PHYSICAL REVIEW D 99, 103003 (2019)
Monochromatic dark neutrinos and boosted dark matter in noble liquid direct detection
David McKeen and Nirmal Raj TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada
(Received 20 December 2018; published 13 May 2019)
If dark matter self-annihilates into neutrinos or a second component of (“boosted”) dark matter that is nucleophilic, the annihilation products may be detected with high rates via coherent nuclear scattering. A future multi-ten-tonne liquid xenon detector such as DARWIN, and a multi-hundred-tonne liquid argon detector, ARGO, would be sensitive to the flux of these particles in complementary ranges of 10–1000 MeV dark matter masses. We derive these sensitivities after accounting for atmospheric and diffuse supernova neutrino backgrounds, and realistic nuclear recoil acceptances. We find that their constraints on the dark neutrino flux may surpass neutrino detectors such as Super-Kamiokande, and that they would extensively probe parametric regions that explain the missing satellites problem in neutrino portal models. The XENON1T and BOREXINO experiments currently restrict the effective baryonic coupling of thermal boosted dark matter to ≲10–100× the weak interaction, but DARWIN and ARGO would probe down to couplings 10 times smaller. Detection of boosted dark matter with baryonic couplings ∼10−3–10−2× the weak coupling could indicate that the dark matter density profile in the centers of galactic halos become cored, rather than cuspy, through annihilations. This work demonstrates that, alongside liquid xenon, liquid argon direct detection technology would emerge a major player in dark matter searches within and beyond the WIMP paradigm.
DOI: 10.1103/PhysRevD.99.103003
I. INTRODUCTION ARGO are billed to be “ultimate detectors” in the direct search for dark matter. By virtue of their large exposures, The hunt for the identity of dark matter is a most riveting they are expected to set the best limits on the dark matter- endeavor. Particle dark matter may reveal itself in products nucleon scattering cross section, probing all the way down of its self-annihilations, in target recoils in scattering to the high-energy “neutrino floor”, i.e., the irreducible experiments, or as missing momenta in colliders. Anni- background of neutrino fluxes from the atmospheric hilation signals hold particular interest because they may scattering of cosmic rays and from relic supernovae. By contain information about the primordial thermal history of virtue of the large dark matter fluxes they would admit, they dark matter, and in particular, how much of its measured would also set the best limits on the dark matter mass, abundance it owes to freezing out of equilibrium in the probing up to and beyond Planck masses [8]. In this work, early Universe. Conservative upper bounds on the total we show that these experiments are also poised to become a annihilation cross section of dark matter may be placed by leading probe of the neutrino flux from dark matter constraining the flux of neutrinos, since they are the least annihilations. We shall henceforth call neutrinos produced detectable Standard Model (SM) states [1,2]. in this way “dark neutrinos”. The future of dark matter searches will depend crucially As we will discuss below, the annihilation channel χχ¯ → on direct detection with a panoply of noble liquid detectors, νν¯ has been constrained using data from large-volume proposed with a view of achieving exposures of Oð10Þ– neutrino detectors [2,9]; we show that DARWIN and ARGO Oð1000Þ tonne-years. These are the xenon-based XENONnT sensitivities would compete with and better them in the [3], LUX-ZEPLIN [4] and the multi-10-ton DARWIN [5], the ∼10–1000 MeV dark matter mass range. This is not argon-based DARKSIDE-20K [6], and a multi-100-ton liquid entirely surprising; while neutrino detectors admit larger argon detector recently christened “ARGO” [7].DARWIN and fluxes and exposures by construction, noble liquid direct detection experiments enjoy enhanced rates thanks to coherent scattering with large nuclei. Moreover, search Published by the American Physical Society under the terms of channels at neutrino detectors are typically sensitive to only the Creative Commons Attribution 4.0 International license. ν ν¯ Further distribution of this work must maintain attribution to e and/or e flavors, which may make up but a fraction of the author(s) and the published article’s title, journal citation, the dark neutrino flux, whereas the coherent nuclear and DOI. Funded by SCOAP3. scattering channel at direct detection is equally sensitive
2470-0010=2019=99(10)=103003(13) 103003-1 Published by the American Physical Society DAVID MCKEEN and NIRMAL RAJ PHYS. REV. D 99, 103003 (2019) to the flavors νe, ν¯e, νμ, ν¯μ, ντ, ν¯τ. These features have been scintillator neutrino detector BOREXINO already outper- exploited to determine direct detection sensitivities to formed those of Ref. [20] from LUX, for dark matter signals of neutrinos from a future core-collapse supernova masses of 100–1000 MeV. Then we show that for burst [10–13], solar neutrinos [14–17], geoneutrinos [18], present-day annihilations of dark matter with a thermal and products of dark matter decay [19] and annihilations cross section, couplings as weak as the weak interaction [20]. Reference [20] used a LUX dataset with 0.027 tonne- may be probed by DARWIN and ARGO, improving on years of exposure to constrain dark neutrinos, but we find Ref. [20]’s limit on the couplings by a factor of ∼500. that these constraints were weaker than those derived from We also argue that detecting boosted dark matter with tiny neutrino experiments in [2,9]; the ∼100–1000 tonne- baryonic couplings may hint at a solution to the “core- year tonne-year data sets at DARWIN and ARGO would cusp” problem and show the relevant parameter space that reverse this hierarchy of bounds. may be probed. Amusingly, a dark neutrino flux could produce a new This paper is laid out as follows. In Sec. II, we derive the neutrino floor emerging ahead of the discovery of the fluxes and event rates, including a careful treatment of standard neutrino floor. Yet, direct detection may not be backgrounds from atmospheric and diffuse supernova able to untangle dark neutrino signals from other exotic neutrinos, and nuclear recoil acceptances essential for sources of neutrinos, such as decaying dark matter [19]. rejecting electron recoil backgrounds from solar neutrinos. Moreover, annual modulation signals are absent. Therefore We then translate these to projected sensitivities and the true discovery of dark neutrinos would entail corrobo- compare with bounds at neutrino detectors such as rating signals at neutrino detectors, which have the ability Super-Kamiokande. In Sec. III, we interpret these results to point to the source of the flux, in our case the Galactic in terms of the neutrino portal model and boosted dark center. This is an advantage when searching for electrically matter. We conclude and discuss future possibilities neutral particles such as neutrinos and photons that are in Sec. IV. produced in the annihilation of dark matter, for the propagation of charged particles would require additional II. FLUXES, SIGNAL RATES, AND SENSITIVITIES astrophysical input such as the effect of magnetic fields, emission of diffuse gamma rays and synchrotron radiation, In this section we estimate the flux of dark neutrinos and and so on. boosted dark matter from Galactic and extragalactic anni- Dark neutrino fluxes arise naturally in neutrino portal hilations of dark matter, which we will use to obtain dark matter models [21–23]. When interpreting our con- scattering rates at xenon and argon detectors. We then straints in terms of this setup, parametric regions that could derive the sensitivities to these fluxes at DARWIN and ARGO, potentially explain the “missing satellites” problem of accounting for realistic event acceptances and irreducible structure formation can be probed extensively. In these neutrino backgrounds. We compare these with bounds from models the local nonrelativistic population of dark matter scattering on nucleons at XENON1T and BOREXINO, and itself scatters with nucleons in direct detection experiments; from other processes at neutrino experiments. however this proceeds through a loop-induced coupling to the Z boson, and the rate is suppressed. Thus, this is an A. Fluxes example of a theory where direct detection could find dark matter not so directly, but rather by detecting its “friends” The differential flux of dark neutrinos or boosted dark such as its annihilation products. Such a detection scenario matter from Galactic annihilations is given by is also a generic prediction of the assisted freeze-out mechanism [24]. In this framework, dark matter maintains 2Φ ρ 2 σ d η r⊙ DM;⊙ J h annvi dN thermal equilibrium with the primordial plasma even ΔΩ ¼ 4π ann 2 ; ð1Þ d dEν mDM dEν though its annihilation products do not belong to the SM, but rather scatter efficiently with SM states. This possibility has given rise to a growing literature on the prospects of where η ¼ 1=2 accounts for dark matter not being self- laboratory detection of these annihilation products, called conjugate, r⊙ ¼ 8.33 kpc is the distance of the Sun from −1 “boosted dark matter” [20,25–40]. While most of these the Galactic center, the ð4πÞ accounts for isotropic ρ 0 4 3 efforts have focused on signals at neutrino experiments, a emission, DM;⊙ ¼ . GeV=cm is the dark matter density few such as [20,35,39] have also focused on discovery at at the solar position [41], mDM is the dark matter mass, σ direct detection experiments. h annvi is the thermally averaged annihilation cross section 2δ − Reference [20] in particular explored boosted dark of dark matter, and dN=dEν ¼ ðEν mDMÞ is the matter with nucleophilic couplings, producing elastic (monochromatic) energy spectrum of dark neutrinos or J nuclear recoils in direct detectors. We will interpret our boosted dark matter. The dimensionless factor ann flux sensitivities in terms of this scenario as well. We will accounts for integrating over the dark matter distribution first show that bounds from proton recoils in the liquid in the line of sight for an angular direction,
103003-2 MONOCHROMATIC DARK NEUTRINOS AND BOOSTED … PHYS. REV. D 99, 103003 (2019) Z qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 2 2 (Galactic þ extragalactic) flux presented in [47]. This J ¼ ρ r⊙ − 2sr⊙ cos θ þ s ds: ann ρ2 DM approach neglects redshifts in momenta, i.e., the annihila- r⊙ DM;⊙ l:o:s: tion products are still taken as monochromatic. For this J We use the interpolation functions for ann provided in reason we do not include the extragalactic flux when [42] to integrate over the 4π sky and obtain for the Navarro- displaying our main results, and only use it to visualize Frenk-White halo profile1 [44], our optimistic sensitivities. Contributions to the flux may also stem from dark matter σ 100 2 density enhancements around intermediate mass black Φ 5 6 10−2 −2 −1 h annvi MeV ¼ . × cm s −25 3 ; holes [48–52], but we will not pursue this possibility. 10 cm =s mDM 2 ð Þ B. Coherent scattering rates σ where we have normalized h annvi to the thermal cross We now determine the cross sections and scattering event section in this range of dark matter masses [45]. rates of dark annihilation products at our detectors, treating Anticipating an interpretation of our results in terms of a the cases of dark neutrinos and boosted dark matter model where dark matter couples dominantly to the tau simultaneously. In addition to coherent nuclear scattering, neutrino, we will display our main results assuming that dark neutrinos also undergo electron scattering at direct dark neutrinos are produced exclusively through the chan- detection; however the rates are many orders of magnitude nel χχ¯ → ντν¯τ. We will also briefly discuss the possibility smaller (see, e.g., [10]), and therefore we will not consider that dark matter annihilates to neutrino mass eigenstates, electron recoil signals in our study. m N Z χχ¯ → νiν¯i (i ¼ 1, 2, 3) with branching fractions propor- For a target nucleus with mass T, neutrons and tional to the squared neutrino masses. This could happen, protons, the differential coherent scattering cross section is e.g., in models where neutrino masses are generated by the given by [53] breaking of lepton number symmetry. In either scenario, the σ 2 flavor content of the dark neutrinos after propagation d GT 2 1 − mTER 2 ðEν;ERÞ¼4π QWmT 2 F ðERÞ; ð3Þ through astrophysical distances and arrival at Earth is dER 2Eν irrelevant for coherent scattering at direct detection experi- − 1 − 4 2 θ 2 θ 0 2387 ments. It would, however, be important for neutrino where QW ¼ N ð sin WÞZ, with sin W ¼ . experiments, where searches depend on the flavor of the the weak mixing angle at low energies [54], and GT is a neutrinos and/or antineutrinos being detected. coupling strength that depends on both the annihilation The total flux of dark neutrinos or boosted dark matter product and target element, given by [55] could also receive a contribution from dark matter anni- hilations in extragalactic sources. These may be divided GF for dark neutrinos; G ¼ pffiffiffi into unclustered and clustered populations. The unclustered T 2 GBððN þ ZÞ=QWÞ for boosted dark matter: contribution is trivially negligible: the ðcosmic densityÞ2 of ð4Þ dark matter is ∼10−10× the ðlocal densityÞ2. The exact contribution of the clustered population depends sensitively −5 −2 Here G ¼ 1.1664 × 10 GeV is the Fermi constant, and on the astrophysical modeling of enhancement factors from F G is an effective baryonic coupling of boosted dark matter, halo substructure. For instance, using the redshift-depen- B whose origins we spell out in Sec. III B. The above equation dent enhancement factors in [46], we find that the extra- implies that, for boosted dark matter, G =G ¼f2.471; galactic flux is Oð10Þ smaller than the Milky Way flux for T B 2.670; 31.288 for the target nuclei 132Xe; 40Ar; 1H . the case of noninteracting dark matter. For the case of dark g f54 18 1 g matter interacting strongly with dark neutrinos, a scenario The nuclear form factor FðERÞ is best parametrized by that we consider in Sec. III A, Ref. [46] finds that this flux the Helm form factor [56] for the momentum transfers we is smaller by one more order of magnitude. are concerned with and is given by However, Ref. [47] has determined that the extragalactic j1 qr 2 2 3 ð nÞ −q s =2 flux is comparable to the Galactic one, by using different FðERÞ¼ e ; ð5Þ models of substructure enhancement. In what follows, qrn we will show the possible sensitivities of our detectors where j1 is the spherical Besselffiffiffiffiffiffiffiffiffiffiffiffiffiffi function, s ¼ 0.9 fm is the obtainable from such a flux. To do so, we simply p2 nuclear skin thickness, q ¼ mTER is the momentum rescale our Galactic flux in Eq. (2) with the total 2 7 2 2 2 1=2 transfer, and rn ¼ðc þ 3 π a − 5s Þ parametrizes the nuclear radius, with c and a ¼ 1.23 A1=3 − 0.6 fm and 1Using a different halo profile could change the flux slightly, e.g., a cored Burkert profile that is shown to be consistent with 0.52 fm respectively. σ Milky Way data [43], gives a 4π-sky flux that is ≃0.55 times In the left panel of Fig. 1 we show d =dER versus ER smaller than the NFW profile. with xenon and argon targets, for neutrino energies 30 MeV
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FIG. 1. Left. Differential cross section for coherent scattering of neutrinos with xenon and argon nuclei, for neutrino energies 30 MeV and 300 MeV. Argon, being lighter, recoils to higher energies. The effect of the Helm form factor, which suppresses the cross section at high recoil energies, is seen here as a bump in the cross section and is only important at recoil energies ≳103 keV—which far exceeds 2 the cutoff ∼10 keV below which we accept events for our study. Right. The scattering rate of dark neutrinos [GT ¼ GF in Eq. (3)] per −23 3 tonne-year of exposure at liquid xenon and argon detectors, assuming dark matter annihilation cross section hσannvi¼10 cm =s and an NFW halo profile. Events are integrated in the recoil energy window 5 keV–100 keV for xenon and 17 keV–110 keV for argon; the lower ends of these ranges correspond to neutrino energy ≃17 MeV. Also shown for reference is the rate of atmospheric and diffuse supernova neutrinos, which make up our primary irreducible background. and 300 MeV. Note that the maximum recoil energy limited end is once again chosen to evade the solar ν background, by kinematics is and the upper end is chosen to approximately match with the DARWIN range. The choice of these ER ranges also 2 2 kinem Eν ensures that the contribution of inelastic processes (qua- ER;max ¼ 2 : ð6Þ sielastic scattering, production of resonant states and deep mT þ Eν inelastic scattering) to the total event rate is negligible [59]. In the right panel of Fig. 1 we show as a function of mDM The differential scattering rate (per tonne of detector the integrated event rate per tonne-year for scattering of mass) is now obtained from Eqs. (1) and (3) as dark neutrinos (i.e., setting GT ¼ GF) with a flux corre- σ 10−23 3 Z sponding to h annvi¼ cm =s. Also shown as hori- ∞ Φ σ dR ton d d zontal dashed lines are the integrated rates of atmospheric ¼ N dEν ; ð7Þ T and diffuse supernova neutrino scattering taken from [58], dER Eν;min dEν dER which constitute our main background. The signal rate at ton 4 57 1028 1 51 1027 argon detectors peaks at lower neutrino energies compared where NT ¼ . × ( . × ) is thep numberffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of 2 to xenon detectors since Ekinem in Eq. (6) attains the nuclei per tonne of liquid Xe (Ar), and Eν;min ¼ mTER= R;max is the minimum Eν required to induce a nuclear recoil of maximum ER imposed by us here at a lower Eν for argon than for xenon. We will find below that this allows DARWIN energy ER. In order to apply the above treatment to future noble and ARGO to probe some regions in complementary ranges liquid detectors, we assume the following fiducial detector of dark matter mass. Figure 1 also shows that the signal rate masses: at xenon detectors is roughly an order of magnitude higher than at argon detectors, implying that the latter require ∼10 DARWIN∶ 40 tonnes; × the exposure of the former to achieve comparable sensitivities. ARGO∶ 300 tonnes: C. Sensitivities and other constraints The DARWIN mass is as advertised in [5], and the ARGO mass is a realistic possibility [57]. We now obtain the sensitivities for various detector To obtain the total event count at DARWIN, we integrate exposures. In a realistic detector, the rejection of electronic ∈ the rate in Eq. (7) over the range ER [5 keV, 100 keV]. recoil (ER) backgrounds comes at the cost of nuclear recoil Below this range solar neutrinos would populate a steep (NR) acceptance. It was determined by [14] that at DARWIN, “wall” of background events [58,59]; the upper end of this where ERs and NRs are distinguished by comparing S1 and range is chosen for showing conservative limits. At ARGO, S2 scintillation pulses, it is possible to achieve 99.98% ER ∈ – we use the range ER [17 keV, 110 keV], where the lower rejection with 30% 50% NR acceptance, which is at a level
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FIG. 2. 90% C.L. sensitivities of the liquid xenon DARWIN (left) and liquid argon ARGO (right) detectors, with fiducial masses of 40 tonnes and 300 tonnes respectively, to hσannvi× the coupling of the annihilation products to nucleons (normalized to the Fermi constant), as a function of dark matter mass. An NFW halo profile is assumed. The sensitivities are shown for 1, 5 and 10 years of exposure, and for nuclear recoil acceptances of 30% and 50% for DARWIN, and 60% and 80% for ARGO. The electronic recoil rejection is assumed to be at a level that renders background leakage from solar neutrino-electron scattering negligible. See Sec. II C for more details. that renders ER backgrounds negligible. This study was due to the atmospheric and diffuse supernova neutrino ∈ performed with ER [5 keV, 20.5 keV] to optimize for background, the sensitivities do not improve linearly with signal vs background for light WIMPs, which have rapidly the exposure. falling recoil spectra. Our signal spectra fall much more In the left panel of Fig. 3 we show the 10-year DARWIN ∈ slowly (Fig. 1), and we use ER [5 keV, 100 keV]; and ARGO sensitivities with 50% and 80% NR acceptances nevertheless we adopt the above NR acceptances to set our respectively, along with sensitivities from a possible future limits. At liquid argon detectors, which use the pulse extragalactic flux obtained by the rescaling procedure shape discrimination technique to reject ER backgrounds, described in Sec. II A. It must be noted that the true the NRs are better distinguished, yielding higher NR sensitivity lies somewhere between these curves due to the acceptances. We assume that acceptances at the level of nonmonochromatic nature of the extragalactic neutrino 60%–80% would be achieved at ARGO [57] with an ER flux. Due to the effect of the maximum ER imposed by rejection rate that renders ER backgrounds negligible. kinematics and our range of integration (see Sec. II B), We next assume that atmospheric and diffuse supernova these two detectors would probe small cross sections in neutrinos constitute our sole background. With the above complementary mDM ranges. We also show with red curves ϵ NR acceptances (which we denote by NR)atDARWIN and the sensitivity of current-generation liquid xenon detectors ARGO, we may safely neglect the leakage of solar neutrino- (e.g., XENON1T, LUX, PandaX), if operated over the same electron scattering events into our neutrino-nucleus scatter- recoil energy range as DARWIN, after 1 tonne-year of ing regions. The number of signal and background events at exposure. Recently XENON1T conducted a search for a detector before and after accounting for the NR acceptance WIMPs with this exposure [60] in nuclear recoil energies ϵ ϵ ∈ is simply related by Sacc ¼ NRS, Bacc ¼ NRB. Using ER [4.9 keV, 40.9 keV], with a signal selection efficiency Poisson statistics, the 90% C.L. bound is then obtained of 85% and with an ER-induced NR background of two by solving events. The NR selection efficiency after ER-discrimination is not quoted, but one expects this to be near 50% for xenon Γ 1 ðBacc þ ;Sacc þ BaccÞ 0 1 TPCs (as reflected in the projection for DARWIN). For ! ¼ . ; ð8Þ ∈ Bacc deriving our sensitivity, we take the range ER [5 keV, 100 keV] to compare with DARWIN, 50% signal selection, where Γ is the incomplete gamma function. This allows us and no backgrounds. These choices make our estimated ϵ to set NR-dependent bounds on the flux of dark neutrinos sensitivity slightly stronger than the actual bound one and boosted dark matter. would obtain from recasting the XENON1T WIMP search. In Fig. 2 we show the sensitivity of DARWIN and ARGO Lastly, we also show with green curves bounds from after exposure times of 1, 5, and 10 years. We show this measurements of harder-than-solar neutrinos by the liquid as a function of dark matter mass for the quantity scintillator neutrino experiment BOREXINO [61]. In the 2 2 σ ðGT=GFÞh annvi, which collects the unknown parameters Appendix B we describe the details of this bound, including in Eq. (7). The solid and dashed curves indicate NR the method used for extracting information about dark acceptances of 50% and 30% respectively at DARWIN, matter-proton scattering from electron recoil energies. and 80% and 60% respectively at ARGO. As expected, BOREXINO constrains the dark neutrino flux worse than
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FIG. 3. Left. Same sensitivities as Fig. 2, of the detectors DARWIN (with 10 years of run-time and 50% NR acceptance), ARGO (with 10 years of run-time and 80% NR acceptance), and XENON1T after 1 tonne-year of exposure. Also shown is the bound from proton recoils in BOREXINO (derived in Appendix B). For all these bounds an NFW halo profile is assumed. These are compared with sensitivities from a possible extragalactic flux, which we compute using the approximate method described in Sec. II A. Right. Comparison of DARWIN and ARGO sensitivities (as shown in the left panel) to a Galactic flux of dark neutrinos from the channel χχ¯ → ντν¯τ, with current and future neutrino detectors. Direct detection would surpass the bound from Super-K relic neutrino searches [9] and that derived by Yuksel, et al. [2] in the dark matter mass range 35 MeV–800 MeV. If dark neutrinos are produced instead as mass eigenstates in majoron- mediated dark matter annihilations, χχ¯ → νiν¯i (i ¼ 1,2,3), the bounds from neutrino experiments would be weakened by an Oð10Þ factor while the DARWIN and ARGO sensitivities are not affected. See Sec. II C for more details.
XENON1T, but constrains boosted dark matter at compa- above; at the liquid argon detector DUNE it is the charged 40 rable and stronger levels, as we will see in Sec. III B. current process νe=ν¯e þ Ar → e þfXg (where fXg In the right panel of Fig. 3 we show our sensitivities to are nuclei); and at the liquid scintillator detector JUNO the annihilation cross section of χχ¯ → ντν¯τ by setting these are inverse beta decay and absorption in carbon 12 þ 12 12 − 12 GT ¼ GF. Strictly speaking, of course, this sensitivity must (ν¯e þ C → e þ B and νe þ C → e þ N). For this be multiplied by the branching fraction into this annihila- study a run-time of 3000 days was assumed, and the tion channel (taken here to be 100%). The dark neutrino backgrounds were estimated by rescaling those of the flux is assumed to originate from dark matter in the Super-K analysis above; these sensitivities also depend Milky Way alone. For DARWIN, we assume 50% NR on the energy resolution assumed for each detector. Finally, acceptance, and for ARGO, 80% NR acceptance. These the black curve is the bound (with unspecified C.L.), as are compared with bounds from neutrino experiments. The derived by Yuksel, et al. [2], from atmospheric neutrino brown curve is obtained from a 90% C.L. limit set by the measurements by Super-K, Fr´ejus, and AMANDA. liquid scintillator detector experiment KamLAND [62] on For the neutrino experiment bounds, we accounted for ¯ extraterrestrial νe fluxes in the 8.3–18.3 MeV energy the fact that the signal flux for Dirac dark matter is halved 2 range. The magenta curve is the 90% C.L. limit, as recast compared to self-conjugate dark matter. Moreover, for the by [9], from a search for diffuse supernova neutrinos by reaches of the future detectors Hyper-K, DUNE and JUNO we the water Ĉerenkov detector Super-Kamiokande [64] rescaled the total fluxes used in [47] by the method using 2853 days of data. The relevant search channels described in Sec. II A to account for dark matter annihi- þ are inverse beta decay (ν¯e þ p → e þ n) and absorption lations in the Milky Way alone. 16 in oxygen (νe=ν¯e þ O → e þ X), sought in the positron We see in Fig. 3 that DARWIN and ARGO would rival, even energy range 16–88 MeV, which allows for probing Eν ≤ outdo, the bounds from Super-K diffuse neutrino searches 130 MeV [9]. (Boehm, et al.) and atmospheric neutrino measurements The dashed curves are 90% C.L. sensitivities, as esti- (Yuksel, et al.). This is because, as mentioned in the mated by [47], of the future neutrino detectors Hyper- Introduction, though large-volume neutrino detectors oper- Kamiokande, DUNE, and JUNO. The search channels at the ate at greater exposures than dark matter detectors, the latter water Ĉerenkov detector Hyper-K are the same as Super-K would compensate via the higher event rates of coherent nuclear scattering. Furthermore, the neutrino detector bounds depend on the 2The neutrino flux in this energy range can also be potentially fraction of the dark neutrino flux that is electron-flavored. bounded by dark matter direct detection searches that look for In the case of χχ¯ → ντν¯τ, the propagation of neutrinos over electronic recoils in ionization signals from nuclear recoils [63]; galactic distances washes out coherent oscillations, so that however, the uncertainties are too large for these searches to compete with dedicated neutrino experiments such as this fraction is simply the combined electron component of KamLAND. the mass eigenstates produced at the source. We calculate
103003-6 MONOCHROMATIC DARK NEUTRINOS AND BOOSTED … PHYS. REV. D 99, 103003 (2019) this fraction in Appendix A, finding that the e∶μ∶τ flavor imply that dark matter acquired the observed abundance ratio upon arrival at Earth is 11: 19: 20, i.e., the electron through a nonstandard cosmological history, such as, fraction is 0.22. We have accounted for this reduction of e.g., late decays of long-lived states into a dark matter effective flux when presenting our neutrino experiment population. bounds. Another interesting case is that of dark matter annihilating directly into neutrino mass eigenstates, D. Distinguishing between dark neutrinos χχ¯ → ν ν¯ i i, so that no oscillations occur. In theories where and boosted dark matter neutrinos acquire masses through lepton number breaking If a novel flux of coherently scattering particles is (see [65] and references therein), such annihilations are discovered at dark matter direct detection searches, it mediated in the s-channel by the majoron, the pseudoscalar would be of vital importance to identify the species associated with the symmetry breaking, which couples to detected. As said in the Introduction, dark neutrinos may the mass eigenstates in proportion to the neutrino eigen- 3 be distinguished from nonrelativistic WIMPs and boosted mass mν;i. Then the branching fractions into νiν¯i are 2 dark matter if corroborating, directional signals are proportional to mν;i. In this case, assuming normal hier- obtained at neutrino experiments. We now show that it archy of neutrino masses we find that the flavor ratio upon is in principle possible to distinguish between dark neu- arrival at Earth is 3: 52: 45 (see Appendix A), so that the trinos and boosted dark matter as well, given sufficient electron fraction of the flux is 0.03. A scenario such as this statistics. would therefore weaken the bounds from neutrino experi- First we note that there is a degeneracy among the ments shown in Fig. 3 by an order of magnitude, so that σ unknown parameters GT, h annvi and mDM in the scattering direct detection bounds are far stronger. rate, Eq. (7). If both DARWIN and ARGO see positive signals, While we have shown the reaches of future neutrino then hσ vi may be eliminated in the ratio of integrated ≲100 ann experiments for energies MeV, there are no existing rates at either detector, Events =Events .Now studies on these reaches for energies between 100 MeVand DARWIN ARGO we recall that GT is species-dependent [Eq. (4)], since 1 GeV. The exact sensitivities should depend on back- neutrinos scatter preferentially on neutrons whereas grounds from atmospheric neutrinos, and the systematics boosted dark matter scatters democratically on both neu- and energy resolutions of these detectors in this energy trons and protons, as well as is target-dependent, since range. Estimating these is beyond the scope of our xenon and argon nuclei comprise different nucleon pop- work; however, on the strength of the reaches in the ulations. Thus EventsDARWIN=EventsARGO would distin- sub-100 MeV range, it may be surmised that the reaches guish between dark neutrinos and boosted dark matter for a 100 in the > MeV energy range may be somewhat stronger given projectile energy (= dark matter mass). We have than DARWIN and ARGO in most regions for the case of tau- plotted this quantity (with the backgrounds subtracted) for flavored dark neutrinos. For the case of majoron-mediated the two species in Fig. 4, as a function of mDM. The dark neutrinos discussed above, dark matter direct detec- scattering rates have been integrated over the E ranges tion reaches may still be stronger in most regions. To make R matters even more interesting, the liquid scintillator detec- tor JUNO may see proton recoils from dark neutrinos that are not electron-flavored, ala` BOREXINO as discussed above. Therefore, in the event of discovery, an intricate interplay of dark matter and neutrino experiments will be required to discern whether dark neutrinos are produced in flavor or mass eigenstates. We end this subsection by noting that the smallest annihilation cross sections that may be probed by direct detection experiments would exceed 10−25 cm3=s, the value required for obtaining the observed dark matter relic 2 abundance (Ωχh ¼ 0.12) via thermal freeze-out. If a dark neutrino flux is detected at DARWIN and ARGO, this would
3 FIG. 4. A simple diagnostic to distinguish between dark Obtaining a large annihilation cross section in this scenario is neutrinos and boosted dark matter, as described in Sec. II D. a model-building challenge that is beyond the scope of our work. Shown here is the ratio of background-subtracted events at An interesting related possibility is a “secluded” scenario [66] where the dark matter annihilates with a large cross section to a DARWIN and ARGO after equal run-times, as a function of dark pair of on shell mediators which then each decay dominantly to matter mass. Since neutrinos scatter preferentially on neutrons ν3ν¯3. Such neutrinos are no longer monochromatic, yielding whereas boosted dark matter scatters equally on neutrons and interesting signatures at direct detection and neutrino protons, and since xenon and argon contain different numbers of experiments. nucleons, this ratio separates the two cases.
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−L ϕχν¯ mentioned in Sec. II B, and equal run-times at both int ¼ yLUl4 þ H:c: ð10Þ experiments are assumed. The remaining degeneracy, that of dark matter mass, may be broken by inspecting the recoil The orthogonal combination pairs up withqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNR to form a spectrum at high energies, as the kinematic endpoint is set 2 2 2 heavy Dirac neutrino with mass M ¼ λ v þ m . The by this mass [Eq. (6)]. l N We point out another virtue in simultaneously inspecting active-sterile mixing angle is Ul4 ¼ λlv=M. Note that this DARWIN ARGO mixing angle need not be tiny for the mostly active neutrino recoil spectra at and . If a dark neutrino flux 5 is detected with a small number of signal events, the to be extremely light. 2 background model used for the atmospheric and diffuse We assume that mDM
4It is also possible to have ϕ lighter than χ, so that ϕ is now the dark matter and χ the mediator. However, the dark matter 5Simple extensions to the model can confer finite masses to the annihilation proceeds in the p-wave, so that annihilation signals light neutrinos while keeping the mixing angle relatively large; today are absent. see [23] for details.
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whose interactions with baryons are mediated by a gauged 1 Uð ÞB vector [19,55,73], or when it is a fermion whose interactions with SM fermions are mediated by a scalar that mixes with the Higgs boson [20]. The effective coupling to 2 nucleons is then GB ¼ gxgq=mMED, where gx and gq are the mediator couplings with the boosted dark matter and quarks respectively, and mMED is the mediator mass. It ≲ has been determined that in both these models, GB 7000 GF is experimentally viable [20]. We take the boosted ’ ≪ dark matter s mass mDM, and this implies that its population can contribute to the energy density of radiation in the early Universe, constrained by measurements of Neff ; FIG. 5. Interpretation of our results in the left panel of Fig. 3 in however, this contribution is within observed limits [20]. terms of the neutrino portal dark matter model described in Using Eq. (4) and the results in Fig. 3, we may obtain Sec. III A. Bounds are shown in the plane of the effective 6 bounds on GB for a flux corresponding to a thermal coupling Yτ [Eq. (12)] vs dark matter mass, with regions above annihilation cross section hσ vi ¼ 10−25 cm3=s; the curves excluded. Dashed black curves indicate parameters ann thermal these are shown in the left panel of Fig. 6 as constraints that result in suppression of the growth of structures below a mass cutoff of 109 and 107 solar masses, thus explaining the “missing on the ratio GB=GF as a function of dark matter mass. Here satellites” problem. These regions are seen to be extensively we have neglected the attenuation of flux due to passage probed by direct detection. The dashed orange curve denotes through the Earth, since the couplings being probed are too parameters that correspond to a dark matter-nucleon scattering small for this effect to be important. cross section associated with the standard “neutrino floor” in The BOREXINO bounds, which were the weakest in the xenon. The dashed blue line corresponds to a thermal annihilation case of the dark neutrino flux, now outdo XENON1T for cross section ¼ 10−25 cm3=s. dark matter masses ≥ 200 MeV. This is because the relative size of the cross sections for scattering with protons We find that direct detection of dark neutrinos could vs xenon is much smaller for neutrinos than for boosted extensively probe these regions. For reference, we also dark matter; see Eqs. (3) and (4). The BOREXINO and XENON1T bounds on G are also 2 or 3 orders show the value of Yτ that yields a thermal annihilation cross B −25 3 of magnitude stronger than those placed by [20] using a section of hσ vi¼10 cm =s. ann 0.027 tonne-year LUX data set. [We have adapted As discussed in the Introduction, in this model dark matter ’ σ 500 develops an effective loop-induced coupling to the Z boson, Ref. [20] s bound on h annvi for GB=GF ¼ to present through which it could scatter with nuclei at direct detection the bound on ðGB=GFÞjthermal.] experiments. In Fig. 5 we show with a dashed orange curve We see that DARWIN and ARGO would improve the sensitivity to GB by a factor of 10, probing all the way values of the coupling Y that correspond to this scattering 1–2 down to the weak coupling size × GF for dark matter cross section at the xenon neutrino floor, as done in [23].In ∼25–100 regions above this curve, an interesting possibility may masses MeV. This is one of the main results of occur: direct detection experiments may register events from our paper. coherent nuclear scattering of both the local, nonrelativistic The core-cusp problem. While probing thermal freeze- dark matter and the relativistic dark neutrino fluxes. However out is of inherent interest, another worthwhile target for these regions are already disfavored by the atmospheric direct detection is to probe scenarios that address the small neutrino bounds of Yuksel, et al. (see Fig. 3). scale structure of the Universe. In Sec. III A, we explored Finally, we point to the existence of other dark matter how direct detection signals of dark neutrinos could help models that would result in monochromatic dark neutrinos. address the missing satellites problem. Now we show For example, such dark matter could be supersymmetric briefly that direct detection signals could tackle the so- sneutrinos [52] or an adjoint fermion in a hidden confining called core-cusp problem as well. gauge group [72]. For variations on the neutrino portal From N-body simulations of noninteracting cold dark model presented in this section, with all possible spins of matter, we expect its density to rise steeply near the centers the dark matter and the mediator, see [9]. of galactic halos, but observations indicate flat density profiles in these regions. Reference [74] posited that if dark B. Boosted dark matter 6 We now consider the possibility that the annihilation Since for thermal annihilation cross sections the detectable values of GB turn out to be >GF, one may reasonably assume products of dark matter are a second, subdominant com- that the boosted annihilation products, by virtue of scattering with ponent of dark matter that is nucleophilic. This is realized nucleons, keep dark matter in thermal equilibrium in the early when the boosted dark matter is a “baryonic neutrino” Universe until freeze-out.
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2 2 σ FIG. 6. Interpretation of our constraints on ðGT=GFÞh annvi vs dark matter mass in the left panel of Fig. 3, in terms of the boosted dark matter models described in Sec. III B. Left. Bounds as a function of dark matter mass on the baryonic coupling GB (normalized to the 10−25 3 Fermi constant GF) such that the boosted dark matter flux is obtained for a thermal annihilation cross section ¼ cm =s. The bounds obtained by Cherry, et al. [20] used LUX data. The erstwhile bound from BOREXINO proton recoils (derived in Appendix B) and the current bound from XENON1T are seen to be stronger. DARWIN and ARGO can be seen to probe GB all the way down to the weak ∼25–100 coupling GF in the mDM range MeV. Right. Addressing the core-cusp problem with boosted dark matter detection. Shown are values of GB=GF ruled out by BOREXINO and XENON1T, and those to be probed by DARWIN and ARGO, for an annihilation cross section [Eq. (14)] that would ensure that dark matter is depleted from halo cores. matter annihilated today with large rates, it would be matter, now commonly known as boosted dark matter, that especially depopulated in overdense regions, and uniform is nucleophilic. We derived the reaches of a 40-tonne halo cores would result. The requisite s-wave annihilation xenon-based detector, DARWIN, and a 300-tonne argon- cross section is far above the thermal cross section for our based detector, ARGO, after accounting for imminent back- dark matter masses of interest, grounds from atmospheric and diffuse supernova neutrinos, as well as realistic nuclear recoil acceptances. To the best of −20 3 mDM our knowledge, this is the first work to study a next-to-next hσ vi − ¼ 3 × 10 cm =s : ð14Þ ann core cusp 100 MeV generation liquid argon detector for a concrete theoretical scenario. Liquid argon technology exploits the pulse shape The annihilation products must not yield photons, since discrimination technique, which is not possible in liquid γ such large fluxes are well excluded. Nor could the xenon, and this enables superior electron recoil rejection. annihilation products be neutrinos, though they are the We have shown that by virtue of this, ARGO would set limits hardest SM states to detect, as this too is excluded (see on dark matter parameters that are closely comparable and Fig. 3). But if the annihilation products are even harder to complementary to DARWIN. Due to their differing tech- detect than neutrinos, such as when they are boosted dark nologies, thresholds and energy ranges of interest, a matter with tiny couplings to the SM, then a large flux of positive signal at both DARWIN and ARGO would help to them could have gone unnoticed, keeping this solution to mitigate uncertainties in the modeling of backgrounds, the core-cusp problem alive. In the right panel of Fig. 6 we especially if signal events are few in number. It would also show the values of the coupling G (relative to G ) that are B F help to characterize the particle species detected, e.g., excluded by XENON1T and BOREXINO proton recoils, and neutrinos vs boosted dark matter. probeable by DARWIN and ARGO, if the boosted dark matter We found that after 10 years of exposure these experi- flux corresponded to the annihilation cross section in ments could probe dark neutrino fluxes beyond the reach of Eq. (14). We see that in this scenario DARWIN and ARGO neutrino experiments. There are two main reasons for this: would be sensitive to couplings ∼10−3–10−2 × G for dark F (i) while neutrino detectors admit larger fluxes and sustain matter masses ∼20–1000 MeV. greater exposures, direct detection experiments benefit from high event rates due to coherent nuclear scattering, IV. CONCLUSIONS AND DISCUSSION (ii) while search channels at most neutrino experiments In this paper we explored the sensitivity of future noble such as Super-Kamiokande rely on the νe and/or ν¯e fraction liquid-based direct detection experiments to the flux of of the dark neutrino flux, which may be as small as particles produced in the annihilation of dark matter in the Oð10−2Þ depending on the dark matter model with which sky. Our main results are summarized in Figs. 3, 5, and 6. the bounds are interpreted, the search channel of coherent The particle species we considered are neutrinos, which we nuclear scattering at direct detection is agnostic to neutrino call “dark neutrinos”, and a second component of dark flavor and self-conjugation.
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We also derived current bounds and sensitivities on the APPENDIX A: FLAVOR COMPONENTS AFTER boosted dark matter flux, which are set in complementary NEUTRINO PROPAGATION dark matter mass ranges by 1 tonne-year of data from While coherent nuclear scattering at direct detection XENON1T and by a limit on proton recoils at BOREXINO. searches is blind to neutrino flavor, other channels, used in For a thermal annihilation cross section, these bounds neutrino experiments, are sensitive to the flavor component limit the effective baryonic coupling of the boosted dark being detected. These components depend both on the matter to G ≲ ð10–100Þ× the Fermi constant G ; in the B F distribution of flavors in the neutrino states produced at the future, DARWIN and ARGO would push this down to source and neutrino mixing parameters. In this Appendix G ≲ ð1–10Þ × G . For an annihilation cross section cor- B F we calculate these components for the cases of dark matter responding to that which is required to deplete dark matter from halo cores, and thus solve the core-cusp problem, annihilations into either flavor or mass eigenstates, which ∼ we use in Sec. II to present bounds from neutrino DARWIN and ARGO would probe couplings down to GB 10−3–10−2 experiments. × GF. We begin with the case of χχ¯ → ναν¯α, where α is a flavor There are several related avenues of exploration that we index. Since these dark neutrinos travel galactic distances had not entered in this work. While we had assumed that our signals were sourced by dark matter annihilations in before arriving at detectors, the effect of coherent oscil- lations is negligible, so that the probability of detecting free space, monochromatic fluxes may also originate in β annihilations in the Sun, ala` Refs. [75] and [76–79]. flavor is given simply by Nonmonochromatic neutrinos may be sourced by “cascade X3 ” 2 2 annihilations , i.e., annihilations of dark matter into medi- Pαβ ¼ jUβij jUαij ; ðA1Þ ators or SM states that may subsequently decay to neutrinos i¼1 in the energy range of interest for direct detection. While U we had implicitly assumed a symmetric population of dark where is the PMNS matrix. It is usually parametrized as 2 32 32 3 matter, an interpretation of our flux limits in terms of an iδ 10 0 c13 0 s13e CP c12 s12 0 asymmetric population is possible, especially in the case of 6 76 76 7 boosted dark matter, where our limits on the (symmetric) 40 c23 s23 54 01054−s12 c12 05; 10−25 3 — −iδ annihilation cross section could be < cm =s see 0 −s23 c23 −s13e CP 0 c13 001 [80] for more details. If signals appear in more than one direct detection experiment, a halo-independent analysis where cab and sab denote cos θab and sin θab respectively. for relativistic fluxes may be undertaken, such as in [20]. The most recent best-fit values [83,84] (without the error An exciting possibility is the double signal briefly men- bars) are tioned in Sec. III A, comprising of the scattering of both θ 33 62 θ 47 2 θ 8 54 δ 234 local, nonrelativistic dark matter, and relativistic particles 12 ¼ . °; 23 ¼ . °; 13 ¼ . °; CP ¼ °; produced in dark matter annihilations. While the parametric regions for this to transpire in the simple neutrino portal from which we obtain using Eq. (A1) the following model we had explored are already excluded, there may be conversion probabilities: other theories where this is still viable, especially in models 2 3 2 3 of boosted dark matter. Pee Peμ Peτ 0.55 0.23 0.22 Goodman and Witten [81] originally proposed dark 6 7 6 7 4 Pμ Pμμ Pμτ 5 ¼ 4 0.23 0.39 0.38 5: ðA2Þ matter direct detection following the proposal of Drukier e 0 22 0 38 0 40 and Stodolsky [82] for detecting neutrinos—from solar, Pτe Pτμ Pττ . . . atmospheric, terrestrial, supernova, reactor, and spallation χχ¯ → ν ν¯ sources—in coherent elastic neutral current scattering. Next we turn to the case of i i, where i runs over Should the “ultimate detectors” discover dark matter by mass eigenstates. Inspired by majoron-mediated models, ∝ 2 catching neutrinos sourced by dark matter, the revolutionary we assume that the branching fractions mν;i. As these moment would draw a decades-long search program to a neutrinos do not oscillate, the probability of detecting satisfying close. flavor α is X3 . X3 ACKNOWLEDGMENTS 2 2 2 Pα ¼ mν;ijUαij mν;i : ðA3Þ This work has benefited from conversations with Joe i¼1 i¼1 Bramante, Pietro Giampa, David Morrissey, and Tien-Tien 2 2 2 0 7 40 10−5 2 494 10−3 2 Yu. It is supported by the Natural Sciences and Engineering Using fmν;1;mν;2;mν;3g¼f ; . × ; . × geV , Research Council of Canada (NSERC). TRIUMF receives which is consistent with solar and atmospheric neutrino federal funding via a contribution agreement with the oscillation data [83,84] if a normal mass hierarchy is National Research Council Canada. assumed, we get
103003-11 DAVID MCKEEN and NIRMAL RAJ PHYS. REV. D 99, 103003 (2019) 2 3 2 3 Pe 0.03 and tau neutrinos from a supernova burst. The apparent 6 7 6 7 electron equivalent recoil energy Ee in a liquid scintillator 4 Pμ 5 ¼ 4 0.52 5: ðA4Þ R is related to the proton recoil energy Ep by Birks’ formula 0 45 R Pτ normal . for quenching, 2 2 2 Z For an inverted mass hierarchy, fm ;m ;m g¼ p ν;1 ν;2 ν;3 ER −3 −3 2 e p 0p 1 −1 2.42 × 10 ; 2.494 × 10 ; 0 eV is consistent with data, ERðERÞ¼ dE Rð þ kBhdT=dxiÞ : ðB1Þ f g 0 and we get 2 3 2 3 We only consider elastic scattering on hydrogen nuclei in Pe 0.48 6 7 6 7 the organic scintillator, as scattering on carbon is greatly 4 Pμ 5 ¼ 4 0.24 5: quenched and unobservable [85,86]. Reference [87] esti- 0 28 mated that the scattering rate per proton is restricted to be Pτ inverted . 2 10−39 −1 e 12 5 It is also possible that the neutrino mass spectrum is heavy Rp < × s for ER > . MeV 2 ≃ 2 ≃ 2 ⇒ p 19 7 and near-degenerate, mν;1 mν;2 mν;3, in which case we ER > . MeV: ðB2Þ have 2 3 2 3 The last line of this equation is obtained by numerically ¯ ’ 0 011 Pe 0.33 solving Eq. (B1) with a Birks factor kB ¼ . cm=MeV 6 7 6 ¯ 7 dT=dx E0p 4 Pμ 5 ¼ 4 0.33 5: [88] and by obtaining h i (as a function of R) with ¯ tables from [89] for toluene, a good approximation for the Pτ 0.33 near−degenerate BOREXINO scintillator, pseudocumene. 2 2 σ The bound on ðGT=GFÞh annvi is then obtained from Eqs. (1), (3) and (B2), where we now use the dipole form APPENDIX B: PROTON RECOILS AT 2 2 2 2 factor Fðq Þ¼1=ð1 þ q =ð0.71 GeV ÞÞ [19] in Eq. (3). BOREXINO We note that the rate of inelastic processes that may induce To derive our bound from BOREXINO, we follow the fragmentation or excitation of the proton is highly sup- method originally developed by [85,86] for detecting muon pressed for the momentum transfers considered here [19].
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