Diurnal Effect of Sub-Gev Dark Matter Boosted by Cosmic Rays
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Diurnal Effect of Sub-GeV Dark Matter Boosted by Cosmic Rays Shao-Feng Ge,1,2, ∗ Jianglai Liu,2,1, † Qiang Yuan,3, 4, 5, ‡ and Ning Zhou2, § 1Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China 2School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE) & Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai 200240, China 3Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210033, China 4School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China 5Center for High Energy Physics, Peking University, Beijing 100871, China We point out a new type of diurnal effect for the cosmic ray boosted dark matter (DM). The DM- nucleon interactions not only allow the direct detection of DM with nuclear recoils, but also allow cosmic rays to scatter with and boost the nonrelativistic DM to higher energies. If the DM-nuclei scattering cross sections are sufficiently large, the DM flux is attenuated as it propagates through the Earth, leading to a strong diurnal modulation. This diurnal modulation provides another prominent signature for the direct detection of boosted sub-GeV DM, in addition to signals with higher recoil energy. Introduction – Overwhelming evidence from astrophys- signals in large neutrino experiments [44–46]. ical and cosmological observations supports the existence For sub-GeV DM, the DM-nucleon scattering cross sec- of dark matter (DM) [1], which is gravitationally interact- tion with a contact interaction can be quite sizable, e.g., ing but invisible via electromagnetic interactions. How- as large as 10−31cm2 (see [47] and the references in [35]), ever, the physical nature of DM is poorly understood: in contrast to the light mediator case [48]. With this al- the DM identity is unknown with a possible mass spans lowed interaction strength, DM particles can experience nearly 80 orders of magnitude [2]. The DM direct detec- multiple scatterings and become attenuated when trav- tion [3] aims to verify the existence of DM particles and eling through the Earth [49–52]. If the CRDM flux is measure their interactions via the recoil of target nuclei anisotropic, a diurnal flux modulation at direct detec- or electrons, which is believed to be the most direct way tion experiments is expected [53, 54]. This is different to unveil the nature of DM particles [4, 5]. from the conventional diurnal effect that is mainly for Conventionally, direct detection experiments assume nonrelativistic DM. the existence of nonrelativistic DM confined in the Sub-GeV Dark Matter Boosted by Cosmic Rays – The Galaxy. The gravitational potential of the Galaxy results spatial and spectral distributions of the CRDM flux de- pend on the DM and CR distributions in the Galaxy in an upper limit on the DM velocity of vχ . 600 km/s above which DM can escape [6, 7]. Because of the en- as well as the CRDM scattering processes. Both the DM ergy threshold, which is typically O(keV), the sensitive density and CR intensities vary with their locations in the mass window of direct detection experiments can only Galaxy, becoming more concentrated toward the Galaxy extend down to O(1) GeV via the conventional nuclear center (GC). Therefore, CRs are much more likely to recoil channel. In recent years, to enhance the sensitivity scatter with and boost the DM in the inner Galaxy re- of detecting sub-GeV DM, many approaches have been gion. Even for isotropic scattering, the CRDM flux is highly anisotropic over the sky. arXiv:2005.09480v2 [hep-ph] 9 Mar 2021 explored, including expanding the nuclear recoil detec- tion capability via a low threshold bolometer [8, 9] as Although the CRDM scattering also affects the CRs, well as via the Bremsstrahlung [10] and Migdal [11–17] the effect is important only for a very large scattering −27 2 effects, the direct detection of DM-electron recoils [18– cross section (σχp > 10 cm )[35]. For simplicity, 23], and various novel detection proposals [24–34]. we assume that the CR distribution is unaffected. The CRDM emissivity, which describes its spatial and spec- Another interesting possibility has been recently trum distributions, is given by [36] pointed out: nonrelativistic DM can be boosted by cos- r ∞ r mic rays (CRs) [35, 36] or the solar reflection [37–39]. r ρχ(| |) nCR,i( ,Ti) ζχ( ,Tχ)= dTi max As long as DM has finite interactions with matter, it is mχ T min Tχ (Ti) i=p,He Z i inevitable for the nonrelativistic DM to be scattered and X ×v σ G2(Q2), (1) boosted by the energetic CRs. Although the flux of the i χi i CR-boosted DM (CRDM) is a tiny fraction compared to where Ti and Tχ are the kinetic energies of the CR species min the nonrelativistic DM, it allows explorations of a certain i and the boosted DM with mass mχ, Ti is the mini- parameter space of sub-GeV DM that was previously in- mum CR energy required to boost the DM kinetic energy max accessible [36, 40–43] in direct detection, thus expanding to Tχ, and Tχ is the maximum DM kinetic energy given the sensitive mass region. The CRDM can also produce Ti [36]. There are three main ingredients in Eq. (1): the 2 σ -32 2 -4 GC direction, χp=10 cm 10 ) -1 -7 sr 10 -1 -5 -4 10 -4 -8 halo × 10 mχ=10 GeV 10 (cm s β ) -6 -9 /d 10 -1 10 10-3 GeV Φ )d -10 sr χ 10 -7 ρ -2 / -1 10 10 GeV β s χ 10-11 -2 (m -8 10-4 10-3 10-2 10-1 100 10 β 10-1 GeV (cm -9 χ 10 /dT -10 100 GeV Φ 10 d χ -11 101 GeV T 10 10-12 10-13 10-3 10-2 10-1 100 101 102 103 Tχ (GeV) FIG. 2. The CRDM energy spectra at the GC direction for DM masses 10−4, 10−3, 10−2, 0.1, 1.0, and 10 GeV from top to bottom. The scattering cross section σχp is assumed to be 10−32 cm2. The inset is the distribution of DM velocities, β = v/c, compared to the Maxwellian distribution of the Standard DM Halo. For a clear comparison, we rescale the Standard DM Halo curve by 10−4 (labeled as halo ×10−4 in the inset) so that all curves have a similar height. ing CR spatial distribution, please see the Supplemental Material [67]. FIG. 1. Relative sky maps of CRDM fluxes in the Galactic The DM-nucleus interaction is the least known part in coordinates with amplitude in the GC direction set to unity. Eq. (1). For simplicity, we assume that the DM-nucleus The upper and lower panels are for the NFW and Isothermal cross section σχA has a coherent enhancement, DM density profiles, respectively. m (m + m ) 2 σ = σ A2 A χ p , (2) χA χp m (m + m ) p χ A DM density ρχ(|r|) at location r, the CR density nCR,i times its velocity vi, and the scattering cross section σχi. where σχn = σχp is the constant DM-nucleon cross sec- 2 2 2 2 tion, while m and m are the proton and nuclear masses The form factor Gi(Q ) ≡ 1/(1 + Q /Λi ) [55] is a func- p A tion of the momentum transfer Q with Λp ≈ 770 MeV for the CR. For mχ ≪ mp,mA, the enhancement mainly 2 and ΛHe ≈ 410 MeV [56] for proton and helium, respec- comes from the A factor. Extra enhancement may come 2 2 tively. from (mχ + mp) /mp when mχ goes beyond mp. The dipole hadronic form factor G (Q2) in Eq. (1) suppresses For the DM density ρχ(|r|), we adopt the i nfw the interaction at large momentum transfer Q. Navarro-Frenk-White (NFW) [57] profile, ρχ (r) = 2 The CRDM flux arriving at the Earth along a given ρs/[(r/rs)(1 + r/rs) ] with rs = 20 kpc and −3 direction nˆ is a line-of-sight integral of all contributions ρs = 0.35 GeV cm , as the benchmark DM mass distribution. For comparison, a cored isothermal distri- along the way, iso 2 bution, ρχ (r) = ρs/[1 + (r/rs) ] with rs = 5 kpc and dΦ 1 −3 ˆn r ρ = 1.56 GeV cm , is also studied. These parameters ( ,Tχ)= ζχ( ,Tχ) dl. (3) s dT 4π correspond to a local DM density of 0.4 GeV cm−3 in χ Z our Solar System [58] for both profiles. The difference Fig. 1 shows the relative all-sky maps of the CRDM fluxes between the two profiles and more details are given in in the Galactic coordinate, a spherical coordinate with the Supplemental Material [67]. The amplitudes of the the Sun as its center, the latitude measuring the angle diurnal modulation vary by only around 7% for different above/below the galactic plane, and the longitude mea- density profiles. suring the azimuth angle from the GC. The peak value at For the CR contribution in Eq. (1), we employ the the GC is set to 1. The top (bottom) panel presents the GALPROP [59] code (version 54) to simulate its distri- NFW (isothermal) profile. The CRDM fluxes are clearly bution. In this Letter, we only consider the dominating anisotropic, with the maximum (the GC direction) and proton and helium species of CRs, and leave the rest, in the minimum differing by about two orders of magnitude. particular electrons and positrons, for future discussions.