Direct Detection of Light Dark Matter from Evaporating Primordial Black Holes Roberta Calabrese,1, 2, ∗ Marco Chianese,1, 2, y Damiano F.G. Fiorillo,1, 2, z and Ninetta Saviano2, 3, x 1Dipartimento di Fisica \Ettore Pancini", Universit`adegli studi di Napoli \Federico II", Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy 2INFN - Sezione di Napoli, Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy 3Scuola Superiore Meridionale, Universit`adegli studi di Napoli \Federico II", Largo San Marcellino 10, 80138 Napoli, Italy (Dated: July 29, 2021) The direct detection of sub-GeV dark matter interacting with nucleons is hampered by the low recoil energies induced by scatterings in the detectors. This experimental difficulty is avoided in the scenario of boosted dark matter where a component of dark matter particles is endowed with large kinetic energies. In this Letter, we point out that the current evaporation of primordial black holes with masses from 1014 to 1016 g is a source of boosted light dark matter with energies of tens to hundreds of MeV. Focusing on the XENON1T experiment, we show that these relativistic dark matter particles could give rise to a signal orders of magnitude larger than the present upper bounds. Therefore, we are able to significantly constrain the combined parameter space of primordial black holes and sub-GeV dark matter. In the presence of primordial black holes with a mass of 1015 g and an abundance compatible with present bounds, the limits on DM-nucleon cross-section are improved by four orders of magnitude. Introduction.| Though Dark Matter (DM) is one model-independent constraints on the DM-nucleon cross- of the backbones of the standard cosmological model, section at the level of 10−31 cm2. ∼ its nature is still unknown [1]. So far, all the evidences In this Letter, we propose the evaporation of Primor- of its existence are related only to its gravitational im- dial Black Holes (PBHs) at present times as a source prints, while we have no clue about its non-gravitational of boosted light DM particles (hereafter denoted as χ). interactions [2,3]. Among the different ways to probe Throughout this work, we refer to this scenario as ePBH- DM properties, direct detection experiments are achiev- DM. PBHs are hypothetical black holes formed soon after ing very stringent constraints on DM-nucleon [4{18] and the inflationary epoch through the gravitational collapse DM-electron [19{25] interactions (see Ref. [26] for a re- of density fluctuations in the early universe [48, 49]. As cent review). These experiments search for the nuclear a result of combining quantum field theory and general and electron recoil energy caused by the possible scat- relativity, PBHs emit Hawking radiation in the form of terings with DM particles that surround us. Due to a graybody spectrum with a temperature TPBH inversely rapidly decreasing sensitivity at low recoil energies, the proportional to the PBH mass [50{56]. PBHs with a mass 15 constraints on DM interactions dramatically weaken for MPBH = (10 g) are evaporating at the present times, DM masses smaller than about 1 GeV (1 MeV) for DM process thatO has been employed to set stringent upper interactions with nuclei (electrons), thus leaving light bounds on the PBHs abundance [57{64] (see Ref. [65] DM candidates poorly explored by direct searches. There for a comprehensive review). DM particles with a mass are complementary approaches to the exploration of light mχ < TPBH are also emitted with (semi)-relativistic mo- DM. Fermionic DM particles lighter than 0.1 keV are menta by PBHs. This mechanism has been vastly stud- highly constrained by phase-space arguments [27, 28] and ied as a way to produce DM particles in the early Uni- structure formation [29]. Other model-dependent con- verse [66{75]. However, the production of DM particles straints are placed by astrophysical and cosmological ob- in the present Universe, to our knowledge, has never been servations, as well as by colliders [30{39]. investigated. The experimental limitation of direct detection can arXiv:2107.13001v1 [hep-ph] 27 Jul 2021 Here we explore for the first time the phenomenological be circumvented in the framework of boosted dark mat- implications of the ePBH-DM scenario in direct detection ter, where a fraction of DM particles gains a velocity experiments. Remarkably, we find that even a tiny frac- higher that the virial one due to a number of differ- tion of evaporating PBHs is enough to give rise to a size- ent mechanisms [40{42]. In recent years, it has been able flux of boosted light DM particles (see Fig.1). This pointed out that light DM particles can be upscattered translates into a detectable event rate in current experi- to (semi-)relativistic velocities through collisions with ments such as XENON1T in case DM particles interact cosmic-rays [43{47]. The unavoidable presence of such a with nucleons (see Fig.2). Hence, the existence of PBHs subdominant boosted DM component has improved the would imply incredibly strong constraints on the DM pa- rameter space, and viceversa, as shown in Fig.3. We find that, assuming PBHs abundances compatible with ∗ [email protected] current bounds, the limits on the spin-independent (SI) y [email protected] DM-nucleon cross-section are improved up to four orders z dfgfi[email protected] of magnitude. Conversely, the non-observation of the x [email protected] ePBH-DM signal allows us to deduce upper bound on 2 100 the graybody factor, which we compute by means of the Galactic BlackHawk code [76]. sr] 2 Extragalactic From the differential spectrum we can compute the 10− / s MPBH,15 = 8 .0 flux of DM particles reaching the Earth. It consists of a / 2 4 galactic (gal:) and an extragalactic (egal:) component: 10− cm gal: egal: / dφχ dφχ dφχ 6 = + : (3) 10− dT dΩ dT dΩ dT dΩ ,15 = 1 .0 MeV MPBH / 8 The first component can be written as 10− gal: Z +1 .5 dφχ fPBH dNχ NFW dΩ [1 MPBH,15 = 0 10 10 = ds ρχ (r) : (4) T − dT dΩ 4π MPBH dtdT 0 d / χ 12 Here, the quantity fPBH = ρPBH/ρχ is the fraction of φ 10− d mχ = 1 MeV PBHs with respect to the average DM density ρχ of the 14 Universe, which is determined by Planck [77]. The galac- 10− 3 2 1 0 1 2 3 10− 10− 10− 10 10 10 10 tic flux is proportional to the integral over the line-of- sight distance s of the galactic DM density, denoted as Kinetic energy, T [MeV] NFW ρχ , for which we assume a Navarro-Frank-White pro- file [78]. This is a function of the galactocentric distance FIG. 1. Diffuse DM flux from evaporating PBHs. We 2 2 1=2 r = (r + s 2 s r cos ` cos b) with r = 8:5 kpc and show the diffuse flux of DM particles incident at the Earth (b; `) the galactic− coordinates. as a function of the kinetic energy. The galactic (solid) and For the extragalactic component in Eq. (3), the differ- extragalactic (dashed) lines are shown separately. Different ential flux takes the expression colors are used to identify different PBH masses (MPBH;15 = 15 MPBH=10 g). The PBH abundance is chosen as the max- egal: Z tmax dφχ fPBH ρχ dNχ imum value allowed by the present constraints [65]: fPBH is −10 −7 −4 = dt [1 + z(t)] ; (5) equal to 2:9 10 , 3:9 10 , 3:7 10 for a PBH mass dT dΩ 4π MPBH tmin dtdT of 0:5, 1:0, and× 8:0 in units× of 1015 g,× respectively. Effects of energy losses in Earth and atmosphere are not included. where we take into account the effect of redshift z(t) on the energy in the DM emission rate, and we integrate from the time of matter-radiation equality (tmin) to the the PBHs abundance a few orders of magnitude stronger age of the Universe (tmax). We only consider PBHs which than current constraints, depending on the strength of are still not completely evaporated. Differently from the DM-nucleon interactions. galactic component, which is enhanced towards the galac- DM flux from evaporating PBHs.| The first tic center, the extragalactic DM flux is isotropic. step of our work consists in obtaining the DM emission Given the evaporation temperatures of PBHs from rate from an evaporating PBH. We here make a conserva- Eq. (1), DM particles are mainly produced at energies tive choice by considering chargeless and spinless PBHs. between 1 MeV and 100 MeV, for PBHs masses from 1014 Spinning PBHs would evaporate faster, thus enhancing and to 1016 g. Hence, DM particles lighter than about the DM emission rate. For the sake of concreteness, we 1 MeV are emitted by PBHs with ultra-relativistic veloci- examine the case of DM Dirac fermions with four degrees ties. In a sense, the evaporation of PBHs is a new mecha- of freedom, gχ = 4. However, this framework can be eas- nism for boosted DM. In Fig.1, we show the galactic and ily extended to scalar and vector DM particles. Differ- extragalactic diffuse flux of DM particles at the Earth, ently from Ref. [64], the addition of only one new species averaged over the whole solid angle, for a reference DM to the Standard Model particle content does not signif- mass mχ = 1 MeV and for different PBH masses. The icantly alter the standard emission rate of the Hawking kinetic energy distribution of particles peaks at different radiation. The Hawking temperature of an evaporating energies depending on the PBH temperature, which can PBH with mass MPBH is given by [51, 54{56] be much larger than the DM mass.