Cosmic-Neutrino-Boosted Dark Matter ($\Nu $ BDM)

YHEP-COS-21-01

Cosmic-Neutrino-Boosted Dark Matter (νBDM)

1, 2, 1, 1, Yongsoo Jho, ∗ Jong-Chul Park, † Seong Chan Park, ‡ and Po-Yan Tseng § 1Department of Physics and IPAP, Yonsei University, Seoul 03722, Republic of Korea 2Department of Physics and Institute of Quantum Systems (IQS), Chungnam National University, Daejeon 34134, Republic of Korea A novel mechanism of boosting dark matter by cosmic neutrinos is proposed. The new mechanism is so significant that the arriving flux of dark matter in the mass window 1 keV . mDM . 1 MeV on Earth can be enhanced by two to four orders of magnitude compared to one only by cosmic electrons. Thereby we firstly derive conservative but still stringent bounds and future sensitivity limits for such cosmic-neutrino-boosted dark matter (νBDM) from advanced underground experiments such as Borexino, PandaX, XENON1T, and JUNO.

I. INTRODUCTION indeed the case for gauged lepton number as mediator, for instance [22, 23]. The existing conclusions regarding Revealing the properties of dark matter (DM) is defi- cosmic-electron-induced BDM should be re-examined. nitely one of the most pressing issues in particle physics, astrophysics, and cosmology. Direct detection experiments of DM have particular importance as they aim to II. BOOST MECHANISM BY COSMIC probe interaction of DM with standard model (SM) par- NEUTRINO ticles [1]. However, there exists fundamental limitation in detecting a sub-MeV dark matter set by the maximum Cosmic neutrino inputs. Near Earth, our Sun pro- kinetic energy of the DM particle in halo: Sun vides the dominating neutrino flux dΦν /dKν in the max < 6 < neutrino energy Kν . 10 MeV reaching the maximum KDM 10− mDM 1 eV (1) 8 2 1 1 ∼ ∼ (10 ) [cm− s− keV− ] around Kν 0.3 MeV [19– 3 'O ' with the velocity v 10− . This low kinetic energy 21], which gives the total number of neutrino emission causes a significant problem∼ in detecting light dark mat- rate per unit energy ter since the recoil energy of scattered SM particle is also limited by the kinetic energy 1. On the other hand, dN˙ Sun dΦSun ν ν (4πD2 ) , (2) there still exists a chance to detect a subcomponent of dKν ≡ dKν DM, dubbed ‘boosted dark matter’ (BDM), which may carry much larger energy beyond threshold due to vari- where D = 1 AU is the distance between Sun and

ous mechanisms [4–10] including scattering by energetic Earth. The neutrinos can boost non-relativistic light cosmic-ray particles [11–17]. We note that focus has DM, leaving distinctive signals at terrestrial experiments, been given to cosmic-ray electron and proton so far even e.g. XENON1T [24, 25]. The total contributions from though the chance is not exclusively open for charged all stars for νBDM could be significant compared to the particles. BDM flux by the solar neutrinos. The overall neutrino In this letter, we focus on a noble class of cosmic- flux from all stars in the Milky Way (say, cosmic-neutrino neutrino-boosted-dark matter (νBDM) extending previ- flux) has not been measured by astrophysical observa- ous studies: there exist a huge number of cosmic-ray tions, and could be highly anisotropic, which is different arXiv:2101.11262v1 [hep-ph] 27 Jan 2021 neutrinos arriving at the solar system from various ori- from the isotropic diffused cosmic electrons. In general, gins [18]. Our Sun is also generating a large number DM particles can be boosted by the neutrino flux from of neutrinos [19–21] so that they may boost DM within the nearest star, instead of diffused neutrinos. Keep this the solar system. We find that νBDM can be a domi- philosophy in mind, we will compute the νBDM flux by nant part of the whole BDM when DM-neutrino inter- starting with single star contribution in the following sec- action is as strong as DM-electron interaction, which is tion, then integrate the entire star distribution in the Milky Way.

Cosmic neutrino and DM scattering. The halo DM ∗ [email protected] is boosted by neutrino through the process ν + χ † [email protected]; co-corresponding author → ‡ [email protected]; co-corresponding author ν + χ, which may originate from the exchange of the § [email protected] U(1)Le Li gauge boson or dim-6 eﬀective operators in- − µ 1 Several ideas have been suggested to detect signals with low recoil cluding (`γ¯ `)(¯χγµχ) or (``¯ )(¯χχ). The resulting BDM energies by lowering the threshold energies at detectors (see [2, 3] kinetic energy KDM can be determined from the kinetic and references therein). energy of incoming neutrino Kν . At the halo DM rest AAAB83icbVBNSwMxEJ2tX7V+VT16CRbBU9kVQb0VRfBYwX5At5Rsmm1Ds9klmRXL0r/hxYMiXv0z3vw3pu0etPXBwOO9mWTmBYkUBl332ymsrK6tbxQ3S1vbO7t75f2DpolTzXiDxTLW7YAaLoXiDRQoeTvRnEaB5K1gdDP1W49cGxGrBxwnvBvRgRKhYBSt5PvInzC7pRqHk1654lbdGcgy8XJSgRz1XvnL78csjbhCJqkxHc9NsJvZxwSTfFLyU8MTykZ0wDuWKhpx081mO0/IiVX6JIy1LYVkpv6eyGhkzDgKbGdEcWgWvan4n9dJMbzsZkIlKXLF5h+FqSQYk2kApC80ZyjHllCmhd2VsCHVlKGNqWRD8BZPXibNs6p3Xr26P6/UrvM4inAEx3AKHlxADe6gDg1gkMAzvMKbkzovzrvzMW8tOPnMIfyB8/kDjgiSCw== AAAB8HicbVDLSgNBEJyNrxhfUY9eFoPgKeyKoN6CevAiRDAPSZYwO+kkQ2Zml5leMSz5Ci8eFPHq53jzb5wke9DEgoaiqpvurjAW3KDnfTu5peWV1bX8emFjc2t7p7i7VzdRohnUWCQi3QypAcEV1JCjgGasgcpQQCMcXk38xiNowyN1j6MYAkn7ivc4o2ilhzbCE6bXt+NOseSVvSncReJnpEQyVDvFr3Y3YokEhUxQY1q+F2OQUo2cCRgX2omBmLIh7UPLUkUlmCCdHjx2j6zSdXuRtqXQnaq/J1IqjRnJ0HZKigMz703E/7xWgr3zIOUqThAUmy3qJcLFyJ1873a5BoZiZAllmttbXTagmjK0GRVsCP78y4ukflL2T8sXd6elymUWR54ckENyTHxyRirkhlRJjTAiyTN5JW+Odl6cd+dj1ppzspl98gfO5w/4a5CK AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUG9FLx4r2A9oQ9lsJ+3SzSbsbool9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU8epYthgsYhVO6AaBZfYMNwIbCcKaRQIbAWju5nfGqPSPJaPZpKgH9GB5CFn1Fip1R0jy56mvXLFrbpzkFXi5aQCOeq98le3H7M0QmmYoFp3PDcxfkaV4UzgtNRNNSaUjegAO5ZKGqH2s/m5U3JmlT4JY2VLGjJXf09kNNJ6EgW2M6JmqJe9mfif10lNeO1nXCapQckWi8JUEBOT2e+kzxUyIyaWUKa4vZWwIVWUGZtQyYbgLb+8SpoXVe+yevNwWand5nEU4QRO4Rw8uIIa3EMdGsBgBM/wCm9O4rw4787HorXg5DPH8AfO5w+1w4/W

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 ~x ~z

Galactic Disk AAAB7XicbVDLSgNBEOz1GeMr6tHLYBA8hV1R9Bj04jGCeUCyhNnJbDJmdmaZ6RVCyD948aCIV//Hm3/jJNmDJhY0FFXddHdFqRQWff/bW1ldW9/YLGwVt3d29/ZLB4cNqzPDeJ1pqU0ropZLoXgdBUreSg2nSSR5MxreTv3mEzdWaPWAo5SHCe0rEQtG0UmNDg440m6p7Ff8GcgyCXJShhy1bumr09MsS7hCJqm17cBPMRxTg4JJPil2MstTyoa0z9uOKppwG45n107IqVN6JNbGlUIyU39PjGli7SiJXGdCcWAXvan4n9fOML4Ox0KlGXLF5oviTBLUZPo66QnDGcqRI5QZ4W4lbEANZegCKroQgsWXl0njvBJcVvz7i3L1Jo+jAMdwAmcQwBVU4Q5qUAcGj/AMr/Dmae/Fe/c+5q0rXj5zBH/gff4ApUmPLA== ~y Star ✓

AAAB8HicbVDLSgNBEOyNrxhfUY9eFoPgKeyKosdgDnqMYB6SLGF2MkmGzMwuM71iWPIVXjwo4tXP8ebfOEn2oIkFDUVVN91dYSy4Qc/7dnIrq2vrG/nNwtb2zu5ecf+gYaJEU1ankYh0KySGCa5YHTkK1oo1IzIUrBmOqlO/+ci04ZG6x3HMAkkGivc5JWilhw6yJ0xvqpNuseSVvRncZeJnpAQZat3iV6cX0UQyhVQQY9q+F2OQEo2cCjYpdBLDYkJHZMDalioimQnS2cET98QqPbcfaVsK3Zn6eyIl0pixDG2nJDg0i95U/M9rJ9i/ClKu4gSZovNF/US4GLnT790e14yiGFtCqOb2VpcOiSYUbUYFG4K/+PIyaZyV/Yuyd3deqlxnceThCI7hFHy4hArcQg3qQEHCM7zCm6OdF+fd+Zi35pxs5hD+wPn8Aes9kHs= (d , 0, 0) ~x GC Earth [] []

FIG. 2. The unit-normalized arrival direction θ distributions of the νBDM spectral ﬂux ϕBDM ≡ dΦDM/dKDM for two benchmark values of KDM: 10 keV (left) and 1 MeV (right) varying mDM = 5 keV – 5 MeV with a ﬁxed mediator mass,

AAACHHicbVDLSgMxFM3UV62vqks3wSK4KjM+0GVRF4IIFewDOqVk0ts2NPMwuSOWoR/ixl9x40IRNy4E/8a0nYWtHgicnHMuyT1eJIVG2/62MnPzC4tL2eXcyura+kZ+c6uqw1hxqPBQhqruMQ1SBFBBgRLqkQLmexJqXv985NfuQWkRBrc4iKDps24gOoIzNFIrf+jY1EV4wIT2oTqkroQ7etVKXOXTi+v07thToVa+YBftMehf4qSkQFKUW/lPtx3y2IcAuWRaNxw7wmbCFAouYZhzYw0R433WhYahAfNBN5PxckO6Z5Q27YTKnADpWP09kTBf64HvmaTPsKdnvZH4n9eIsXPaTEQQxQgBnzzUiSXFkI6aom2hgKMcGMK4EuavlPeYYhxNnzlTgjO78l9SPSg6x0X75qhQOkvryJIdskv2iUNOSIlckjKpEE4eyTN5JW/Wk/VivVsfk2jGSme2yRSsrx+zKZ/n AAACGnicbVDLSgMxFM34rPVVdekmWARXZUYUXRZ1IUihgn1Ap5RMetuGZh4md8Qy9Dvc+CtuXCjiTtz4N6btLGrrgcDJOeeS3ONFUmi07R9rYXFpeWU1s5Zd39jc2s7t7FZ1GCsOFR7KUNU9pkGKACooUEI9UsB8T0LN61+O/NoDKC3C4A4HETR91g1ER3CGRmrlHIe6CI+Y0BJUh9SVcE9vWomrfHpVSu+OPZ1p5fJ2wR6DzhMnJXmSotzKfbntkMc+BMgl07rh2BE2E6ZQcAnDrBtriBjvsy40DA2YD7qZjFcb0kOjtGknVOYESMfq9ETCfK0HvmeSPsOenvVG4n9eI8bOeTMRQRQjBHzyUCeWFEM66om2hQKOcmAI40qYv1LeY4pxNG1mTQnO7MrzpHpccE4L9u1JvniR1pEh++SAHBGHnJEiuSZlUiGcPJEX8kberWfr1fqwPifRBSud2SN/YH3/Al76nzc= mX = 700 keV. 10 keV KDM 100 keV 1 MeV K 10 MeV    DM 

�

� � be determined by Kν and KDM via kinematic relations:

-� -� ) ) y y ~ ~ ( Earth ( 2 2 P GC P GC Earth p K -� 10 10 ¯ 0 DM AAACDXicbVC7SgNBFJ2NrxhfUUubwSjEJuyKomXQxsIignlANoTZyU0yZPbBzN1gWPYHbPwVGwtFbO3t/Bsnj0ITD1w4nHMv997jRVJotO1vK7O0vLK6ll3PbWxube/kd/dqOowVhyoPZagaHtMgRQBVFCihESlgvieh7g2ux359CEqLMLjHUQQtn/UC0RWcoZHa+SMX4QGT27CXthPHTqnrM+xzJpNKWnSHwJNRetLOF+ySPQFdJM6MFMgMlXb+y+2EPPYhQC6Z1k3HjrCVMIWCS0hzbqwhYnzAetA0NGA+6FYy+Salx0bp0G6oTAVIJ+rviYT5Wo98z3SOb9Xz3lj8z2vG2L1sJSKIYoSATxd1Y0kxpONoaEco4ChHhjCuhLmV8j5TjKMJMGdCcOZfXiS105JzXrLvzgrlq1kcWXJADkmROOSClMkNqZAq4eSRPJNX8mY9WS/Wu/Uxbc1Ys5l98gfW5w/OzJwE AAACDXicbVC7SgNBFJ2NrxhfUUubwSjEJuyKomXQxsIignlANoTZyU0yZPbBzN1gWPYHbPwVGwtFbO3t/Bsnj0ITD1w4nHMv997jRVJotO1vK7O0vLK6ll3PbWxube/kd/dqOowVhyoPZagaHtMgRQBVFCihESlgvieh7g2ux359CEqLMLjHUQQtn/UC0RWcoZHa+SMX4QGT27CXthPHTqnrM+xzJpNKWnSHwJNRetLOF+ySPQFdJM6MFMgMlXb+y+2EPPYhQC6Z1k3HjrCVMIWCS0hzbqwhYnzAetA0NGA+6FYy+Salx0bp0G6oTAVIJ+rviYT5Wo98z3SOb9Xz3lj8z2vG2L1sJSKIYoSATxd1Y0kxpONoaEco4ChHhjCuhLmV8j5TjKMJMGdCcOZfXiS105JzXrLvzgrlq1kcWXJADkmROOSClMkNqZAq4eSRPJNX8mY9WS/Wu/Uxbc1Ys5l98gfW5w/OzJwE Log Log Kν (KDM, θ) = − , (5) -� -� 2 p cos θ¯ K 0 − DM -� -� 2 2 dKν (p0 KDM)p0 ¯ -� = sin θ , (6) ¯ − 2 0 dθ θ¯=θ¯ 2 p cos θ¯ K 0 0 0 − DM p 2 where p0 2mDMKDM + KDM is 3-momentum of FIG. 1. [Top] Schematic description of BDM production by ≡ 2 BDM in the halo DM frame. dKν /dθ¯ 1/ cos θ¯ and the neutrino from a single star. [Bottom] Areal density of ¯ ∝ unit-normalized distribution of the νBDM flux from stars in large scattering angle θ π/2 is favoured for mDM ¯ ' ¯ 2 our galaxy P(~y) ≡ 1 dΦDM [kpc−2], for two representative KDM, whereas dKν /dθ 1/(cos θ 1) makes the for- ΦDM dAy ∝ − ward scattering θ¯ 0 dominate for mDM KDM. ranges of KDM: 10 – 100 keV (left) and 1 – 10 MeV (right). The neutrino flux' attenuation due to propagation is dAy is the areal element of the Galactic disk, defined by po- sition of star, ~y. determined by the exponential function in Eq. (4), and the mean free path is obtained as d 1/[(ρ /m ) ν ≡ DM DM · σνDM] where the total ν-DM cross section is

max Z KDM frame, the allowed range of KDM is given by [26] dσνDM σνDM(Kν ) dKDM . (7) ≡ 0 dKDM 2 max 2mDM(Kν + 2mν Kν ) In the derivation of Eq. (4), we use point-like star ap- 0 KDM KDM 2 . (3) ≤ ≤ ≡ (mDM + mν ) + 2mDMKν proximation, by starting with finite star radius Rstar then (1) taking Rstar 0. The final result of dΦDM(−→y )/dKDM is finite. Due→ to the distance-squared suppression, the The BDM flux by neutrinos from a Sun-like star is dominating νBDM fluxes originate either from halo DM at the vicinity of Earth or the galatic center (GC). ! From Eq. (4), we can calculate the BDM flux by neutri- dΦ(1) ( y ) 1 dN˙ Sun Z ρ ( z ) 1 DM −→ f˜ ν d3 z DM |−→| nos from Sun by taking −→x −→y = D . Even though Sun dK ' 8π2 1 dK −→ m x z 2 | − | DM ν DM |−→ − −→| provides the largest neutrino flux to Earth, only small ! ! volume of nearby DM halo compromises the BDM flux. dKν dσνDM Therefore, we need to consider the entire stellar contribu- ¯ dK × dθ θ¯=θ¯0 DM θ¯=θ¯0 tions in the Milky Way by convolving Eq. (4) with stellar 1 1 z y distribution nstar(−→y ): exp |−→ − −→| , (4) ¯ 2 ×sin θ0 −→z −→y × − dν Z (1) | − | dΦDM 3 dΦDM(−→y ) = d −→y nstar(−→y ) . (8) dKDM dKDM where the schematic diagram of the coordinate system Here we assume stars distribute within the galactic disk, is shown in the top panel of Fig. 1, and −→x , −→y , and −→z shown in the top panel of Fig. 1, with radius R 20 kpc represent the positions of Earth, Star, and halo DM, re- ≤ ˜ and thickness h 1 kpc. Using the observation [28] spectively. The correction factor f1 takes into account and integrating| out| ≤ the h, the stellar distribution on 2- the variances of stellar properties from Sun [27] and ρDM dimensional galactic disk is given by is the DM halo density profile. The differential ν-DM 11 3 2 cross section depends on scattering angle θ¯, and θ¯ can n (R) f˜ 1.2 10 /(R/kpc) [kpc− ] , (9) 0 star ' 2 × ×

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6 AAACEHicbVA9SwNBEN3z2/gVtbRZDKKN4U4ULUO0sBEUjAaSEPb25pIle3vH7pwkHPkJNv4VGwtFbC3t/DduPgpNfDDw9r0Zdub5iRQGXffbmZmdm19YXFrOrayurW/kN7fuTJxqDhUey1hXfWZACgUVFCihmmhgkS/h3u+cD/z7B9BGxOoWewk0ItZSIhScoZWa+f06QhczHptIcNqH0fNQqCDlENDyxRUNZdrtN/MFt+gOQaeJNyYFMsZ1M/9VD2KeRqCQS2ZMzXMTbGRMo+AS+rl6aiBhvMNaULNUsQhMIxse1Kd7VgloGGtbCulQ/T2RsciYXuTbzohh20x6A/E/r5ZieNbIhEpSBMVHH4WppBjTQTo0EBo4yp4ljGthd6W8zTTjaDPM2RC8yZOnyd1R0TspujfHhVJ5HMcS2SG75IB45JSUyCW5JhXCySN5Jq/kzXlyXpx352PUOuOMZ7bJHzifPymTnUU= mX = 700 keV,mDM =5MeV,gX gDM = 10 e CR-induced BDM flux - cosmic e-induced BDM flux a few AUs around Earth. Three bumps of the νBDM solar ⌫-induced BDM flux flux correspond to the pp, 13N+15O, and 8B production - Total star ⌫-induced BDM flux

AAAB9HicbVBNS8NAEN3Ur1q/qh69BIvgqSSi6LFUD16ECvYDmlA222m7dLOJu5NiCf0dXjwo4tUf481/47bNQVsfDDzem2FmXhALrtFxvq3cyura+kZ+s7C1vbO7V9w/aOgoUQzqLBKRagVUg+AS6shRQCtWQMNAQDMYXk/95giU5pF8wHEMfkj7kvc4o2gk35OJh/CEafXmbtIplpyyM4O9TNyMlEiGWqf45XUjloQgkQmqddt1YvRTqpAzAZOCl2iIKRvSPrQNlTQE7aezoyf2iVG6di9SpiTaM/X3REpDrcdhYDpDigO96E3F/7x2gr0rP+UyThAkmy/qJcLGyJ4mYHe5AoZibAhliptbbTagijI0ORVMCO7iy8ukcVZ2L8rO/XmpUs3iyJMjckxOiUsuSYXckhqpE0YeyTN5JW/WyHqx3q2PeWvOymYOyR9Ynz/iaJIr

AAAB9XicbVBNS8NAEN34WetX1aOXYBG8WBJR9FiqBy9CBfsBTSyb7aRdutmE3YlaQv+HFw+KePW/ePPfuP04aOuDgcd7M8zMCxLBNTrOt7WwuLS8sppby69vbG5tF3Z26zpOFYMai0WsmgHVILiEGnIU0EwU0CgQ0Aj6lyO/8QBK81je4SABP6JdyUPOKBrp3pOph/CE2XHl6mbYLhSdkjOGPU/cKSmSKartwpfXiVkagUQmqNYt10nQz6hCzgQM816qIaGsT7vQMlTSCLSfja8e2odG6dhhrExJtMfq74mMRloPosB0RhR7etYbif95rRTDCz/jMkkRJJssClNhY2yPIrA7XAFDMTCEMsXNrTbrUUUZmqDyJgR39uV5Uj8puWcl5/a0WK5M48iRfXJAjohLzkmZXJMqqRFGFHkmr+TNerRerHfrY9K6YE1n9sgfWJ8/UDaSYg== AAAB/3icbZDLSsNAFIYnXmu9RQU3boJFcGNJRNFlaV24ESrYCzShTKaTduhkEmZOxBKz8FXcuFDEra/hzrdx2mahrT8MfPznHM6Z3485U2Db38bC4tLyymphrbi+sbm1be7sNlWUSEIbJOKRbPtYUc4EbQADTtuxpDj0OW35w9q43rqnUrFI3MEopl6I+4IFjGDQVtfcd4E+QFrLXJFM8aR6dZN1zZJdtiey5sHJoYRy1bvml9uLSBJSAYRjpTqOHYOXYgmMcJoV3UTRGJMh7tOORoFDqrx0cn9mHWmnZwWR1E+ANXF/T6Q4VGoU+rozxDBQs7Wx+V+tk0Bw6aVMxAlQQaaLgoRbEFnjMKwek5QAH2nARDJ9q0UGWGICOrKiDsGZ/fI8NE/LznnZvj0rVap5HAV0gA7RMXLQBaqga1RHDUTQI3pGr+jNeDJejHfjY9q6YOQze+iPjM8fQ3eWPw==

] Astrophysical uncertainty inC⌫ CN-BDM-BDM⌫BDM-BDM processes of solar neutrinos [19]. Assuming g = g , the e ν -

- νBDM ﬂux can be two to four orders of magnitude larger -

than that induced by cosmic electrons for KDM 50 keV. - . - [ This feature is quite robust for other DM and mediator - masses as shown in the bottom panel.

- There are several factors that can make our estimations different. i ) The DM halo profile, especially around the - GC. We take the NFW profile. ii ) The ν flux varies with [] the type and age of stars [27]. iii ) The star distribution

AAACHXicbZBNSwMxEIazflu/qh69BIvgQcquVupFKOrBi6BgP6Bblmw61dBkd0lmxbL0h3jxr3jxoCAevIj/xrRW0OpA4OV9ZpjMGyZSGHTdD2dicmp6ZnZuPrewuLS8kl9dq5k41RyqPJaxboTMgBQRVFGghEaigalQQj3sHg94/Qa0EXF0ib0EWopdRaIjOENrBfk9FTToIS27LvURbjGjXaj1d6hPVZD5WtGTs77l+9/0zNIgX3CL7rDoX+GNRIGM6jzIv/ntmKcKIuSSGdP03ARbGdMouIR+zk8NJIx32RU0rYyYAtPKhsf16ZZ12rQTa/sipEP350TGlDE9FdpOxfDajLOB+R9rptg5aGUiSlKEiH8t6qSSYkwHSdG20MBR9qxgXAv7V8qvmWYcbZ45G4I3fvJfUd8teqWi512UCpWjUR5zZINskm3ikTKpkFNyTqqEkzvyQJ7Is3PvPDovzutX64Qzmlknv8p5/wS/QJ8k mX = 700 keV,mDM =5MeV in the Milky Way. All the above uncertainties are hard

AAACH3icbVBNS8NAEN34WetX1KOXxSJ4kJJIS70IRT14ESpYW2hK2GynunQ3CbsTsYT+Ei/+FS8eFES8+W/c1h78ejDweG+GmXlRKoVBz/twZmbn5hcWC0vF5ZXVtXV3Y/PKJJnm0OSJTHQ7YgakiKGJAiW0Uw1MRRJa0eBk7LduQRuRxJc4TKGr2HUs+oIztFLoVlXYpke05nk0QLjDnA7garRPA6rCPNCKnp6PrF/96YduySt7E9C/xJ+SEpmiEbrvQS/hmYIYuWTGdHwvxW7ONAouYVQMMgMp4wN2DR1LY6bAdPPJeyO6a5Ue7SfaVox0on6fyJkyZqgi26kY3pjf3lj8z+tk2D/s5iJOM4SYfy3qZ5JiQsdZ0Z7QwFEOLWFcC3sr5TdMM4420aINwf/98l/SOij7lbLvX1RK9eNpHgWyTXbIHvFJjdTJGWmQJuHknjySZ/LiPDhPzqvz9tU640xntsgPOB+f5mOftg== mX = 700 keV,mDM = 500 keV

AAACHnicbVA9SwNBEN2LXzF+RS1tFoNgIeFOItoIohY2QgRjArlw7G0myZLdu2N3TgxH/oiNf8XGQkEEK/03bmIKoz4YeLw3w8y8MJHCoOt+OrmZ2bn5hfxiYWl5ZXWtuL5xY+JUc6jxWMa6ETIDUkRQQ4ESGokGpkIJ9bB/NvLrt6CNiKNrHCTQUqwbiY7gDK0UFCsqaNBjeui61Ee4w4z24Wa4R32qgszXip5fDq1/MGUHxZJbdsegf4k3ISUyQTUovvvtmKcKIuSSGdP03ARbGdMouIRhwU8NJIz3WRealkZMgWll4++GdMcqbdqJta0I6Vj9OZExZcxAhbZTMeyZ395I/M9rptg5amUiSlKEiH8v6qSSYkxHUdG20MBRDixhXAt7K+U9phlHG2jBhuD9fvkvqe+XvUrZ864qpZPTSR55skW2yS7xyCE5IRekSmqEk3vySJ7Ji/PgPDmvztt3a86ZzGySKTgfX2m4n3w= ] m = 700 keV,m = 50 keV to be included in the calculation. In order to show the - X DM - AAACHXicbVDJSgNBEO1xjXGLevTSGAQPEmZc0IsQ1IMXIYJZIBOGnk5Fm3TPDN01YhjyIV78FS8eFMSDF/Fv7CwHNT4oeLxXRVW9MJHCoOt+OVPTM7Nz87mF/OLS8spqYW29ZuJUc6jyWMa6ETIDUkRQRYESGokGpkIJ9bB7NvDrd6CNiKNr7CXQUuwmEh3BGVopKOyroEFP6JHrUh/hHjPahVp/l/pUBZmvFT2/7Fv/8KcbFIpuyR2CThJvTIpkjEpQ+PDbMU8VRMglM6bpuQm2MqZRcAn9vJ8aSBjvshtoWhoxBaaVDZ/r022rtGkn1rYipEP150TGlDE9FdpOxfDW/PUG4n9eM8XOcSsTUZIiRHy0qJNKijEdJEXbQgNH2bOEcS3srZTfMs042jzzNgTv78uTpL5X8g5Knnd1UCyfjvPIkU2yRXaIR45ImVyQCqkSTh7IE3khr86j8+y8Oe+j1ilnPLNBfsH5/AbtMJ9C mX = 700 keV,mDM =5keV

AAACHXicbZDJSgNBEIZ73I1b1KOXxiB4kDCjEb0Ioh68CApmgUwYejqVpEn3zNBdI4YhD+LFV/HiQUE8eBHfxs4iuBU0/PxfFdX1h4kUBl33w5mYnJqemZ2bzy0sLi2v5FfXKiZONYcyj2WsayEzIEUEZRQooZZoYCqUUA27pwNevQFtRBxdYy+BhmLtSLQEZ2itIL+ngho9op7rUh/hFjPahUp/h/pUBZmvFT276Fu+/0UvLA3yBbfoDov+Fd5YFMi4LoP8m9+MeaogQi6ZMXXPTbCRMY2CS+jn/NRAwniXtaFuZcQUmEY2PK5Pt6zTpK1Y2xchHbrfJzKmjOmp0HYqhh3zmw3M/1g9xdZhIxNRkiJEfLSolUqKMR0kRZtCA0fZs4JxLexfKe8wzTjaPHM2BO/3yX9FdbfolYqed1UqHJ+M85gjG2STbBOPHJBjck4uSZlwckceyBN5du6dR+fFeR21TjjjmXXyo5z3T7Uanx4=

robustness of the results, we conservatively vary 0.1 mX = 100 keV,mDM =5MeV .

AAACHHicbZBNSwMxEIazftb6VfXoJVgED1J2S0UvQlEPXgoK1ha6ZcmmUxua7C7JrFiW/g8v/hUvHhTEiwfBf2NaK/g1EHh5nxkm84aJFAZd992Zmp6ZnZvPLeQXl5ZXVgtr65cmTjWHOo9lrJshMyBFBHUUKKGZaGAqlNAI+8cj3rgGbUQcXeAggbZiV5HoCs7QWkGhrIImPaSeS32EG8xoHy6Hu9SnKsh8rehJbWjx3hetWRoUim7JHRf9K7yJKJJJnQWFV78T81RBhFwyY1qem2A7YxoFlzDM+6mBhPE+u4KWlRFTYNrZ+LYh3bZOh3ZjbV+EdOx+n8iYMmagQtupGPbMbzYy/2OtFLsH7UxESYoQ8c9F3VRSjOkoKNoRGjjKgRWMa2H/SnmPacbRxpm3IXi/T/4rGuWSVyl53nmlWD2a5JEjm2SL7BCP7JMqOSVnpE44uSX35JE8OXfOg/PsvHy2TjmTmQ3yo5y3DzzinuQ= - - mX = 10 keV,mDM =5MeV ˜

f 10 in Eq. (4) and (8), depicted as a blue band in the - . [ - top panel of Fig. 3.

Attenuation of the BDM ﬂux.

The attenuation ef- - fect of the cosmic-neutrino flux scattered by halo DM is taken into account by the exponential factor in Eq. 4. - We estimate the mean free path of cosmic neutrino dν [] 28 34 2 by taking σνDM 10− 10− cm . For the nDM '6 3 − 22 ∼ (keV/mDM) 10 cm− , dν (mDM/keV) (10 FIG. 3. [Top] BDM fluxes by solar neutrinos, cosmic neutri- 28 × ' × − nos, and cosmic electrons. We assume σ comes from a vec- 10 ) cm, which is larger than the size of the Milky Way νDM and results in negligible effect. tor boson X coupling to both DM and leptons (gX = ge = gν ) −6 with (mDM, mX , gX gDM) = (5MeV, 700keV, 10 ). The un- Next, we estimate the mean free path of BDM in- certainty band for νBDM corresponds to 0.1 ≤ f˜ ≤ 10. [Bot- side Earth by assuming σeDM = σνDM. For σeDM = 33 2 tom] BDM fluxes for different mX and mDM with f˜ = 1. 10− cm with electron number density of Earth ne 24 3 4 ' Solid and dotted lines are νBDM and cosmic electron BDM 10 cm− , the mean free path 1/(ne σeDM) 10 km is · ' 29 2 fluxes, respectively. comparable to the size of Earth. For σeDM = 10− cm , the BDM mean free path reduces to (km). Most of DM direct detection detectors locate a fewO kilometers un- where f˜2 factor includes the uncertainties from detailed derground, rendering the νBDM signal be substantially 29 2 structures of the Milky Way, e.g. spiral arms and density suppressed for σeDM & 10− cm . Thus, the attenua- fluctuations. tion of BDM inside Earth will provide upper limits on The νBDM fluxes with two KDM regimes are shown experimental sensitivities as shown in Fig. 4. in the bottom panels of Fig. 1. Due to the high stellar and DM number densities around the GC, the BDM flux contribution from the GC region exceeds that from III. EXPERIMENTAL SENSITIVITIES the vicinity of Earth. Fig. 2 shows the θ dependence of the νBDM fluxes 1 ϕBDM at Earth where θ rep- ϕBDM dθ resents the angle between the νBDM arrival direction To estimate experimental sensitivities, we use two ap- and the GC. For K m in the right panel, the proaches for DM models. i ) Heavy mediator: the inter- DM DM eff forward scattering (θ¯ 0) is preferred, so that νBDM actions can be described by effective cross sections σνDM 0 ' eff from the GC dominates and thus θ 0. In the left panel, and σeDM. ii ) Light mediator: the X boson from the ' gauged U(1) couples to DM and leptons. KDM mDM prefers large-angle scattering (θ¯0 90◦), Le Li ' − i which enhances the flux for θ & 40◦ originating relatively For the approach ), the differential cross section is far from the GC. The θ dependence of the νBDM flux can defined as

be used to determine mDM in the future. eff eff In the top panel of Fig. 3, we compare the BDM fluxes dσνDM,eDM σνDM,eDM max min . (10) via solar neutrinos, cosmic neutrinos, and cosmic-ray dKDM ≡ KDM KDM electrons by fixing f˜ f˜ f˜ =1. The νBDM flux is − ≡ 1 · 2 three orders of magnitude larger than that by solar neu- On the other hand, for the U(1)Le Li model, the trinos, because the later is relevant to DM only within neutrino-DM scattering cross section is− given by [29] 4

dσ (g g )2 2m (m + K )2 K (m + m )2 + 2m K + m K2 νDM X DM DM ν ν − DM ν DM DM ν DM DM = 2 2 2 . (11) dKDM 4π (2mν Kν + Kν )(2mDMKDM + mX )

3600 meter water equivalent (m.w.e.) and Borexino [38] -28 10 is at 3800 m.w.e while PandaX [39] is shielded by 2400 m ] 2 10-29 marble overburden ( 6800 m.w.e.). The most shallow ∼ -30 SK JUNO detector [33], located at 700 m deep underground [cm 10 excluded by XENON1T

-31 HK ( 2000 m.w.e.), has the best upper sensitive to νBDM eDM 10 ∼ 28 2 σ -32 XENONnT with σeDM 10− cm . = 10 Borexino 1σ ' PandaX SENSEI

DM -33

ν 10 σ CDMS HVeV σ 2 EDELWEISS 10-34 JUNO DAMIC 10-35 IV. DISCUSSIONS 10-3 10-2 10-1 100 101 102 mDM [MeV] The flux of the cosmic-neutrino-boosted-DM (νBDM) FIG. 4. νBDM contributions to XENON1T electron re- is substantially larger than the one of the cosmic- eff eff coil, assuming σνDM = σeDM, where the 1σ (green) and 2σ electron-boosted-DM so that it contributes dominantly (white) regions from χ2 analysis, and the gray-shaded re- in direct detection experiments on Earth. Due to the gion is excluded more than 2σ. The expected sensitivities distributions of the sources of neutrinos in Milky Way from other underground detectors are depicted: Brexino [30], and the dark matter in halo, the angular distribution of PandaX [31], XENONnT [32], and JUNO [33]. For compari- the νBDM is kinematically correlated with the DM mass. son, existing limits are shown together: CDMS HVeV [34], Therefore precise measurement of directional information DAMIC [35], EDELWEISS [36], and SENSEI [37]. The helps in determination of the DM mass. cosmic-electron-BDM constraints from Super-K and Hyper- K [14]. The existing underground detectors probe the parameter region of neutrino-DM interaction and electron-DM 34 2 28 2 interaction in 10− cm . σνDM = σeDM . 10− cm with 1 keV . mDM . 100 MeV based on the effective For KDM (keV) and mDM mX (MeV), it cross section approach. Since the DM flux is enhanced 'O ' 'O makes dσνDM/dKDM almost independent of KDM. by neutrino-boost, we find parameter regions for the re- We perform the model-independent χ2 analysis for the cent XENON1T anomaly (see Fig. 4). However, they are eff eff effective cross section (mDM, σνDM = σeDM) in Fig. 4. still hardly consistent with other DM searches. There are five disconnected 1σ regions for the XENON1T Finally, we discuss various factors of future refinement excess [25], which originate from the three bumps of of the current study. Here we only assumed that nuclear the νBDM flux spectrum in Fig. 3. The 2σ exclusion activities inside each star are on average same as in our region is gray-shaded. The νBDM provides stringent Sun, so that the neutrino fluxes from each star are all eff eff constraint on σνDM = σeDM for unexplored small mass similar. Obviously, this is a crude estimation and actual mDM . MeV, compared with the current limits from DM neutrino fluxes differ from star to star. Also, the GC direct detection experiments including CDMS HVeV [34], region has the largest population of main sequence stars DAMIC [35], EDELWEISS [36], and SENSEI [37]. and also red giants [40, 41], which enhances f˜ f˜ factor 1 · 2 We evaluate the sensitivities of νBDM with other cur- over unity [27]. Last but not least, we point out the po- rent (Brexino [30], PandaX [31]) and future experiments tential modification due to the extra galactic neutrinos. (XENONnT [32], JUNO [33]). To estimate the sensitiv- Even though extra galactic contributions in neutrino flux ities, we take the four ton-year exposure for XENONnT is subdominant in the energy range for νBDM [18] , it and 20 kton-year exposure for JUNO assuming no ex- can lead modification in e.g. spatial and kinetic distri- cess above the expected background and dominance of butions of νBDM. All those factors of improvement are statistical uncertainty. Borexino and JUNO have higher reserved for the future work. energy threshold above 100 keV but huge statistics. JUNO has the best sensitivity for mDM . 0.5 MeV, ACKNOWLEDGMENTS while XENON1T/nT are better than JUNO for mDM & 0.5 MeV. PandaX has a slightly weaker limit due to the smaller 0.276 ton-year exposure than XENON1T of The work is supported in part by Basic Sci- 29 2 0.65 tonne-year. For σeDM & 10− cm , the earth crust ence Research Program through the National Re- attenuates the BDM flux; specifically, XENON1T and search Foundation of Korea (NRF) funded by the XENONnT [24] are located underground at a depth of Ministry of Education, Science and Technology 5

[NRF-2018R1A4A1025334, NRF-2019R1A2C1089334 (SCP), NRF-2019R1C1C1005073 (JCP) and NRF- 2020R1I1A1A01066413 (PYT)].

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