Cosmic-Ray Upscattered Inelastic Dark Matter

MI-HET-758 Cosmic-ray Upscattered Inelastic Dark Matter Nicole F. Bell,1, ∗ James B. Dent,2, y Bhaskar Dutta,3, z Sumit Ghosh,3, x Jason Kumar,4, { Jayden L. Newstead,1, ∗∗ and Ian M. Shoemaker5 1ARC Centre of Excellence for Dark Matter Particle Physics, School of Physics, The University of Melbourne, Victoria 3010, Australia 2Department of Physics, Sam Houston State University, Huntsville, Texas 77341, USA 3Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843,USA 4Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA 5Center for Neutrino Physics, Department of Physics, Virginia Tech University, Blacksburg, Virginia 24601, USA Light non-relativistic components of the galactic dark matter halo elude direct detection constraints because they lack the kinetic energy to create an observable recoil. However, cosmic-rays can upscatter dark matter to significant energies, giving direct detection experiments access to previously unreachable regions of parameter-space at very low dark matter mass. In this work we extend the cosmic-ray dark matter formalism to models of inelastic dark matter and show that previously inaccessible regions of the mass-splitting parameter space can be probed. Conventional direct detection of non-relativistic halo dark matter is limited to mass splittings of δ ∼ 10 keV and is highly mass dependent. We find that including the effect of cosmic-ray upscattering can extend the reach to mass splittings of δ ∼ 100 MeV and maintain that reach at much lower dark matter mass. I. INTRODUCTION threshold. This relativistic population can thus provide the leading channel at direct detection experiments. Until recent years low-mass dark matter (DM) was rel- Although non-relativistic inelastic DM scattering has atively unconstrained by direct detection experiments. been studied in-depth in the context of the DAMA ex- The difficulty low-mass DM presents is that the recoil cess, inelastic scattering is in fact a generic feature of energy deposited is proportional to the DM mass, typi- some classes of DM models. As an illustrative exam- cally falling below the detector threshold for masses less ple, we can consider DM which couples to the Standard than a few GeV. While low-threshold detector technolo- Model (SM) by exchange of a dark photon. The DM gies have made advances in recent years, new analysis vector current can only be non-vanishing if the DM is a strategies have lead the field in constraining low-mass complex degree of freedom. But if the continuous sym- DM [1{32]. Two particularly useful strategies, which metries under which the DM is charged are all sponta- have been the subject of several recent studies, are the neously broken, then the DM generically splits into two Migdal effect [18, 23, 32{40] and cosmic-ray boosted dark real degrees of freedom, and the vector current is neces- matter (CRDM) [19, 41, 42]. These studies have all fo- sarily off-diagonal, mediating inelastic scattering. cused on elastic nuclear scattering. However, inelastic Previous model building efforts of inelastic DM have DM scattering is a generic feature of many classes of DM focused on small mass splittings, motivated by a desire to models [43{61]. Here we explore the prospects for inelas- either explain an experimental anomaly or to stay in con- tic DM detection within the CRDM paradigm. tact with experimentally accessible signals. More gener- In the CRDM paradigm, rather than finding a channel ally, there is no reason to presuppose that the mass split- through which small energy depositions can be detected arXiv:2108.00583v1 [hep-ph] 2 Aug 2021 ting be O(keV). In the example given above, the mass (e.g. Migdal electrons), one instead finds a population splitting need only be small relative to the symmetry of fast moving DM which can yield larger energy deposi- breaking scale and could easily be O(MeV-GeV). Such tion. When energetic cosmic rays (mostly protons) scat- large mass splittings are inaccessible to non-relativistic ter off non-relativistic DM particles in the halo, they can direct detection experiments and have only been probed produce a small population of relativistic DM. If these in collider experiments [59, 62]. relativistic DM particles scatter at a direct detection ex- periment, then the deposited energy can be well above For CRDM, the initial inelastic upscattering process can have a much larger center-of-mass energy, dictated by the cosmic-ray energies available in the interstellar medium. As a result, much larger mass splittings are ac- ∗ [email protected] cessible in this scenario as compared to the standard nu- y [email protected] z [email protected] clear recoil case. Given the long path-length from cosmic- x [email protected] ray upscatter to the detector, we consider two cases: one { [email protected] in which all upscattered particles reach the Earth before ∗∗ [email protected] decaying where they exothermically scatter in a detector, and one in which all upscattered particles decay before 10-6 reaching the detector, where they endothermically scat- elastic mχ1 = 100 MeV δ=0.1 MeV ter. mA = 1 GeV ) δ=1 MeV The plan of this paper is as follows: in Section II, we 1 -7 gχgN = 0.5 - 10 δ=10 MeV s derive the energy spectrum of CR-upscattered inelastic 2 - δ=100 MeV DM (CRiDM). In Section III we present the recoil spec- cm ( trum arising from the inelastic scattering of CRiDM, and χ 10-8 dT comment on the distinguishability of the scenarios under / ϕ consideration. In SectionIV, we describe the bound on d χ CRiDM which are placed by XENON1T. Lastly, in Sec- T 10-9 tionV, we conclude with a discussion of our results and future avenues. 10-10 CRDM flux, II. COSMIC-RAY UPSCATTERING OF INELASTIC DM 10-11 10-5 10-4 10-3 10-2 10-1 100 101 CRDM kinetic energy,T (GeV) The direct detection of DM relies on a non-zero cross χ section for the DM scattering on nucleons or electrons. 10-2 m = 1 MeV elastic Consequently, there is also the possibility that DM can χ1 δ=0.1 MeV first be upscattered by cosmic-rays before it reaches the -3 mA = 1 MeV 10 -3 δ=1 MeV ) gχgN = 10 1 detector [19]. Light DM candidates (below a GeV) can - δ=10 MeV s 2 δ=100 MeV be upscattered to relativistic energies, making their re- - 10-4 cm coils visible to experiments that were previously insensi- ( χ tive to them. Previous analyses have explored CRDM in -5 dT 10 / the context of simplified models [41], scattering on elec- ϕ d trons [22], and inelastic hadronic scattering [42]. In this χ -6 work we consider the effect of inelastic scattering due to T 10 the DM candidate which couples to nucleons. Since we will consider processes in which the center- 10-7 of-mass energy may be much larger than the mass of the CRDM flux, mediating particle, it will be necessary to provide a model 10-8 for DM-SM interactions beyond the contact approxima- tion. For simplicity, we assume that dark sector particles 10-9 10-5 10-4 10-3 10-2 10-1 100 101 are two Majorana fermions, χ1;2 (mχ2 − mχ1 ≡ δ > 0), which couple to a spin-1 particle (A0) through an inter- CRDM kinetic energy,T χ (GeV) 0 µ µ 0 action gχAµ(¯χ2γ χ1 − χ¯1γ χ2). A also couples to nu- 0 µ FIG. 1. Sample spectra of dark matter after upscattering by cleons through an interaction gN Aµnγ¯ n. In particular, we consider the case in which A0 couples to protons and cosmic rays (χ2, dashed) and after subsequently decaying (χ1, solid). The approximate non-relativistic total cross sections neutrons with equal strength. −31 2 these couplings correspond to is:σ ~0 = 10 cm andσ ~0 = Note that there are some important consistency con- 5 × 10−30cm2, for the top and bottom respectively. ditions associated with this effective interaction, in order to ensure that it arises from a consistent theory. For example, if the coupling gN remains fixed, then in the limit mA0 ! 0 the gauge symmetry is unbroken, and one must have δ ! 0 as a result of gauge-invariance. More gen- erally, in order for our tree-level calculation of the cross section to be consistent, one should require g . 1, and δ mχ=g. The latter condition ensures that the Yukawa . 3 couplings which generate the mass splitting are also per- where ρχ = 0:3 GeV=cm is the local DM density, and LIS turbative. In our subsequent analysis, we will focus on dΦi =dTi is the local interstellar flux of the ith species regions of parameter space where these constraints are of incident cosmic-rays (here we include contributions satisfied. from protons and helium only, with the spectra taken The double-differential rate of cosmic-rays scattering from [63]). Ti is the incoming CR kinetic energy and Tχ2 on DM within an infinitesimal volume element is is the outgoing DM kinetic energy. σχi(Ti;Tχ2 ) is the cross section for scattering of DM with the ith cosmic 2 LIS d Γ ρχ dσχi dΦ ray species. The total upscattered DM flux at Earth is = i dV; (1) obtained by integrating this over the relevant volume and dTidTχ2 mχ1 dTχ2 dTi 2 cosmic-ray spectrum, which are the maximum and minimum kinetic energy of max the incoming cosmic ray, such that it is kinematically Z Z Ti 3 dΦχ2 dV d Γ possible for the outgoing χ2 to have kinetic energy Tχ2 : = 2 dTi ; (2) dTχ 4πd min dTidTχ dV 2 V Ti 2 max Z Ti LIS To account for the variation in the DM density ρχ dσχi dΦi = Deff dTi ; (3) throughout the diffusion zone, within which the cosmic- min mχ1 T dTχ2 dTi i ray flux is assumed to be constant, an effective diffusion zone parameter D is found by integrating over the where Deff is an effective diffusion zone parameter.

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