YHEP-COS-21-01

Cosmic-Neutrino-Boosted Dark Matter (νBDM)

Yongsoo Jho,1, ∗ Jong-Chul Park,2, † Seong Chan Park,1, ‡ and Po-Yan Tseng1, §

1Department of Physics and IPAP, Yonsei University, Seoul 03722, Republic of Korea2Department 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 mechanismis so significant that the arriving flux of dark matter in the mass window 1 keV . mDM . 1 MeV onEarth 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 forsuch cosmic-neutrino-boosted dark matter (νBDM) from advanced underground experiments suchas Borexino, PandaX, XENON1T, and JUNO.

I. INTRODUCTION

Revealing the properties of dark matter (DM) is defi-nitely one of the most pressing issues in particle physics,astrophysics, and cosmology. Direct detection experi-ments of DM have particular importance as they aim toprobe interaction of DM with standard model (SM) par-ticles [1]. However, there exists fundamental limitationin detecting a sub-MeV dark matter set by the maximumkinetic energy of the DM particle in halo:

KmaxDM

<∼ 10−6mDM<∼ 1 eV (1)

with the velocity v ∼ 10−3. This low kinetic energycauses a significant problem in detecting light dark mat-ter since the recoil energy of scattered SM particle isalso limited by the kinetic energy 1. On the other hand,there still exists a chance to detect a subcomponent ofDM, dubbed ‘boosted dark matter’ (BDM), which maycarry much larger energy beyond threshold due to vari-ous mechanisms [4–10] including scattering by energeticcosmic-ray particles [11–17]. We note that focus hasbeen given to cosmic-ray electron and proton so far eventhough the chance is not exclusively open for chargedparticles.

In this letter, we focus on a noble class of cosmic-neutrino-boosted-dark matter (νBDM) extending previ-ous studies: there exist a huge number of cosmic-rayneutrinos arriving at the solar system from various ori-gins [18]. Our Sun is also generating a large numberof neutrinos [19–21] so that they may boost DM withinthe solar system. We find that νBDM can be a domi-nant part of the whole BDM when DM-neutrino inter-action is as strong as DM-electron interaction, which is

∗ jys34@yonsei.ac.kr† jcpark@cnu.ac.kr; co-corresponding author‡ sc.park@yonsei.ac.kr; co-corresponding author§ tpoyan1209@gmail.com1 Several ideas have been suggested to detect signals with low recoilenergies by lowering the threshold energies at detectors (see [2, 3]and references therein).

indeed the case for gauged lepton number as mediator,for instance [22, 23]. The existing conclusions regardingcosmic-electron-induced BDM should be re-examined.

II. BOOST MECHANISM BY COSMICNEUTRINO

Cosmic neutrino inputs. Near Earth, our Sun pro-vides the dominating neutrino flux dΦSun

ν /dKν in theneutrino energy Kν . 10 MeV reaching the maximum' O(108) [cm−2 s−1 keV−1] around Kν ' 0.3 MeV [19–21], which gives the total number of neutrino emissionrate per unit energy

dNSunν

dKν≡ dΦSun

ν

dKν(4πD2

�) , (2)

where D� = 1 AU is the distance between Sun andEarth. The neutrinos can boost non-relativistic lightDM, leaving distinctive signals at terrestrial experiments,e.g. XENON1T [24, 25]. The total contributions fromall stars for νBDM could be significant compared to theBDM flux by the solar neutrinos. The overall neutrinoflux from all stars in the Milky Way (say, cosmic-neutrinoflux) has not been measured by astrophysical observa-tions, and could be highly anisotropic, which is differentfrom the isotropic diffused cosmic electrons. In general,DM particles can be boosted by the neutrino flux fromthe nearest star, instead of diffused neutrinos. Keep thisphilosophy in mind, we will compute the νBDM flux bystarting with single star contribution in the following sec-tion, then integrate the entire star distribution in theMilky Way.

Cosmic neutrino and DM scattering. The halo DMis boosted by neutrino through the process ν + χ →ν + χ, which may originate from the exchange of theU(1)Le−Li

gauge boson or dim-6 effective operators in-cluding (¯γµ`)(χγµχ) or (¯ )(χχ). The resulting BDMkinetic energy KDM can be determined from the kineticenergy of incoming neutrino Kν . At the halo DM rest

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10P

(~y)

<latexit sha1_base64="AO/WszN+HVZY+SS2wiANGhHnK9Q=">AAACDXicbVC7SgNBFJ2NrxhfUUubwSjEJuyKomXQxsIignlANoTZyU0yZPbBzN1gWPYHbPwVGwtFbO3t/Bsnj0ITD1w4nHMv997jRVJotO1vK7O0vLK6ll3PbWxube/kd/dqOowVhyoPZagaHtMgRQBVFCihESlgvieh7g2ux359CEqLMLjHUQQtn/UC0RWcoZHa+SMX4QGT27CXthPHTqnrM+xzJpNKWnSHwJNRetLOF+ySPQFdJM6MFMgMlXb+y+2EPPYhQC6Z1k3HjrCVMIWCS0hzbqwhYnzAetA0NGA+6FYy+Salx0bp0G6oTAVIJ+rviYT5Wo98z3SOb9Xz3lj8z2vG2L1sJSKIYoSATxd1Y0kxpONoaEco4ChHhjCuhLmV8j5TjKMJMGdCcOZfXiS105JzXrLvzgrlq1kcWXJADkmROOSClMkNqZAq4eSRPJNX8mY9WS/Wu/Uxbc1Ys5l98gfW5w/OzJwE</latexit> Log

10P

(~y)

FIG. 1. [Top] Schematic description of BDM production bythe neutrino from a single star. [Bottom] Areal density ofunit-normalized distribution of the νBDM flux from stars inour galaxy P(~y) ≡ 1

ΦDM

dΦDMdAy

[kpc−2], for two representative

ranges of KDM: 10 – 100 keV (left) and 1 – 10 MeV (right).dAy is the areal element of the Galactic disk, defined by po-sition of star, ~y.

frame, the allowed range of KDM is given by [26]

0 ≤ KDM ≤ KmaxDM ≡

2mDM(K2ν + 2mνKν)

(mDM +mν)2 + 2mDMKν. (3)

The BDM flux by neutrinos from a Sun-like star is

dΦ(1)DM(−→y )

dKDM' 1

8π2

(f1dNSun

ν

dKν

)∫d3−→z ρDM(|−→z |)

mDM

1

|−→x −−→z |2

×(dKν

dθ

∣∣∣∣θ=θ0

)(dσνDM

dKDM

∣∣∣∣θ=θ0

)

× 1

sin θ0

1

|−→z −−→y |2 × exp

(−|−→z −−→y |dν

), (4)

where the schematic diagram of the coordinate systemis shown in the top panel of Fig. 1, and −→x ,−→y , and −→zrepresent the positions of Earth, Star, and halo DM, re-spectively. The correction factor f1 takes into accountthe variances of stellar properties from Sun [27] and ρDM

is the DM halo density profile. The differential ν-DMcross section depends on scattering angle θ, and θ0 can

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mDM = 5 MeV<latexit sha1_base64="yVOVmvP5lMAQmfnmYuT38u9vTgc=">AAACBXicbVA9SwNBEN2LXzF+RS21WAyCVbgTgzZCUAsbIYL5gCSEvc0kWbJ7d+zOieFIY+NfsbFQxNb/YOe/cfNRaOKDgcd7M8zM8yMpDLrut5NaWFxaXkmvZtbWNza3sts7FRPGmkOZhzLUNZ8ZkCKAMgqUUIs0MOVLqPr9y5FfvQdtRBjc4SCCpmLdQHQEZ2ilVnZftZKGVvTqZkjPacF1aQPhARPah8qwlc25eXcMOk+8KcmRKUqt7FejHfJYQYBcMmPqnhthM2EaBZcwzDRiAxHjfdaFuqUBU2CayfiLIT20Spt2Qm0rQDpWf08kTBkzUL7tVAx7ZtYbif959Rg7Z81EBFGMEPDJok4sKYZ0FAltCw0c5cASxrWwt1LeY5pxtMFlbAje7MvzpHKc9wp59/YkV7yYxpEme+SAHBGPnJIiuSYlUiacPJJn8krenCfnxXl3PiatKWc6s0v+wPn8ARQVlwg=</latexit>

mDM = 500 keV<latexit sha1_base64="QoVn+z3SAtPLX+1BCr0xa5mdPzw=">AAACBHicbVA9SwNBEN2LXzF+RS3TLAbBKtyJQRshqIWNEMF8QBLC3maSLNm9O3bnxHCksPGv2FgoYuuPsPPfuPkoNPHBwOO9GWbm+ZEUBl3320ktLa+srqXXMxubW9s72d29qgljzaHCQxnqus8MSBFABQVKqEcamPIl1PzB5div3YM2IgzucBhBS7FeILqCM7RSO5tT7aSpFb26GdFzWnRpE+EBEzqA6qidzbsFdwK6SLwZyZMZyu3sV7MT8lhBgFwyYxqeG2ErYRoFlzDKNGMDEeMD1oOGpQFTYFrJ5IkRPbRKh3ZDbStAOlF/TyRMGTNUvu1UDPtm3huL/3mNGLtnrUQEUYwQ8OmibiwphnScCO0IDRzl0BLGtbC3Ut5nmnG0uWVsCN78y4ukelzwigX39iRfupjFkSY5ckCOiEdOSYlckzKpEE4eyTN5JW/Ok/PivDsf09aUM5vZJ3/gfP4Anz2Wzg==</latexit>

mDM = 50 keV<latexit sha1_base64="kVo4lM7P0f5Y90zroTSgrAuxYjY=">AAACA3icbVDLSgNBEJyNrxhfUW96GQyCp7ArBr0IQT14ESKYByQhzE46yZCZ3WWmVwxLwIu/4sWDIl79CW/+jZPHQRMLGoqqbrq7/EgKg6777aQWFpeWV9KrmbX1jc2t7PZOxYSx5lDmoQx1zWcGpAigjAIl1CINTPkSqn7/cuRX70EbEQZ3OIigqVg3EB3BGVqpld1TraShFb26GdJzWqANhAdMaB8qw1Y25+bdMeg88aYkR6YotbJfjXbIYwUBcsmMqXtuhM2EaRRcwjDTiA1EjPdZF+qWBkyBaSbjH4b00Cpt2gm1rQDpWP09kTBlzED5tlMx7JlZbyT+59Vj7Jw1ExFEMULAJ4s6saQY0lEgtC00cJQDSxjXwt5KeY9pxtHGlrEheLMvz5PKcd4r5N3bk1zxYhpHmuyTA3JEPHJKiuSalEiZcPJInskreXOenBfn3fmYtKac6cwu+QPn8wcqppaU</latexit>

mDM = 5 keV

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mDM = 5 MeV<latexit sha1_base64="yVOVmvP5lMAQmfnmYuT38u9vTgc=">AAACBXicbVA9SwNBEN2LXzF+RS21WAyCVbgTgzZCUAsbIYL5gCSEvc0kWbJ7d+zOieFIY+NfsbFQxNb/YOe/cfNRaOKDgcd7M8zM8yMpDLrut5NaWFxaXkmvZtbWNza3sts7FRPGmkOZhzLUNZ8ZkCKAMgqUUIs0MOVLqPr9y5FfvQdtRBjc4SCCpmLdQHQEZ2ilVnZftZKGVvTqZkjPacF1aQPhARPah8qwlc25eXcMOk+8KcmRKUqt7FejHfJYQYBcMmPqnhthM2EaBZcwzDRiAxHjfdaFuqUBU2CayfiLIT20Spt2Qm0rQDpWf08kTBkzUL7tVAx7ZtYbif959Rg7Z81EBFGMEPDJok4sKYZ0FAltCw0c5cASxrWwt1LeY5pxtMFlbAje7MvzpHKc9wp59/YkV7yYxpEme+SAHBGPnJIiuSYlUiacPJJn8krenCfnxXl3PiatKWc6s0v+wPn8ARQVlwg=</latexit>

mDM = 500 keV<latexit sha1_base64="QoVn+z3SAtPLX+1BCr0xa5mdPzw=">AAACBHicbVA9SwNBEN2LXzF+RS3TLAbBKtyJQRshqIWNEMF8QBLC3maSLNm9O3bnxHCksPGv2FgoYuuPsPPfuPkoNPHBwOO9GWbm+ZEUBl3320ktLa+srqXXMxubW9s72d29qgljzaHCQxnqus8MSBFABQVKqEcamPIl1PzB5div3YM2IgzucBhBS7FeILqCM7RSO5tT7aSpFb26GdFzWnRpE+EBEzqA6qidzbsFdwK6SLwZyZMZyu3sV7MT8lhBgFwyYxqeG2ErYRoFlzDKNGMDEeMD1oOGpQFTYFrJ5IkRPbRKh3ZDbStAOlF/TyRMGTNUvu1UDPtm3huL/3mNGLtnrUQEUYwQ8OmibiwphnScCO0IDRzl0BLGtbC3Ut5nmnG0uWVsCN78y4ukelzwigX39iRfupjFkSY5ckCOiEdOSYlckzKpEE4eyTN5JW/Ok/PivDsf09aUM5vZJ3/gfP4Anz2Wzg==</latexit>

mDM = 50 keV<latexit sha1_base64="kVo4lM7P0f5Y90zroTSgrAuxYjY=">AAACA3icbVDLSgNBEJyNrxhfUW96GQyCp7ArBr0IQT14ESKYByQhzE46yZCZ3WWmVwxLwIu/4sWDIl79CW/+jZPHQRMLGoqqbrq7/EgKg6777aQWFpeWV9KrmbX1jc2t7PZOxYSx5lDmoQx1zWcGpAigjAIl1CINTPkSqn7/cuRX70EbEQZ3OIigqVg3EB3BGVqpld1TraShFb26GdJzWqANhAdMaB8qw1Y25+bdMeg88aYkR6YotbJfjXbIYwUBcsmMqXtuhM2EaRRcwjDTiA1EjPdZF+qWBkyBaSbjH4b00Cpt2gm1rQDpWP09kTBlzED5tlMx7JlZbyT+59Vj7Jw1ExFEMULAJ4s6saQY0lEgtC00cJQDSxjXwt5KeY9pxtHGlrEheLMvz5PKcd4r5N3bk1zxYhpHmuyTA3JEPHJKiuSalEiZcPJInskreXOenBfn3fmYtKac6cwu+QPn8wcqppaU</latexit>

mDM = 5 keV

<latexit sha1_base64="mqlw/kS+4kC8kXBGfIuslo8VU7w=">AAACJ3icbVDLSsNAFJ34rPVVdelmsAiuSiKKrqRUF26ECvYBTSmTyaQZOpmEmZtCCfkbN/6KG0FFdOmfOH0stPXAhcM593LvPV4iuAbb/rKWlldW19YLG8XNre2d3dLeflPHqaKsQWMRq7ZHNBNcsgZwEKydKEYiT7CWN7ge+60hU5rH8gFGCetGpC95wCkBI/VKV26gCM2cPHOHRCUh72WuinDt5i7P8dTzFx2jQciA5L1S2a7YE+BF4sxIGc1Q75VeXT+macQkUEG07jh2At2MKOBUsLzoppolhA5In3UMlSRiuptN/szxsVF8HMTKlAQ8UX9PZCTSehR5pjMiEOp5byz+53VSCC67GZdJCkzS6aIgFRhiPA4N+1wxCmJkCKGKm1sxDYkJB0y0RROCM//yImmeVpzzin1/Vq7WZnEU0CE6QifIQReoim5RHTUQRY/oGb2hd+vJerE+rM9p65I1mzlAf2B9/wAToqdM</latexit>

1

'BDM

d'BDM

d✓

<latexit sha1_base64="mqlw/kS+4kC8kXBGfIuslo8VU7w=">AAACJ3icbVDLSsNAFJ34rPVVdelmsAiuSiKKrqRUF26ECvYBTSmTyaQZOpmEmZtCCfkbN/6KG0FFdOmfOH0stPXAhcM593LvPV4iuAbb/rKWlldW19YLG8XNre2d3dLeflPHqaKsQWMRq7ZHNBNcsgZwEKydKEYiT7CWN7ge+60hU5rH8gFGCetGpC95wCkBI/VKV26gCM2cPHOHRCUh72WuinDt5i7P8dTzFx2jQciA5L1S2a7YE+BF4sxIGc1Q75VeXT+macQkUEG07jh2At2MKOBUsLzoppolhA5In3UMlSRiuptN/szxsVF8HMTKlAQ8UX9PZCTSehR5pjMiEOp5byz+53VSCC67GZdJCkzS6aIgFRhiPA4N+1wxCmJkCKGKm1sxDYkJB0y0RROCM//yImmeVpzzin1/Vq7WZnEU0CE6QifIQReoim5RHTUQRY/oGb2hd+vJerE+rM9p65I1mzlAf2B9/wAToqdM</latexit>

1

'BDM

d'BDM

d✓

<latexit sha1_base64="5NZUhXkWPZGtc2sXl0WNWTCkRDY=">AAACBHicbVDJSgNBEO2JW4xb1GMujUHwFGZE0YsQ1IMgQgSzQGYIPZ1K0qRnobtGDEMOXvwVLx4U8epHePNv7CwHTXxQ8Hiviqp6fiyFRtv+tjILi0vLK9nV3Nr6xuZWfnunpqNEcajySEaq4TMNUoRQRYESGrECFvgS6n7/YuTX70FpEYV3OIjBC1g3FB3BGRqplS9ct1JXBfTyZkjPqGNTF+EBU9qH2rCVL9oleww6T5wpKZIpKq38l9uOeBJAiFwyrZuOHaOXMoWCSxjm3ERDzHifdaFpaMgC0F46fmJI943Spp1ImQqRjtXfEykLtB4EvukMGPb0rDcS//OaCXZOvVSEcYIQ8smiTiIpRnSUCG0LBRzlwBDGlTC3Ut5jinE0ueVMCM7sy/Okdlhyjkv27VGxfD6NI0sKZI8cEIeckDK5IhVSJZw8kmfySt6sJ+vFerc+Jq0ZazqzS/7A+vwBYf2WqA==</latexit>

KDM = 10 keV<latexit sha1_base64="+T43/Ba7ALC7uMgWgHk7IUZBmZI=">AAACA3icbVDJSgNBEO1xjXGLetNLYxA8hRlR9CIE9SBIIIJZIBmGnk4ladKz0F0jhiHgxV/x4kERr/6EN//GznLQxAcFj/eqqKrnx1JotO1va25+YXFpObOSXV1b39jMbW1XdZQoDhUeyUjVfaZBihAqKFBCPVbAAl9Cze9dDv3aPSgtovAO+zG4AeuEoi04QyN5ud0bL22qgF6VBvScOrSJ8IApLUF14OXydsEegc4SZ0LyZIKyl/tqtiKeBBAil0zrhmPH6KZMoeASBtlmoiFmvMc60DA0ZAFoNx39MKAHRmnRdqRMhUhH6u+JlAVa9wPfdAYMu3raG4r/eY0E22duKsI4QQj5eFE7kRQjOgyEtoQCjrJvCONKmFsp7zLFOJrYsiYEZ/rlWVI9KjgnBfv2OF+8mMSRIXtknxwSh5ySIrkmZVIhnDySZ/JK3qwn68V6tz7GrXPWZGaH/IH1+QO/q5ZQ</latexit>

KDM = 1 MeV

FIG. 2. The unit-normalized arrival direction θ distributionsof the νBDM spectral flux ϕBDM ≡ dΦDM/dKDM for twobenchmark values of KDM: 10 keV (left) and 1 MeV (right)varying mDM = 5 keV – 5 MeV with a fixed mediator mass,mX = 700 keV.

be determined by Kν and KDM via kinematic relations:

Kν(KDM, θ) =p′2 −K2

DM

2(p′ cos θ −KDM

) , (5)

dKν

dθ

∣∣∣∣θ=θ0

=(p′2 −K2

DM)p′

2(p′ cos θ0 −KDM

)2 sin θ0 , (6)

where p′ ≡√

2mDMKDM +K2DM is 3-momentum of

BDM in the halo DM frame. dKν/dθ ∝ 1/ cos2 θ andlarge scattering angle θ ' π/2 is favoured for mDM �KDM, whereas dKν/dθ ∝ 1/(cos θ − 1)2 makes the for-ward scattering θ ' 0 dominate for mDM � KDM.

The neutrino flux attenuation due to propagation isdetermined by the exponential function in Eq. (4), andthe mean free path is obtained as dν ≡ 1/[(ρDM/mDM) ·σνDM] where the total ν-DM cross section is

σνDM(Kν) ≡∫ Kmax

DM

0

dKDMdσνDM

dKDM. (7)

In the derivation of Eq. (4), we use point-like star ap-proximation, by starting with finite star radius Rstar then

taking Rstar → 0. The final result of dΦ(1)DM(−→y )/dKDM

is finite. Due to the distance-squared suppression, thedominating νBDM fluxes originate either from halo DMat the vicinity of Earth or the galatic center (GC).

From Eq. (4), we can calculate the BDM flux by neutri-nos from Sun by taking |−→x −−→y | = D�. Even though Sunprovides the largest neutrino flux to Earth, only smallvolume of nearby DM halo compromises the BDM flux.Therefore, we need to consider the entire stellar contribu-tions in the Milky Way by convolving Eq. (4) with stellardistribution nstar(

−→y ):

dΦDM

dKDM=

∫d3−→y nstar(

−→y )dΦ

(1)DM(−→y )

dKDM. (8)

Here we assume stars distribute within the galactic disk,shown in the top panel of Fig. 1, with radius R ≤ 20 kpcand thickness |h| ≤ 1 kpc. Using the observation [28]and integrating out the h, the stellar distribution on 2-dimensional galactic disk is given by

nstar(R) ' f2 × 1.2× 1011/(R/kpc)3 [kpc−2] , (9)

3

e CR-induced BDM flux

<latexit sha1_base64="PYwglAHgsYkzITOCOWOrNhUxqD0=">AAACBnicbVA9SwNBEN3zM8avqKUIi0GwMdxJQO2CsbARVEwiJCHs7c3FJXt7x+6cGI5UNv4VGwtFbP0Ndv4bNzGFRh8MPN6bYWaen0hh0HU/nanpmdm5+dxCfnFpeWW1sLZeN3GqOdR4LGN97TMDUiiooUAJ14kGFvkSGn6vOvQbt6CNiNUV9hNoR6yrRCg4Qyt1CltAWwh3mNHq5Z5QQcohoMcnZzSU6d2gUyi6JXcE+pd4Y1IkY5x3Ch+tIOZpBAq5ZMY0PTfBdsY0Ci5hkG+lBhLGe6wLTUsVi8C0s9EbA7pjlYCGsbalkI7UnxMZi4zpR77tjBjemElvKP7nNVMMD9uZUEmKoPj3ojCVFGM6zIQGQgNH2beEcS3srZTfMM042uTyNgRv8uW/pL5f8sqlo4tysXI8jiNHNsk22SUeOSAVckrOSY1wck8eyTN5cR6cJ+fVeftunXLGMxvkF5z3L7UPmAc=</latexit>

solar ⌫-induced BDM flux

<latexit sha1_base64="Q5mgxohbAAH4z1WtZn5ll96fQZQ=">AAACEnicbVA9SwNBEN3z2/gVtbRZDIIWhjsJqF1QCxtBwZhAEsLe3pwu7u0du7OScOQ32PhXbCwUsbWy89+4+Sj8ejDweG+GmXlhJoVB3//0Jianpmdm5+YLC4tLyyvF1bUrk1rNocZTmepGyAxIoaCGAiU0Mg0sCSXUw9vjgV+/A21Eqi6xl0E7YddKxIIzdFKnuNNC6GJuUsk07dOWsiNhV6jIcojo0ckZjaXt9jvFkl/2h6B/STAmJTLGeaf40YpSbhNQyCUzphn4GbZzplFwCf1CyxrIGL9l19B0VLEETDsfvtSnW06JaJxqVwrpUP0+kbPEmF4Sus6E4Y357Q3E/7ymxfignQuVWQTFR4tiKymmdJAPjYQGjrLnCONauFspv2GacXQpFlwIwe+X/5KrvXJQKR9eVErVo3Ecc2SDbJJtEpB9UiWn5JzUCCf35JE8kxfvwXvyXr23UeuEN55ZJz/gvX8Bf2id/g==</latexit>

Total star ⌫-induced BDM flux

<latexit sha1_base64="nP/rVHheJMP/9xm2XHhLDdoTFMs=">AAACF3icbVDJSgNBEO1xN25Rj14ag+DFMCOCehP14EVQyAZJCD09NUljT8/QXS2GIX/hxV/x4kERr3rzb+wsB7cHBY/3qqiqF2ZSGPT9T29qemZ2bn5hsbC0vLK6VlzfqJnUag5VnspUN0JmQAoFVRQooZFpYEkooR7enA39+i1oI1JVwX4G7YR1lYgFZ+ikTrHcQrjDvJIik9Qg03RAW8qO1T2hIsshoqfnlzSW9m7QKZb8sj8C/UuCCSmRCa46xY9WlHKbgEIumTHNwM+wnTONgksYFFrWQMb4DetC01HFEjDtfPTXgO44JaJxql0ppCP1+0TOEmP6Seg6E4Y989sbiv95TYvxUTsXKrMIio8XxVZSTOkwJBoJDRxl3xHGtXC3Ut5jmnF0URZcCMHvl/+S2n45OCgfXx+UTk4ncSyQLbJNdklADskJuSBXpEo4uSeP5Jm8eA/ek/fqvY1bp7zJzCb5Ae/9CyrHn+0=</latexit>

Astrophysical uncertainty in CN-BDM

<latexit sha1_base64="IeF/Dn5wAbTL/E/kUUkQdaGHVrs=">AAACE3icbVA9SwNBEN3zM8avU0ubxSCIYLgTQe00sbBRIpgYSELY20zMkr29Y3dOPI78Bxv/io2FIrY2dv4bNzGFXw8GHu/NMDMviKUw6HkfzsTk1PTMbG4uP7+wuLTsrqzWTJRoDlUeyUjXA2ZACgVVFCihHmtgYSDhKuiXh/7VDWgjInWJaQytkF0r0RWcoZXa7nYT4RazY4M6inupsYakieKgkQmFKRWKls93Sidng7Zb8IreCPQv8cekQMaotN33ZifiSQgKuWTGNHwvxlbGNAouYZBvJgZixvvsGhqWKhaCaWWjnwZ00yod2o20LYV0pH6fyFhoTBoGtjNk2DO/vaH4n9dIsHvQyoSKEwTFvxZ1E0kxosOAaEdo4ChTSxjXwt5KeY9pxtHGmLch+L9f/ktqu0V/r3h4sVc4Ko3jyJF1skG2iE/2yRE5JRVSJZzckQfyRJ6de+fReXFev1onnPHMGvkB5+0TOEqeWA==</latexit>

mX = 700 keV, mDM = 5 MeV, gXgDM = 10�6

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C⌫-BDM<latexit sha1_base64="8lJWykznYgiLbpoPS7hQcUvPXf4=">AAAB9XicbVBNS8NAEN34WetX1aOXYBG8WBJR9FiqBy9CBfsBTSyb7aRdutmE3YlaQv+HFw+KePW/ePPfuP04aOuDgcd7M8zMCxLBNTrOt7WwuLS8sppby69vbG5tF3Z26zpOFYMai0WsmgHVILiEGnIU0EwU0CgQ0Aj6lyO/8QBK81je4SABP6JdyUPOKBrp3pOph/CE2XHl6mbYLhSdkjOGPU/cKSmSKartwpfXiVkagUQmqNYt10nQz6hCzgQM816qIaGsT7vQMlTSCLSfja8e2odG6dhhrExJtMfq74mMRloPosB0RhR7etYbif95rRTDCz/jMkkRJJssClNhY2yPIrA7XAFDMTCEMsXNrTbrUUUZmqDyJgR39uV5Uj8puWcl5/a0WK5M48iRfXJAjohLzkmZXJMqqRFGFHkmr+TNerRerHfrY9K6YE1n9sgfWJ8/UDaSYg==</latexit>

⌫-BDM<latexit sha1_base64="biTeV1/tmKPMujKf/n5yKTBbgU4=">AAAB9HicbVBNS8NAEN3Ur1q/qh69BIvgqSSi6LFUD16ECvYDmlA222m7dLOJu5NiCf0dXjwo4tUf481/47bNQVsfDDzem2FmXhALrtFxvq3cyura+kZ+s7C1vbO7V9w/aOgoUQzqLBKRagVUg+AS6shRQCtWQMNAQDMYXk/95giU5pF8wHEMfkj7kvc4o2gk35OJh/CEafXmbtIplpyyM4O9TNyMlEiGWqf45XUjloQgkQmqddt1YvRTqpAzAZOCl2iIKRvSPrQNlTQE7aezoyf2iVG6di9SpiTaM/X3REpDrcdhYDpDigO96E3F/7x2gr0rP+UyThAkmy/qJcLGyJ4mYHe5AoZibAhliptbbTagijI0ORVMCO7iy8ukcVZ2L8rO/XmpUs3iyJMjckxOiUsuSYXckhqpE0YeyTN5JW/WyHqx3q2PeWvOymYOyR9Ynz/iaJIr</latexit>

⌫BDM

<latexit sha1_base64="dK0YSfXXSeAlmzxhrYFetxCrXXw=">AAACEHicbVA9SwNBEN3z2/gVtbRZDKKN4U4ULUO0sBEUjAaSEPb25pIle3vH7pwkHPkJNv4VGwtFbC3t/DduPgpNfDDw9r0Zdub5iRQGXffbmZmdm19YXFrOrayurW/kN7fuTJxqDhUey1hXfWZACgUVFCihmmhgkS/h3u+cD/z7B9BGxOoWewk0ItZSIhScoZWa+f06QhczHptIcNqH0fNQqCDlENDyxRUNZdrtN/MFt+gOQaeJNyYFMsZ1M/9VD2KeRqCQS2ZMzXMTbGRMo+AS+rl6aiBhvMNaULNUsQhMIxse1Kd7VgloGGtbCulQ/T2RsciYXuTbzohh20x6A/E/r5ZieNbIhEpSBMVHH4WppBjTQTo0EBo4yp4ljGthd6W8zTTjaDPM2RC8yZOnyd1R0TspujfHhVJ5HMcS2SG75IB45JSUyCW5JhXCySN5Jq/kzXlyXpx352PUOuOMZ7bJHzifPymTnUU=</latexit>

cosmic e-induced BDM flux

<latexit sha1_base64="KaOOdF9vaN/awhf23/J7H0LOJrY=">AAACHXicbZBNSwMxEIazflu/qh69BIvgQcquVupFKOrBi6BgP6Bblmw61dBkd0lmxbL0h3jxr3jxoCAevIj/xrRW0OpA4OV9ZpjMGyZSGHTdD2dicmp6ZnZuPrewuLS8kl9dq5k41RyqPJaxboTMgBQRVFGghEaigalQQj3sHg94/Qa0EXF0ib0EWopdRaIjOENrBfk9FTToIS27LvURbjGjXaj1d6hPVZD5WtGTs77l+9/0zNIgX3CL7rDoX+GNRIGM6jzIv/ntmKcKIuSSGdP03ARbGdMouIR+zk8NJIx32RU0rYyYAtPKhsf16ZZ12rQTa/sipEP350TGlDE9FdpOxfDajLOB+R9rptg5aGUiSlKEiH8t6qSSYkwHSdG20MBR9qxgXAv7V8qvmWYcbZ45G4I3fvJfUd8teqWi512UCpWjUR5zZINskm3ikTKpkFNyTqqEkzvyQJ7Is3PvPDovzutX64Qzmlknv8p5/wS/QJ8k</latexit>

mX = 700 keV, mDM = 5 MeV<latexit sha1_base64="9bJm+xV3PCyRjZxpu4jOC/xQNeo=">AAACH3icbVBNS8NAEN34WetX1KOXxSJ4kJJIS70IRT14ESpYW2hK2GynunQ3CbsTsYT+Ei/+FS8eFES8+W/c1h78ejDweG+GmXlRKoVBz/twZmbn5hcWC0vF5ZXVtXV3Y/PKJJnm0OSJTHQ7YgakiKGJAiW0Uw1MRRJa0eBk7LduQRuRxJc4TKGr2HUs+oIztFLoVlXYpke05nk0QLjDnA7garRPA6rCPNCKnp6PrF/96YduySt7E9C/xJ+SEpmiEbrvQS/hmYIYuWTGdHwvxW7ONAouYVQMMgMp4wN2DR1LY6bAdPPJeyO6a5Ue7SfaVox0on6fyJkyZqgi26kY3pjf3lj8z+tk2D/s5iJOM4SYfy3qZ5JiQsdZ0Z7QwFEOLWFcC3sr5TdMM4420aINwf/98l/SOij7lbLvX1RK9eNpHgWyTXbIHvFJjdTJGWmQJuHknjySZ/LiPDhPzqvz9tU640xntsgPOB+f5mOftg==</latexit>

mX = 700 keV, mDM = 500 keV<latexit sha1_base64="TmujfmBcpy8Ir4oTmUDdLxvSB8k=">AAACHnicbVA9SwNBEN2LXzF+RS1tFoNgIeFOItoIohY2QgRjArlw7G0myZLdu2N3TgxH/oiNf8XGQkEEK/03bmIKoz4YeLw3w8y8MJHCoOt+OrmZ2bn5hfxiYWl5ZXWtuL5xY+JUc6jxWMa6ETIDUkRQQ4ESGokGpkIJ9bB/NvLrt6CNiKNrHCTQUqwbiY7gDK0UFCsqaNBjeui61Ee4w4z24Wa4R32qgszXip5fDq1/MGUHxZJbdsegf4k3ISUyQTUovvvtmKcKIuSSGdP03ARbGdMouIRhwU8NJIz3WRealkZMgWll4++GdMcqbdqJta0I6Vj9OZExZcxAhbZTMeyZ395I/M9rptg5amUiSlKEiH8v6qSSYkxHUdG20MBRDixhXAt7K+U9phlHG2jBhuD9fvkvqe+XvUrZ864qpZPTSR55skW2yS7xyCE5IRekSmqEk3vySJ7Ji/PgPDmvztt3a86ZzGySKTgfX2m4n3w=</latexit>

mX = 700 keV, mDM = 50 keV<latexit sha1_base64="myFXlhMerTHRTknZHPu8QPIw3PA=">AAACHXicbVDJSgNBEO1xjXGLevTSGAQPEmZc0IsQ1IMXIYJZIBOGnk5Fm3TPDN01YhjyIV78FS8eFMSDF/Fv7CwHNT4oeLxXRVW9MJHCoOt+OVPTM7Nz87mF/OLS8spqYW29ZuJUc6jyWMa6ETIDUkRQRYESGokGpkIJ9bB7NvDrd6CNiKNr7CXQUuwmEh3BGVopKOyroEFP6JHrUh/hHjPahVp/l/pUBZmvFT2/7Fv/8KcbFIpuyR2CThJvTIpkjEpQ+PDbMU8VRMglM6bpuQm2MqZRcAn9vJ8aSBjvshtoWhoxBaaVDZ/r022rtGkn1rYipEP150TGlDE9FdpOxfDW/PUG4n9eM8XOcSsTUZIiRHy0qJNKijEdJEXbQgNH2bOEcS3srZTfMs042jzzNgTv78uTpL5X8g5Knnd1UCyfjvPIkU2yRXaIR45ImVyQCqkSTh7IE3khr86j8+y8Oe+j1ilnPLNBfsH5/AbtMJ9C</latexit>

mX = 700 keV, mDM = 5 keV<latexit sha1_base64="+ET4WgEuRMk6MSMa+FNi+nFo97A=">AAACHXicbZDJSgNBEIZ73I1b1KOXxiB4kDCjEb0Ioh68CApmgUwYejqVpEn3zNBdI4YhD+LFV/HiQUE8eBHfxs4iuBU0/PxfFdX1h4kUBl33w5mYnJqemZ2bzy0sLi2v5FfXKiZONYcyj2WsayEzIEUEZRQooZZoYCqUUA27pwNevQFtRBxdYy+BhmLtSLQEZ2itIL+ngho9op7rUh/hFjPahUp/h/pUBZmvFT276Fu+/0UvLA3yBbfoDov+Fd5YFMi4LoP8m9+MeaogQi6ZMXXPTbCRMY2CS+jn/NRAwniXtaFuZcQUmEY2PK5Pt6zTpK1Y2xchHbrfJzKmjOmp0HYqhh3zmw3M/1g9xdZhIxNRkiJEfLSolUqKMR0kRZtCA0fZs4JxLexfKe8wzTjaPHM2BO/3yX9FdbfolYqed1UqHJ+M85gjG2STbBOPHJBjck4uSZlwckceyBN5du6dR+fFeR21TjjjmXXyo5z3T7Uanx4=</latexit>

mX = 100 keV, mDM = 5 MeV<latexit sha1_base64="Bc32Y7gOEHabb6fF/3lkng4HkfE=">AAACHHicbZBNSwMxEIazftb6VfXoJVgED1J2S0UvQlEPXgoK1ha6ZcmmUxua7C7JrFiW/g8v/hUvHhTEiwfBf2NaK/g1EHh5nxkm84aJFAZd992Zmp6ZnZvPLeQXl5ZXVgtr65cmTjWHOo9lrJshMyBFBHUUKKGZaGAqlNAI+8cj3rgGbUQcXeAggbZiV5HoCs7QWkGhrIImPaSeS32EG8xoHy6Hu9SnKsh8rehJbWjx3hetWRoUim7JHRf9K7yJKJJJnQWFV78T81RBhFwyY1qem2A7YxoFlzDM+6mBhPE+u4KWlRFTYNrZ+LYh3bZOh3ZjbV+EdOx+n8iYMmagQtupGPbMbzYy/2OtFLsH7UxESYoQ8c9F3VRSjOkoKNoRGjjKgRWMa2H/SnmPacbRxpm3IXi/T/4rGuWSVyl53nmlWD2a5JEjm2SL7BCP7JMqOSVnpE44uSX35JE8OXfOg/PsvHy2TjmTmQ3yo5y3DzzinuQ=</latexit>

mX = 10 keV, mDM = 5 MeV

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FIG. 3. [Top] BDM fluxes by solar neutrinos, cosmic neutri-nos, and cosmic electrons. We assume σνDM comes from a vec-tor boson X coupling to both DM and leptons (gX = ge = gν)with (mDM,mX , gXgDM) = (5MeV, 700keV, 10−6). The un-

certainty band for νBDM corresponds to 0.1 ≤ f ≤ 10. [Bot-

tom] BDM fluxes for different mX and mDM with f = 1.Solid and dotted lines are νBDM and cosmic electron BDMfluxes, respectively.

where f2 factor includes the uncertainties from detailedstructures of the Milky Way, e.g. spiral arms and densityfluctuations.

The νBDM fluxes with two KDM regimes are shownin the bottom panels of Fig. 1. Due to the high stel-lar and DM number densities around the GC, the BDMflux contribution from the GC region exceeds that fromthe vicinity of Earth. Fig. 2 shows the θ dependenceof the νBDM fluxes 1

ϕBDM

ϕBDM

dθ at Earth where θ rep-

resents the angle between the νBDM arrival directionand the GC. For KDM � mDM in the right panel, theforward scattering (θ0 ' 0) is preferred, so that νBDMfrom the GC dominates and thus θ ' 0. In the left panel,KDM � mDM prefers large-angle scattering (θ0 ' 90◦),which enhances the flux for θ & 40◦ originating relativelyfar from the GC. The θ dependence of the νBDM flux canbe used to determine mDM in the future.

In the top panel of Fig. 3, we compare the BDM fluxesvia solar neutrinos, cosmic neutrinos, and cosmic-rayelectrons by fixing f ≡ f1 · f2 =1. The νBDM flux isthree orders of magnitude larger than that by solar neu-trinos, because the later is relevant to DM only within

a few AUs around Earth. Three bumps of the νBDMflux correspond to the pp, 13N+15O, and 8B productionprocesses of solar neutrinos [19]. Assuming ge = gν , theνBDM flux can be two to four orders of magnitude largerthan that induced by cosmic electrons forKDM . 50 keV.This feature is quite robust for other DM and mediatormasses as shown in the bottom panel.

There are several factors that can make our estimationsdifferent. i ) The DM halo profile, especially around theGC. We take the NFW profile. ii ) The ν flux varies withthe type and age of stars [27]. iii ) The star distributionin the Milky Way. All the above uncertainties are hardto be included in the calculation. In order to show therobustness of the results, we conservatively vary 0.1 .f . 10 in Eq. (4) and (8), depicted as a blue band in thetop panel of Fig. 3.

Attenuation of the BDM flux. The attenuation ef-fect of the cosmic-neutrino flux scattered by halo DM istaken into account by the exponential factor in Eq. 4.We estimate the mean free path of cosmic neutrino dνby taking σνDM ' 10−28 − 10−34 cm2. For the nDM ∼(keV/mDM) × 106 cm−3, dν ' (mDM/keV) × (1022 −1028) cm, which is larger than the size of the Milky Wayand results in negligible effect.

Next, we estimate the mean free path of BDM in-side Earth by assuming σeDM = σνDM. For σeDM =10−33 cm2 with electron number density of Earth ne '1024 cm−3, the mean free path 1/(ne ·σeDM) ' 104 km iscomparable to the size of Earth. For σeDM = 10−29 cm2,the BDM mean free path reduces to O(km). Most ofDM direct detection detectors locate a few kilometers un-derground, rendering the νBDM signal be substantiallysuppressed for σeDM & 10−29 cm2. Thus, the attenua-tion of BDM inside Earth will provide upper limits onexperimental sensitivities as shown in Fig. 4.

III. EXPERIMENTAL SENSITIVITIES

To estimate experimental sensitivities, we use two ap-proaches for DM models. i ) Heavy mediator: the inter-actions can be described by effective cross sections σeff

νDMand σeff

eDM. ii ) Light mediator: the X boson from thegauged U(1)Le−Li couples to DM and leptons.

For the approach i ), the differential cross section isdefined as

dσeffνDM,eDM

dKDM≡

σeffνDM,eDM

KmaxDM −Kmin

DM

. (10)

On the other hand, for the U(1)Le−Li model, theneutrino-DM scattering cross section is given by [29]

4

dσνDM

dKDM=

(gXgDM)2

4π

2mDM(mν +Kν)2 −KDM

[(mν +mDM)2 + 2mDMKν

]+mDMK

2DM

(2mνKν +K2ν )(2mDMKDM +m2

X)2. (11)

10-3

10-2

10-1

100

101

102

mDM [MeV]

10-35

10-34

10-33

10-32

10-31

10-30

10-29

10-28

σνD

M=

σe

DM

[cm

2]

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

DAMICEDELWEISS

CDMS HVeVSE

NS

EI

XENONnT

PandaXBorexino

JUNO

1σ

2σ

excluded by XENON1T SK

HK

FIG. 4. νBDM contributions to XENON1T electron re-coil, assuming σeff

νDM = σeffeDM, where the 1σ (green) and 2σ

(white) regions from χ2 analysis, and the gray-shaded re-gion is excluded more than 2σ. The expected sensitivitiesfrom other underground detectors are depicted: Brexino [30],PandaX [31], XENONnT [32], and JUNO [33]. For compari-son, existing limits are shown together: CDMS HVeV [34],DAMIC [35], EDELWEISS [36], and SENSEI [37]. Thecosmic-electron-BDM constraints from Super-K and Hyper-K [14].

For KDM ' O(keV) and mDM ' mX ' O(MeV), itmakes dσνDM/dKDM almost independent of KDM.

We perform the model-independent χ2 analysis for theeffective cross section (mDM, σ

effνDM = σeff

eDM) in Fig. 4.There are five disconnected 1σ regions for the XENON1Texcess [25], which originate from the three bumps ofthe νBDM flux spectrum in Fig. 3. The 2σ exclusionregion is gray-shaded. The νBDM provides stringentconstraint on σeff

νDM = σeffeDM for unexplored small mass

mDM . MeV, compared with the current limits from DMdirect detection experiments including CDMS HVeV [34],DAMIC [35], EDELWEISS [36], and SENSEI [37].

We evaluate the sensitivities of νBDM with other cur-rent (Brexino [30], PandaX [31]) and future experiments(XENONnT [32], JUNO [33]). To estimate the sensitiv-ities, we take the four ton-year exposure for XENONnTand 20 kton-year exposure for JUNO assuming no ex-cess above the expected background and dominance ofstatistical uncertainty. Borexino and JUNO have higherenergy threshold above 100 keV but huge statistics.JUNO has the best sensitivity for mDM . 0.5 MeV,while XENON1T/nT are better than JUNO for mDM &0.5 MeV. PandaX has a slightly weaker limit due tothe smaller 0.276 ton-year exposure than XENON1T of0.65 tonne-year. For σeDM & 10−29 cm2, the earth crustattenuates the BDM flux; specifically, XENON1T andXENONnT [24] are located underground at a depth of

3600 meter water equivalent (m.w.e.) and Borexino [38]is at 3800 m.w.e while PandaX [39] is shielded by 2400 mmarble overburden (∼ 6800 m.w.e.). The most shallowJUNO detector [33], located at 700 m deep underground(∼ 2000 m.w.e.), has the best upper sensitive to νBDMwith σeDM ' 10−28 cm2.

IV. DISCUSSIONS

The flux of the cosmic-neutrino-boosted-DM (νBDM)is substantially larger than the one of the cosmic-electron-boosted-DM so that it contributes dominantlyin direct detection experiments on Earth. Due to thedistributions of the sources of neutrinos in Milky Wayand the dark matter in halo, the angular distribution ofthe νBDM is kinematically correlated with the DM mass.Therefore precise measurement of directional informationhelps in determination of the DM mass.

The existing underground detectors probe the param-eter region of neutrino-DM interaction and electron-DMinteraction in 10−34 cm2 . σνDM = σeDM . 10−28 cm2

with 1 keV . mDM . 100 MeV based on the effectivecross section approach. Since the DM flux is enhancedby neutrino-boost, we find parameter regions for the re-cent XENON1T anomaly (see Fig. 4). However, they arestill hardly consistent with other DM searches.

Finally, we discuss various factors of future refinementof the current study. Here we only assumed that nuclearactivities inside each star are on average same as in ourSun, so that the neutrino fluxes from each star are allsimilar. Obviously, this is a crude estimation and actualneutrino fluxes differ from star to star. Also, the GCregion has the largest population of main sequence starsand also red giants [40, 41], which enhances f1 · f2 factorover unity [27]. Last but not least, we point out the po-tential modification due to the extra galactic neutrinos.Even though extra galactic contributions in neutrino fluxis subdominant in the energy range for νBDM [18] , itcan lead modification in e.g. spatial and kinetic distri-butions of νBDM. All those factors of improvement arereserved for the future work.

ACKNOWLEDGMENTS

The work is supported in part by Basic Sci-ence Research Program through the National Re-search Foundation of Korea (NRF) funded by theMinistry of Education, Science and Technology

5

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

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