic Dark Matter
DDirect Detection Signals from Absorption of Fermionic Dark Matter
Jeff A. Dror,
1, 2
Gilly Elor, and Robert McGehee
2, 1 Theory Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Berkeley Center for Theoretical Physics, University of California, Berkeley, CA 94720, USA Department of Physics, Box 1560, University of Washington, Seattle, WA 98195, U.S.A.
We present a new class of direct detection signals; absorption of fermionic dark matter. Weenumerate the operators through dimension six which lead to fermionic absorption, study theirdirect detection prospects, and summarize additional constraints on their suppression scale. Suchdark matter is inherently unstable as there is no symmetry which prevents dark matter decays.Nevertheless, we show that fermionic dark matter absorption can be observed in direct detectionand neutrino experiments while ensuring consistency with the observed dark matter abundance andrequired lifetime. For dark matter masses well below the GeV scale, dedicated searches for thesesignals at current and future experiments can probe orders of magnitude of unexplored parameterspace.
Introduction.
The search for dark matter (DM) israpidly expanding both theoretically and experimen-tally. Weakly interacting massive particle (WIMP) DMsearches have pushed the limit on the WIMP-nucleoncross-section near the neutrino floor for masses aroundthe weak scale [1–3]. These null results have sparked arenaissance in DM model building, in search of alterna-tive thermal histories which predict lighter DM [4–13].For masses below the GeV scale, DM which scatters offa target will typically deposit energy below the thresh-old of the largest direct detection experiments ( O (keV)),significantly relaxing the direct constraints.To discover these lighter DM candidates, the directdetection program is moving toward detecting smallerenergy deposits with novel scattering targets and lower-threshold detectors [14–23]. Current technology is al-ready sensitive to energy deposits of O (eV) [24] and newproposals could detect energy deposits of O (meV) [25–32]. As the direct detection program pushes the low-massfrontier, it can also broaden its searches for different sig-nals to increase its impact with little additional cost.Particle DM detection strategies can be grouped intotwo classes: scattering and absorption. Searches for scat-tering look for a DM particle depositing its kinetic en-ergy onto a target within the detector, typically a nu-cleus or an electron. In contrast, searches for absorptionlook for signals in which a DM particle deposits its massenergy. Absorption signals have primarily been consid-ered for bosonic DM candidates with studies of fermionicabsorption signals limited to induced proton-to-neutronconversion in Super-Kamiokande [33] and sterile neu-trino DM [34–41] (see also exothermic DM [42] and self-destructing DM [43] for related signals).In this Letter , we systematically study direct detectionsignals from the absorption of fermionic DM. We describenovel signals and their corresponding lowest-dimensionoperators; project the sensitivities of ongoing and pro-posed DM direct detection and neutrino experiments tothese signals; and demonstrate the consistency of thesesignals with the issues of DM stability and abundance.
Signals and operators.
For simplicity, we take DM( χ ) to be a Dirac fermion charged under lepton number,and impose only Lorentz, SU(3) C × U(1) EM , CP, leptonand baryon number symmetries. Baryon number conser-vation is necessary to avoid proton decays while leptonnumber allows the (Dirac) neutrino to remain light. Weenumerate operators in the effective theory with the fields { χ, n, p, e, ν, F µν } , where F µν is the EM field strengthtensor. We do not include other QCD resonances as theyhave no bearing on direct detection.Consider first dimension-6 operators of the form,[ ¯ χ Γ i ν ] (cid:2) ¯ ψ Γ j ψ (cid:3) , where ψ ⊃ { n, p, e, ν } and Γ i = { , γ , γ µ , γ µ γ , σ µν } denotes the different possibleLorentz structures of the bilinear. This “neutral cur-rent” operator generates the first class of new signals weconsider; (—) χ + T → (—) ν + T , where T is a target nucleusor electron which absorbs a fraction of the DM mass en-ergy. We will focus on nuclear absorption, where therates may be coherently enhanced, and leave the signalof (—) χ + e − → (—) ν + e − to future work [44].Next, consider dimension-6 operators of the form,[ ¯ χ Γ i e ] [¯ n Γ j p ]. This generates a class of “charged cur-rent” signals; (—) χ + AZ X → e ± + AZ ∓ X ∓∗ , in which DMinduces β ± decay in a nuclei (which may or may not bestable against β ± decay in a vacuum). This process po-tentially has multiple correlated signals: a detectable e ± ,a nuclear recoil, a prompt γ decay from the excited finalnucleus, and further nuclear decays if the final nucleus isunstable. Induced β + decays have significantly smallerrates relative to β − due to the Coulomb repulsion be-tween the emitted e ± and the nucleus, so we focus onDM-induced β − decays and leave the β + decays for fu-ture work [45] . The same charged current operators canalso shift the endpoint of the β ± distribution for nuclei β + decays induced by DM with m χ (cid:29) MeV were proposed forHydrogen targets in Super-Kamiokande [33]. a r X i v : . [ h e p - ph ] M a y which already undergo β ± decays in vacuum. While thismight be detectable at PTOLEMY [46, 47], these exper-iments are typically much smaller than those consideredin this work and have significant backgrounds and so wedeffer their study for future work [45].Finally, DM candidates which have fermionic absorp-tion signals will generically decay. At dimension-5,the operator ¯ χσ µν νF µν induces decays of χ as do thedimension-6 operators, ¯ χγ ν Γ (5) ∂ µ νF µν , where Γ (5) ≡{ , γ } . At higher dimensions, there exist operators al-lowing multiphoton decays. The single photon channelcan be detected with the usual line search, while themultiphoton channels are constrained by diffuse photonemission. Detectable fermionic absorption signals, con-sistent with indirect detection bounds, typically requirelighter dark matter as the decay rates scale with a largepower of m χ . We include a discussion of decays belowfor each signal and operator we consider. Neutral current signals: nuclear recoils
We first studythe process χ + N → ν + N, where N is a target nucleus.We will focus on two operators: O NC = 1Λ ¯ χγ µ P R ν (¯ nγ µ n + ¯ pγ µ p ) + h.c. . (1)These can arise from a theory of a heavy Z (cid:48) coupledto quarks and χ with some mixing between the righthanded components of χ and ν . The incoming χ is non-relativistic, so its mass dominates its energy resulting ina momentum transfer ( q ) and nuclear recoil energy ( E R ): q (cid:39) m χ , E R (cid:39) m χ M , (2)where M is the mass of the nucleus. For contrast, elasticscattering off a nucleus yields at most E R = 2 v µ /M, where µ is the reduced mass and v is the DM velocity(see [48] for a recent review). This 1 /v increase in E R relative to WIMP scattering allows searches for lighterDM with both direct detection experiments and higher-threshold, neutrino experiments.The differential rate of neutral current nuclear recoilsfrom absorbing fermionic DM is; dRdE R = N T ρ χ m χ |M N | πM δ ( E R − E R )Θ( E R − E th ) , (3)where N T is the number of target nuclei, ρ χ (cid:39) . / cm is the local DM energy density, E R ≡ m χ / M , E th is the experiment’s threshold, and |M N | is the matrix element squared (at q ) averaged over initialspins and summed over final spins. In elastic scattering,the spread in incoming DM velocities leads to a spreadof recoil energies, but in fermionic absorption, the rate issharply peaked at E R = E R . The position of the peakis distinct for every isotope present in the experimentand has a width (∆ E R ) determined by higher order cor-rections to Eq. (2), corresponding to ∆ E R /E R ∼ − . Since the recoil energy is independent of the DM veloc-ity, there are no modulation signals or rate uncertaintiesarising from the DM velocity distribution.The total rate for absorption by multiple nuclei is R = ρ χ m χ σ NC (cid:88) j N T,j A j F j Θ( E R,j − E th ) , (4)where N T,j , A j , E R,j , and F j , are the number, massnumber, recoil energy, and Helm form factor [67] (evalu-ated at momentum transfer, q = m χ and normalized to1) of target isotope j . The cross section per-nucleon is σ NC = m χ / (cid:0) π Λ (cid:1) . Absorption has the unique signatureof correlated, peaked counts in dR/dE R bins containing E R,j = m χ / (2 M j ) for the different target isotopes withmasses M j . This can be a powerful discriminator frombackgrounds since the relative heights and spacing of thepeaks is completely determined. Whether an experimentcan resolve these distinct peaks depends on its energyresolution and the mass splitting between the target iso-topes.For m χ (cid:46) MeV, future experiments are needed toprobe the neutral current signal due to the small nuclearrecoil energy. Detailed projections are challenging due tothe breadth of proposals and possible absorption by col-lective modes of nuclei, so we roughly estimate the sensi-tivity of such future detectors. We project the sensitivityof future experiments in Fig. 1 (
Left ) where, for simplic-ity, we require at least 10 events to set our projections,independent of mass or experiment. The cross sectionsare smaller than those in typical WIMP searches due tothe larger number densities of lighter DM. We considerHydrogen and Lithium targets with energy thresholdsof eV −
100 eV for 1 kg-year and 100 kg-year exposures(see [21] for one possible realization). Since there are twoisotopes in the Lithium target, the ability to detect twocorrelated signals is possible. For m χ ∼ MeV, Li gets E R ∼
90 eV and Li gets E R ∼
80 eV. These peaksshould be distinguishable by a detector with a 10 eV nu-clear recoil energy resolution. For m χ (cid:38) MeV, currentexperiments have sensitivity to the neutral current signalas shown in Fig. 1 (
Right ).Interestingly, which experiments best probe the neu-tral current absorption signal are not always the sameas those which best probe WIMPs (e.g., Borexino). Theedges in Fig. 1 are due to the distinct nuclear recoil en-ergies E R,j of each target isotope in an experiment. Forlarger DM masses, the nuclear recoil energy of each tar-get isotope in an experiment, E R,j , is larger than thethreshold energy E R,j > E th and the projected sensitiv-ity of an experiment is the greatest. For lighter DM E R,j decreases until, one by one, E R,j < E th , leading to eachexperiment losing sensitivity in abrupt steps.We now address the stability of χ . For concreteness, weconsider a model where a heavy Z (cid:48) couples in an isospin-invariant way to quarks, with gauge coupling g Z (cid:48) . Quark FIG. 1:
Left:
Projected sensitivities of future experiments to σ NC . We show two exposures (1/100 kgyr) of two different targetmaterials (Hydrogen in red and Lithium in blue) with three possible nuclear-recoil energy thresholds (1, 10, and 100 eV). Right:
Projected sensitivities of current experiments to σ NC , including CRESST III [49] and CRESST II [50] (“CRESST” in red);EDELWEISS-SURF [51] (orange); NEWS-G [52] (yellow); DAMIC [53] (lime); DarkSide-50 [54, 55] (green); CDMSliteR2 [56]and SuperCDMS [57] (“SuperCDMS” in aqua); PICO-60 run with C F [58] and PICO-60 run with CF I [59] (“PICO” insky blue); COHERENT [60, 61] (blue); Borexino [62] (navy blue); and LUX [2], PandaX-II [63], and XENON1T [64] (“Xenonexpts” in purple). Both panels include LHC bounds [65] and the indirect detection constraints from χ decay [66] for the Z (cid:48) model as described in the text. We show the decay constraints with different levels of fine-tuning between the UV and IRcontributions to kinetic mixing between the photon and Z (cid:48) . loops induce a kinetic mixing, (cid:15) , between the Z (cid:48) andthe photon of order (cid:15) ∼ g Z (cid:48) e/ π allowing the decay χ → νe + e − . Without additional Z or Z (cid:48) mass suppres-sions the decay χ → νγ is forbidden by gauge invari-ance while χ → νγγ is forbidden as a consequence ofcharge conjugation (also known as Furry’s theorem). For m χ (cid:46) MeV the electron channel is kinematically forbid-den and the dominant decay is χ → νγγγ , whose primarycontribution proceeds through a kinetic mixing and theEuler-Heisenberg Lagrangian. Estimating the DM decayrates in this simple UV completion, we find future ex-periments can quickly probe new parameter space whilecross-sections accessible to current experiment are ruledout by current indirect detection bounds [66].However, it is possible to suppress DM decays by fine-tuning the UV contribution to the kinetic mixing againstthe IR piece estimated here. Concretely, we define thisfine-tuning as F.T. ≡ | (cid:15) UV − (cid:15) | /(cid:15) and we show the fine-tuning necessary to evade indirect detection constraintswith dashed gray lines labeled “F.T.” in Fig. 1. We notethat the projected direct detection sensitivities in Fig. 1are insensitive to the details of the UV completion. Westudy ways to reduce the necessary fine-tuning by in-corporating flavor-dependent couplings to suppress (cid:15) infuture work [45].Also shown in Fig. 1 are direct constraints from LHCmono-jet searches on the Z (cid:48) model, which bound newneutral currents below the TeV scale [65]. Cosmologi-cal bounds depend on initial conditions (e.g., the reheat temperature) and the UV completion. We only com-ment that for the parameter space relevant for the neutralcurrent, the freeze-in contribution from the operators inEq. (1) reproduces the correct DM abundance for reheattemperatures below a GeV. Alternatively, one may con-sider freeze-out by incorporating additional interactions.We leave the question of relic abundance for different ini-tial conditions and UV completions to future work [45]. Charged current signals: DM-induced β − decays Next, consider signals from χ + AZ X → e − + AZ +1 X + ∗ (orat the nucleon level, χ + n → p + e − ), which we refer toas an induced β − decay. This process can cause stableelements to become unstable in the presence of DM if m χ is large enough to overcome the kinematic barrier. Sucha signal may proceed through the dimension-6 chargedcurrent vector operator, O CC = 1Λ [ ¯ χγ µ e ] [¯ nγ µ p ] + h.c. . (5)This can be generated by a W (cid:48) which can appear if theelectroweak gauge group is embedded in a large gaugegroup which subsequently breaks in to the SM.In the present work, we consider the vector operator inEq. (5) to leverage known results from the neutrino andnuclear physics literature. The vector-vector interactionprimarily induces Fermi transitions which are character-ized by their conservation of spin ( J ) and parity ( P ) ofthe nucleus [68], also known as J P → J P transitions.However, we emphasize that the DM induced β − decaysignal is more general, with different vertex structuresallowing different transitions. We leave a study of addi-tional interactions to [45].Denoting the mass of a nucleus of mass number A andatomic number, Z , by M A,Z , we focus on isotopes whichsatisfy M A,Z < M ( ∗ ) A,Z +1 + m e , such that the nucleus isstable against β − decay in a vacuum (the ( ∗ ) is includedto emphasize the daughter nucleus may be in an excitedstate, typically 200 keV − β − decay is kinematically allowed if m χ > m β th ≡ M ( ∗ ) A,Z +1 + m e − M A,Z . (6)In these induced decays, χ is absorbed by the target nu-clei and transfers the majority of its rest mass to theoutgoing electron. In the limit where m χ − m β th (cid:29) m e ,the electron and nuclear recoil energies are analogues tothe neutral current case with m χ → m χ − m β th , and aregiven by; E R (cid:39) (cid:40) m χ − m β th (electron) (cid:0) m χ − m β th (cid:1) / M ( ∗ ) A,Z +1 (nucleus) . (7)Therefore, the energetic outgoing electron will shower inthe detector, and can be searched for. The nuclear recoilenergy, as with the neutral current case, is independent ofDM velocity, and can be searched for as well. Additionalcorrelated signals result from the possible de-excitationof the daughter nucleus and of the subsequent decay of AZ +1 X (typically many days later). These multiple signalsmake possible correlated searches to reduce backgrounds.The specific signals depend on the experiment, the par-ticular isotope, and the DM mass.The rate for DM-induced β − decays is; R = ρ χ m χ (cid:88) j N T, j ( A j − Z j ) (cid:104) σv (cid:105) j , (8)where we sum over all isotopes in a given target material, N T, j is the number of target isotope j , and (cid:104) σv (cid:105) j is thecorresponding velocity averaged cross-section, which fora given isotope is (cid:104) σv (cid:105) j = | (cid:126)p e | j πm χ M A j ,Z j |M N j | , (9)where | (cid:126)p e | j = ( m β th , j − m χ )( m β th , j − m χ − m e ) is theelectron’s outgoing 3-momentum in the center of massframe (which is approximately the lab frame), in the limitthat m e , m χ , m β th , j (cid:28) M A j ,Z j . The amplitude M N is forabsorption by the whole nuclei (the momentum transferis not enough to resolve individual nucleons), which canbe related to the nucleon level amplitude M (with thespinors are normalized to p µ p µ = M A j ,Z j ) through theFermi function, F ( Z, E e ) and a form factor, F V ( q ): M N = (cid:112) F ( Z + 1 , E e ) F V ( q ) M . (10) FIG. 2: Projected sensitivities to m χ / π Λ from a ded-icated search for the charged current induced β − transi-tion at Cuore [69] (red); LUX [2], PandaX-II [63], andXENON1T [64] (“Xenon DM expts” in purple); EXO-200 [70] and KamLAND-Zen [71] (“Xenon 0 νββ expts” in skyblue); SuperKamiokande [72] (yellow); CDMS-II [73] (aqua);DarkSide-50 [54, 55] (green); and Borexino [62] (navy blue).Also shown are LHC bounds [74] and indirect constraints from χ decays in our simple UV model [66]. The Fermi function accounts for the Coulomb attractionof the ejected electron and can enhance the cross-sectionby several orders of magnitude for heavier elements. Theform factor is equal to 1 for small momentum transferrelative to the nucleon mass, q (cid:28) m n , while for larger q the dependence can be extracted from the neutrinoliterature [75]. In principle, (9) must contain a sum overall possible nuclear spin states. The assumption madehere is that this sum will be dominated by ∆ J P = 0transitions as is the case of a vector coupling [68]. Ex-citation of additional final states is possible if q (cid:38) r − N ,where r N (cid:39) . A / fm is the nuclear radius [76], howeverfor simplicity we focus on lighter masses such that thesedo not contribute significantly to the rate for any isotopeconsidered here.The total rate is found by summing over the contri-butions from each isotope. Evaluating (9) in the limitwhere m e , m χ , m β th (cid:28) M A,Z , the total rate is; R = ρ χ m χ (cid:88) j N T,j ( A j − Z j ) | (cid:126)p e | j F ( Z j + 1 , E e )2 π Λ ( m χ − m β th , j ) , (11)where we have integrated over all energies with the as-sumption that such a signal could be detected by mostexperiments under consideration here given the multi-tude of correlated high energy signals.We project the sensitivity of current experiments to thecharged current signal in Fig. 2 where we again requireat least 10 events to set our projections, independent ofisotope mass or experiment. Sensitivities are displayed interms of the theoretically interesting quantity m χ / π Λ (to which Eq. (9) reduces in the limit of large M A j ,Z j and m χ (cid:29) m β th , j , modulo the Fermi function). As withthe neutral current case, limits depend on the differentisotopes in a given experiment. In particular, the kinksin Fig. 2 occur at m χ ∼ m β th , j for every relevant isotopein a given experiment.To estimate the DM decay constraints from a typicalUV completion, we consider a model with a W (cid:48) coupledvectorially to up and down quarks without any directcouplings to leptons. When kinetically available, thedominant decay is χ → e + e − ν which arises from a ki-netic mixing between W (cid:48) and the SM W boson of order ∼ g W (cid:48) e/ π . We estimate the decay rate and show theresulting indirect constraints [66] in gray in Fig. 2. Thedecay bounds are much weaker than in the neutral cur-rent case as they are suppressed by both the weak scaleand the W (cid:48) mass.In addition to decays, there are direct bounds fromLHC searches for pp → (cid:96)ν . A search was done by CMSat 8 TeV looking for helicity-non-conserving contact in-teraction models which have contact operators with ver-tex structure different than that of the SM [74] whichsets a powerful constraint on the charged current opera-tors. For the W (cid:48) model this constraint corresponds to ascale in 5 of Λ (cid:38) . V − A gauge structureof the SM [77, 78] and for light fermions in charged piondecays: π ± → e ± χ [79], but find they are subdominantto the CMS constraint. Cosmological constraints requiredetailed assumptions about the initial conditions and thefull set of interactions. However, due to the extended pa-rameter space of the charged current signal relative to theneutral current, freeze-in becomes a more palatable op-tion requiring reheat temperatures around the TeV scaletoward the bottom of Fig. 2. Discussion
In this
Letter , we have introduced a novelclass of signals from fermionic DM absorption in directdetection and neutrino experiments. We have studied thesensitivities of future and current experiments to neu-tral current signals from the process χ + N → ν + N,as shown in Fig. 1. This neutral current causes tar-get isotopes to recoil with distinct energies and corre-lated rates, enabling significant background reduction insearches. We have also studied the sensitivities of cur-rent experiments to induced β − decays from the process χ + AZ X → e − + AZ +1 X + ∗ , as shown in Fig. 2. This chargedcurrent enjoys distinct signatures from a sequence ofevents starting with a nuclear recoil and ejected e − , fol-lowed by a likely γ decay and often a final β decay orelectron capture event several days later. For both sig-nals, ongoing experiments can probe orders of magnitudeof unexplored parameter space by performing dedicatedsearches. Without yet knowing the true nature of DM, it is im-possible to know how it will appear in an experiment.Perhaps, it has been a fermion, depositing its mass en-ergy into unsuspecting targets all along.We thank Artur Ankowski, Carlos Blanco, Tim Cohen,Lawrence Hall, Simon Knapen, Tongyan Lin, Ian Moult,Maxim Pospelov, Harikrishnan Ramani, Tien-Tien Yu,and Zhengkang Zhang for useful discussions, and VetriVelan, Jason Detwiler, and Lindley Winslow for input onthe capabilities of DM direct detection and neutrino ex-periments. We also thank Yonit Hochberg, Tongyan Lin,Lorenzo Ubaldi, Lindley Winslow, and Tien-Tien Yu forhelpful comments on the manuscript. JD is supported inpart by the DOE under contract DE-AC02-05CH11231.GE is supported by U.S. Department of Energy, undergrant number de-sc0011637. RM was supported by theNational Science Foundation Graduate Research Fellow-ship Program for a portion of this work. [1] A. Tan et al. (PandaX-II), Phys. Rev. Lett. , 121303(2016), 1607.07400.[2] D. S. Akerib et al. (LUX), Phys. Rev. Lett. , 021303(2017), 1608.07648.[3] E. Aprile et al. (XENON), Phys. Rev. Lett. , 181301(2017), 1705.06655.[4] K. Griest and D. Seckel, Phys. Rev. D43 , 3191 (1991).[5] M. Pospelov, A. Ritz, and M. B. Voloshin, Phys. Lett.
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