PHYSICAL REVIEW D 102, 103532 (2020)

Pico-charged particles from dark matter decay explain the 511 keV line and the XENON1T signal

† Y. Farzan * and M. Rajaee School of physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

(Received 29 August 2020; accepted 2 November 2020; published 24 November 2020)

There is a robust signal for a 511 keV photon line from the Galactic Center, which may originate from dark matter particles with masses of a few MeV. To avoid the bounds from the delayed recombination and from the absence of the line from dwarf galaxies, in 2017, we have proposed a model in which dark matter first decays into a pair of intermediate pico-charged particles CC¯ with a lifetime much larger than the age of the Universe. The Galactic magnetic field accumulates the relativistic CC¯ that eventually annihilate, producing the e−eþ pair that gives rise to the 511 keV line. The relativistic pico-charged C particles can scatter on the electrons inside the direct dark matter search detectors imparting a recoil energy of Er ∼ keV. We show that this model can account for the electron recoil excess recently reported by the XENON1T experiment. Moreover, we show that the XENON1T electron recoil data set the most stringent bound on the lifetime of the dark matter within this model.

DOI: 10.1103/PhysRevD.102.103532

I. INTRODUCTION few MeV annihilate into e−eþ pairs with a cross section of 10−4 From the cosmological scales down to the galactic pb. This simplistic solution is now ruled out because of two reasons: (i) if the annihilation is through the s channel, scales, dark matter has demonstrated its existence via − þ gravitational effects. The efforts to discover the particles the e e production in the early Universe would result in the composing dark matter by direct and indirect dark matter delayed recombination with signatures on the cosmic micro- search experiments are ongoing. Although no conclusive wave background (CMB) fluctuations that are ruled out [4]; discovery has so far been made, various observations have (ii) the model predicts a 511 keV photon line from dwarf been reported that defy an explanation within the standard galaxies, but the observations refute this prediction [5]. model and may have a dark matter origin. One of them is In [6], we have proposed a solution that avoids these the observation of the 511 keV line from the Galactic constraints. In our model, the dark matter, X, is also a Center. Another signal is the recently reported XENON1T MeVish particle that can be identified with the SLIM electron recoil signal [1]. particles [7], whose abundance in the Universe is set by the νν ν¯ ν¯ The statistical observation of the 511 keV line is quite annihilation into the and pairs through the freeze-out robust, and its morphology is well reconstructed [2]. The scenario. The X particles are metastable with a lifetime shape of this line strongly suggests that it comes from the larger than 10000 times the age of the Universe. In our ¯ decay of nonrelativistic positronium atoms. The intensity of model, X decays into a pair of CC particles, which have an −11 the line is of course proportional to the density of the electric charge of qC ∼ 10 . With such an electric charge, positronium atoms. The measured intensity indicates a the Larmor radius of these particles in the Galaxy will be density for positron in excess of that expected from known smaller than the thickness of the Galactic disk. As a result, sources such as pulsars. The positron excess in the Galactic the CC¯ pair will be accumulated in the Galaxy despite their Center tantalizingly suggests a dark matter origin. In the velocities being larger than the escape velocity. The C and scenario proposed in [3], the dark matter pairs of a mass of a C¯ pairs eventually annihilate and produce e−eþ pairs, explaining the 511 keV line. At the recombination, the ¯ *[email protected] density of C and C would be too small to lead to a † − þ [email protected] significant entropy dump through the e e production. Moreover, the magnetic fields in the dwarf galaxies are Published by the American Physical Society under the terms of ¯ the Creative Commons Attribution 4.0 International license. typically too small to accumulate CC and lead to a Further distribution of this work must maintain attribution to discernible 511 keV line. the author(s) and the published article’s title, journal citation, In Ref. [6], we had predicted a signal for the electron and DOI. Funded by SCOAP3. recoil excess in direct dark matter search experiments.

2470-0010=2020=102(10)=103532(10) 103532-1 Published by the American Physical Society Y. FARZAN and M. RAJAEE PHYS. REV. D 102, 103532 (2020)

μν μν Recently, the XENON1T detector has reported an excess of AμνA BμνB δ μν 1 2 − − − AμνB − ð∂μσ þM1Aμ þϵM1BμÞ ; scattered electrons with recoil energies 1–7 keV over the 4 4 2 2 β background. Although one possible solution is the decay ð1Þ of the residue tritium nuclei in the sample [1] (see also [8]), this observation has instilled a considerable activity in the where δ, ϵ ≪ 1. Going to the canonic kinetic and mass – field [9 13]. In this paper, we show that our model can basis, we shall have three neutral gauge bosons; i.e., the SM simultaneously explain the 511 keV line and the XENON1T γ and Z bosons plus a new gauge boson called the dark 0 excess. An alternative solution is proposed in [14]. photon, Aμ. To the linear order in ϵ and δ, we find that the Some of the ideas proposed in the literature to explain the 0 mass of A is decoupled from the Z mass and is equal to M1. excess include axions [1,9], the nonstandard interaction for Neglecting Oðϵ2; δ2Þ, we find the following coupling the solar pp neutrinos [10], and the absorption of the between the SM charged fermions, f and A0: background vector dark matter of a mass of a few keV [11]. The shape of the electron recoil spectrum cannot be 0 ¯ μ 0 0 q fγ fAμ where q ¼ e cos θ ðϵ − δÞQ ; ð2Þ explained by the vanilla WIMP dark matter scattering as W f the recoil energy off the electrons will be smaller than 1 eV in which θW is the weak (Weinberg) mixing angle. Notice and below the detection threshold. However, boosted dark that the mass and couplings of the dark photon can have matter may be able to account for the observed excess [12]; arbitrary values independent of the SM gauge boson see, however, [15]. Another possibility is down scattering masses. The intermediate C particles into which the X of inelastic dark matter with a splitting of a few keV [13].In ¯ dark matter particle decays are charged under the new our model, the C and C particles wandering in the Galactic 0 UXð1Þ symmetry. That is, their coupling to A is given by plane have relativistic velocities. As a result, despite their μ 0 μ g J Aμ, where J is the current of the C particles. The small mass, the scattering of the C particles off the electrons X C C electric charge of the C particles is can impart a sizable recoil energy. In this model, the interaction of the C particles with the electrons (as well as q ¼ −g ϵ cos θ : with the protons) takes place via the t-channel virtual SM C X W photon (i.e., via Coulomb interaction) and dark photon Notice that q is suppressed by the mass mixing between exchanges. In the majority of the unconstrained parameter C the SM photon and the dark photon, ϵ, and can be space, the former dominates so the energy spectrum of the arbitrarily small. As we shall see below, in order to keep recoiled electron, dN=dEr, is inversely proportional to the −2 the relativistic C particles produced by dark matter decay square of the recoil energy, Er , as expected for Coulomb inside the Galactic disk, the electric charge of these C interaction. We however show that there is a possibility of particles, q , should be of order of or larger than cancellation between the contributions from the SM and C dark photon exchanges at a given energy bin, which q ∼ 10−11: provides a better fit to the data. We also use the C XENON1T electron data to derive an upper bound on ð1Þ ¯ The UX gauge symmetry can be identified with the C and C abundance (i.e., on the fraction of dark matter − 0 ν ν¯ ν ν¯ ¯ Lμ Lτ. In this case, A can decay to μ μ and to τ τ. particles that decay into CC). As we shall discuss in Sec. III, this can relax some of the This paper is organized as follows: In Sec. II, we present bounds from supernova and beam dump experiments. We the model. In Sec. III, we review the bounds on the should however notice that gauging Lμ − Lτ is not an parameters of the model. In Sec. IV, we show how the essential part of the scenario, and in fact, in Ref. [6], we did XENON1T electron recoil excess can be explained within not identify the U ð1Þ gauge symmetry with Lμ − Lτ. our model and derive a lower bound on the lifetime of dark X Reference [6] focuses on the limit of equality of kinetic and matter particles. Conclusions are summarized in Sec. IV. mass mixings, δ ¼ ϵ. In this limit, the coupling of A0 to the SM fermions, q0, vanishes, and in the absence of 0 0 II. THE MODEL A → νμν¯μ; ντν¯τ, the lifetime of A becomes much larger 45 The model proposed in Ref. [6] is based on adding a new than the age of the Universe; i.e., > 7 × 10 years. An ∼ 10−11 ¯ U ð1Þ gauge symmetry to the Standard Model (SM) gauge electric charge of qC is too small to bring C, C, and X 0 group. The new gauge boson has a mixing with the photon A into thermodynamical equilibrium with the plasma, but it 0 0 ¼ both via the kinetic term and via the mass term through the can lead to a background A with a density of nA =nγ −4 −11 2 0 Stuckelberg mechanism. This aspect of the model is 10 ðqC=10 Þ [6]. In the limit of vanishing q , we shall elaborated on in Ref. [16]. Following the notation of therefore have a background of A0 with a mass of a few keV, [16], the kinetic and Stuckelberg mass terms for the new which will act as a subdominant dark matter component as gauge field Aμ and the hypercharge gauge field Bμ can be long as 10 eV

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0 j ¼h 0 iðρ j hρ iÞ then approximated as nA local nA DM local= DM .In particles can lose energy by scattering off the background the limit discussed in [6], since A0 does not couple to the A0 particles and can cool down. As pointed out in [6],ifA0 electron, no constraint comes from the stellar cooling particles decay, another subdominant dark matter compo- consideration. However, in general, for an arbitrary ratio nent can be introduced to play the role of the coolant. of δ=ϵ, the coupling of A0 to the electrons, q0, can be Let us denote this particle with Y. Similarly to [6], we take 10 10 j ¼ðρ j hρ iÞh i nonzero. In this paper, we shall focus on the general case eV

103532-3 Y. FARZAN and M. RAJAEE PHYS. REV. D 102, 103532 (2020) age of the Universe. The magnetic field in the Galaxy keeps weak interaction. This can affect the neutrino emission ¯ ∼ 10−11 the C and C particles with qC inside the Galaxy. duration as well as the flavor composition of the emitted The annihilation of CC¯ into e−eþ explains the 511 keV line neutrinos, which can be tested in the case of a future from the center of the Galaxy. C and C¯ can scatter off the observation of a neutrino burst from a supernova explosion. electrons in a direct dark matter detector. (4) Background At this range of the parameters, when the temperature drops 0 coolant particles, Y, with a mass of a few keV coupled to C below mA0 in the early Universe, A is both in thermody- and C¯ . The role of these coolants is to compensate the namical equilibrium with the neutrinos and with the energy pump from the supernova shock waves to the C and electrons so, unlike dark matter which interact either with ν 0 C¯ particles in the Galaxy. In the next section, we will the plasma or with [4], the A decay does not lead to a new discuss the various bounds on the model. contribution to Neff. In the range 100 keV spin one particle such as the core, q0 ∼ 10−9–10−10 can still be compatible with the ob- A0 cannot decay into a pair of photons [23]. A0 with a servations of neutrinos from SN1987a and with the famous 0 mass of keV can however decay into γγγ via an electron supernova cooling constraint. Taking mA0 ∼ 100 keV, q ∼ 0 3 2 3 2 2 ∼ 0 ð Þ ð100π ð16π Þ Þ −9 −10 < −9 loop with a rate of mA q e = .For 10 –10 and gτ−μ∼10 , the bounds both from supernova 100 0 100 eV few × 10 ðMeV=mA0 Þ , A can XENON1T excess [10]. decay inside the supernova core to νμν¯μ and ντν¯τ, with a Remember that to prevent the expulsion of the C decay length much smaller than the supernova core size, so particles by the supernova shock waves, we introduce a 0 the bound on q can be relaxed. Indeed, Lμ − Lτ gauge background coolant particle Y in the Galaxy. At each ¯ interaction at a one-loop level induces δ with δ ¼ collision of C and C on a coolant Y, they lose only a small 2 2 2 fraction of the energy, but since m ≪ m , the same recoil ðegτ−μ=12π Þ log½mτ =mμ ≃ 0.014gτ−μ [27]. Taking gτ−μ ∼ Y C −5 −7 0 1=2 energy is enough to make the velocity of Y larger than the 10 and δ ∼ 10 , the value of ðq gτ−μÞ will be below escape velocity and repel Y from the Galaxy. Within the bound from Borexino [28,29] and GEMMA [29,30]. the timescale of 100 Myr, each C or C¯ particle scatters Moreover, the bounds from the beam dump experiments off the following number of the Y particles: [24] as well as from supernova cooling are relaxed because 0 ¯ ¯ Z of the fast decay of A to νμνμ and ντντ pairs. Thus, with dE −5 −7 C ∼ 400ðm =3 Þð10 =m Þ: m 0 ∼ few MeV, gτ−μ ∼ 10 and δ ∼ 10 (therefore, C MeV keV Y A ΔEC q0 ∼ 3 × 10−8), all the bounds will be respected. However, neutrinos obtain a new flavor-dependent self Let us take the fraction of dark matter particles that decay interaction with a rate comparable (or even larger than) the to be

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f ¼ ΓXt0; [32] and DarkSide [33] can be satisfied. The CRESST detector is made of CaWO4 and aims at a detection threshold in which ΓX is the decay rate of X and t0 ¼ 13 Gyr is the of 100 eV, but Emax scattering off even the oxygen nucleus age of the Galaxy. Each X decay produces a pair of CC¯ ,so will be 1 order of magnitude below this state-of-the-art the number of the Y particles per unit volume repelled by detection threshold [34]. the CC¯ particles during the history of the Galaxy can be The spectrum of recoiled electrons from a unit of mass of estimated as the detector can be estimated as Z Z 2 ρ dN Z ρ dσ δ ∼ t0 f DM dEC ð Þ ¼ out 2f X f ðvÞ vdv; nY Δ : 5 C tSNW mX EC dEr mN mX dEr

Taking δnY xenon, mN GeV. Zout is the number of the m m ρ =ρ electrons per nucleus with binding energy smaller than the f<10−3 X Y Y DM : 10 MeV 10 keV 0.1 recoil energy. As shown in [35], taking the step function of the binding energy for the cross section is a valid approxi- ¼ 44 As discussed in [6], there is a stronger upper bound on f, mation. For xenon, we take Zout , which is the number from the requirement that CC¯ in the Galaxy do not of the electrons in the outer orbitals with a principal annihilate away to A0A0, quantum number n ¼ 3, 4, 5. For these electrons, unlike the electrons in the inner orbitals, we can neglect the 0 25 4 2 electron velocity. f ðvÞ gives the velocity distribution of C 3 10−4 mX . mC ð Þ C f< × : 6 and C¯ particles. As discussed before, we shall take f ðvÞ¼ 10 MeV gX 3 MeV C δðv − vfÞ for simplicity. As far as jϵj=2meEr ≫ jϵ − δj= ð2 þ 2 Þ meEr mA0 , the t-channel photon exchange gives the IV. PREDICTIONS FOR DIRECT DARK MATTER dominant contribution to the C particles scattering off the SEARCH EXPERIMENTS electrons. The differential cross section of the scattering of ¯ As we found out in the previous section, the pico- the C and C particles with an electric charge of qC off the charged particles, C, move around us with a velocity of electrons can be written as [36] ∼ 0 08 vf . . The Larmor radius in the vicinity of the Earth 5 108 ð10−11 Þð 3 Þð0 5 Þ dσ e2q2 1 m 2 is × km =qC mC= MeV . Gauss=B × ¼ C ¼ 2 2 C ð 0 08Þ 2 2 where Er

103532-5 Y. FARZAN and M. RAJAEE PHYS. REV. D 102, 103532 (2020) 1225 2 2 2 dN ¼ keV qC −11 dEr ton · year · keV Er 10 10 0 08 f MeV . Θð − Þ ð Þ × −4 Emax Er : 10 10 mX vf

Let us now analyze the XENON1T data within the framework of our model. Throughout our analysis, we take ¼ 0 08 ¼ 10−11 ¼ 10 vf . , qC , and mX MeV. We use the binned data shown in Fig. 4 of [1] and define χ2 as follows:

X ½Npred − Nobs2 χ2 ¼ i i ; ð Þ σ2 11 bins i FIG. 1. XENON1T electron recoil data compared with the obs prediction of our model without considering the contribution where Ni is the number of the observed events at each bin 0 pred from the A exchange [Eq (9)]. The black dots represent the and Ni is the predicted number of events which is the XENON1T data with their experimental errors shown by the sum of the background and the signal from the C scattering vertical bars [1]. The blue curve indicates the expected signal plus obs ¼ 4 in the ith bin. The values of σi (the uncertainty), N and background plotted for mC MeV and for our best fit point of i −6 the background at each bin are extracted from Fig. 4 of [1]. f ¼ 4 × 10 , excluding the first bin (fitting the bins with 2 8 Since the reported excess shows up at E < 8 keV, we only keV

103532-6 PICO-CHARGED PARTICLES FROM DARK MATTER DECAY … PHYS. REV. D 102, 103532 (2020) the first energy bin of the XENON1T electron excess, the bound relaxes to 10−5. Notice that these are the strongest bounds on f so far. Remembering that f ¼ ΓXt0, the upper bound on f can be interpreted as a lower bound on the X lifetime. That is, we have found that the lifetime of X should be larger than 105–106 times the age of the Universe. The natural question that arises is that whether with this stringent bound the model can still explain the 511 keV line. To account for the 511 keV line with f ¼ Oð10−7Þ, as shown in Ref. [6], the annihilation cross ¯ −4 −7 2 section of CC should be 10 bð10 =fÞ ðmX=10 MeVÞ. The CC¯ pair first annihilate to the intermediate ϕ particles, which eventually decay into e−eþ pairs [6].Tohave such annihilation, we may introduce quartic coupling λ jϕj2j j2 FIG. 3. XENON1T electron recoil data compared with the ϕC C . An annihilation cross section of 0.1 mb can prediction of our model taking into account the contribution from −3 0 be obtained with λϕC ∼ 6 × 10 . the A exchange [Eq. (9)]. The blue curve shows the signal plus Let us now consider the correction in Eq. (9) and check background assuming mA0 > 1 MeV and taking the best fit −7 3 2 0 ¼ 10 ðδ − ϵÞ ϵ ¼ −2 10 ð 0 Þ whether by considering the contribution from the A values, f and = × mA =MeV . The exchange, the first data point can also be fitted. As green (olive) curve shows the signal plus background assuming 0 ¼ 0 1 0 ¼ 0 2 100 0 mA . MeV (mA . MeV) and taking the best fit values: we discussed in Sec. III, for keV light dark matter particles with a mass of ∼10 that in this range, 2meEr in the denominator of Eq. (9) MeV. This scenario was originally proposed in [6] cannot be neglected, and we should use the whole to account for the 511 keV line coming from the Galactic ¯ formula to fit the data. Taking mC ¼ 4 MeV and mA0 ¼ Center. The magnetic field of the Galaxy keeps the C and C ¯ 100 keV (mA0 ¼ 200 keV), the best fit will correspond to pico-charged particles inside the Galaxy. The C and C ðδ − ϵÞ=ϵ ¼ −13.9 and f ¼ 6.6 × 10−7 [ðδ − ϵÞ=ϵ ¼ −76 particles can interact with the electrons and protons inside and f ¼ 2 × 10−7] and to the minimum χ2 ¼ 4.11 the detector. The recoil energy imparted on the nuclei will (χ2 ¼ 4.5), which is again an excellent fit thanks to the be much smaller than the detection threshold but that cancellation at the first bin. As Fig. 3 demonstrates, imparted on the electrons can be around a few keV and in the predictions corresponding to these fits are very close the detectable range for XENON1T. 0 to each other. Notice that for such values of δ, q will The C particles, having an electric charge of qC, interact be just slightly above the bound from supernova: with the electron via t-channel photon exchange. If the q0 ∼ 10−10–10−9. As discussed in the previous section, dominant interaction mode is this virtual photon

103532-7 Y. FARZAN and M. RAJAEE PHYS. REV. D 102, 103532 (2020) exchange, the dependence of the scattering will have an no upper bound on mC provided that mC

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