Dark Matter and the Xenon1T electron recoil excess Kristjan Kannike, Martti Raidal, and Hardi Veerm¨ae National Institute of Chemical Physics and Biophysics, R¨avala10, Tallinn 10143, Estonia Alessandro Strumia Dipartimento di Fisica dell’Universit`adi Pisa, Italia Daniele Teresi Dipartimento di Fisica dell’Universit`adi Pisa and INFN, Italia (Dated: November 10, 2020) We show that the electron recoil excess around 2 keV claimed by the Xenon collaboration can be fitted by DM or DM-like particles having a fast component with velocity of order ∼ 0:1. Those particles cannot be part of the cold DM halo of our Galaxy, so we speculate about their possible nature and origin, such as fast moving DM sub-haloes, semi-annihilations of DM and relativistic axions produced by a nearby axion star. Feasible new physics scenarios must accommodate exotic DM dynamics and unusual DM properties. INTRODUCTION into account a Maxwellian-like tail of their velocity dis- tribution around or above the cut-off due to the escape The Xenon collaboration reported results of searches velocity from the Milky Way, 0:0015 < vesc < 0:002 [15] for new physics with low-energy electronic recoil data in natural units. As we will see, the Xenon1T excess recorded with the Xenon1T detector [1]. They claim an needs a flux of fast (and possibly even relativistic) parti- excess of events over the known backgrounds in the recoil cles. energy ER range 1-7 keV, peaked around 2.4 keV. The In this work we demonstrate that a flux of fast DM can local statistical significance is around 3-4σ, although part provide a good fit to the Xenon1T excess, and determine of the excess could be due to a small tritium background the necessary flux and velocity. Our results show that in the Xenon1T detector [1]. adding a free tritium abundance to the detector does not The statistical significance of the excess is 3:5σ when improve the fit. We later speculate about possible origins interpreted in terms of axions [2{4] emitted by thermal of such a fast DM component. processes in the Sun. This interpretation, considered by the Xenon collaboration [1], depends on the axion- FAST DM FIT TO XENON1T DATA electron coupling gae, that dominates both the detec- tion and the production in the Sun. Interestingly, the 0 Sun emits such axions in the desired energy range with We consider an elastic DM e ! DM e scattering be- a spectrum that can fit the excess. Although the so- tween a DM particle with initial velocity ~vDM and an lar axion scenario has all the ingredients to explain the electron with initial velocity ~ve that acquires final veloc- 0 anomaly, the needed parameter space is excluded by stel- ity ~ve. Assuming, for simplicity, that they are parallel lar cooling bounds on the axion-electron coupling [5{9]. and non-relativistic, the transferred recoil energy is Indeed, to fit the excess, the Xenon collaboration re- −12 ER ≡ Ee0 − Ee = 2µvrelvCM quires gae ≈ 3:7 · 10 while stellar cooling constraints < −12 2m v (v − v ) for m m ; (1) imply gae 0:3 · 10 . As the Xenon1T rate scales as DM e DM e DM e arXiv:2006.10735v3 [hep-ph] 9 Nov 2020 ∼ ' 4 2mevDM(vDM − ve) for mDM me; gae, bounds from cooling of hotter stars rule out this sce- nario quite convincingly. Neutrinos with a hypothetical and the transferred momentum is magnetic moment are similarly excluded [1, 10]. Parti- 0 cles with small renormalizable interactions are less con- q ≡ mDM(vDM − vDM) = −2µvrel strained by hotter stars [11, 12]. Still, this study demon- 2mDM(vDM − ve) for mDM me; (2) strates the need for a flux of fast particles in order to fit ' − 2me(vDM − ve) for mDM me; the data. Since DM exists, it is interesting to study whether where vCM ≡ (meve + mDMvDM)=(me + mDM) is the the Xenon1T anomaly can be explained in some DM center-of-mass velocity, vrel ≡ vDM − ve is the relative scenario. A narrow peak in the recoil energy ER can velocity, and µ ≡ memDM=(me + mDM) is the reduced be provided by absorption of a light bosonic DM parti- mass. We see that the desired ER ∼ 2:4 keV can be cle [1, 13] or by DM DM e ! DM e semi-absorption [14]. obtained for mDM me with vDM ≈ 0:1 or for mDM Scatterings of DM particles provide a broader structure, me and faster DM, that becomes relativistic for mDM ∼ 2 2 but cold DM particles are too slow, even when taking 0:1me. Notice that ER ' qvCM so that q ≈ (40 keV) . 2 fit both with negligible and free tritium abundance. In ) 100 the latter case, the tritium signal shape is taken from [19] and its magnitude is fitted. 80 Fig.1 compares the Xenon1T data to sample spectra ton yr keV /( of the electron excess, computed for some values of the 60 DM mass and velocity. Fig.2 shows which values of these parameters best fit A:m =1 GeV,v/c= 0.1 40 DM the energy spectrum of the excess. We find that DM m v c B: DM=10 MeV, / = 0.1 heavier than the electron with velocities v ∼ 0:1 fits 20 m v c DM C: DM=3 MeV, / = 0.05 the excess well. On the other hand, lower masses do D:m DM=5 GeV,v/c= 0.01 Binned rate in events 0 not provide sufficiently high electron recoil (unless the 2 4 6 8 10 DM velocity is increased to relativistic values), whereas Electron recoil energy in keV slower DM (even if heavier, to provide sufficient recoil) tends to give a too large signal in the first bin 1{2 keV. Allowing for a free amount of tritium background (dotted FIG. 1. Sample spectra for different values of DM mass contours in fig.2) does not shift significantly the best-fit and velocity. The gray curve is the background claimed by regions because tritium reproduces the energy spectrum (assuming negligible tritium contribution) and the Xenon1T of the excess less well than fast DM. data points are shown in black. Fig.3 shows the values of the number density of the fast DM component times its cross section on elec- We validate the above estimates by performing a de- trons needed to reproduce the excess rate claimed by tailed computation taking into account the Xe atomic Xenon1T. structure, along the lines of [16, 17]. In particular, we We assumed that DM has a velocity distribution use the relativistic wave-functions for the ionization fac- peaked at any given v and constant σe. If the cross sec- tor provided in [17]. tion σe were velocity-dependent, our fit applies with σe For a fixed DM velocity vDM (hereafter denoted by v evaluated at v. If the velocity distribution has a width, to simplify the notation), the differential cross-section is the fit still holds until it exceeds the Xenon energy res- olution. Non-monochromatic velocity distributions pro- Z q+ dσv σe 2 2 duce broader signals. In particular, the required popula- = a0 q dqjF (q)j K(ER; q); (3) dER 2mev q− tion of fast DM particles cannot arise from a high-velocity tail of a broad distribution (e.g. thermal), because such where σe is the free electron cross-section at fixed mo- scenarios would be produce a too strong signal in the mentum transfer q = 1=a0, where a0 = 1=(αme) is the lower energy bin at 1{2 keV. Bohr radius. The limits of integration are q 2 2 q± = mDMv ± mDMv − 2mDMER: (4) DISCUSSION AND SPECULATIONS We assume the DM form factor F (q) = 1 obtained, We have seen that the Xenon1T electron recoil ex- e.g., from heavy mediators. The atomic excitation factor cess can be interpreted as due to a flux of high veloc- K(ER; q) is taken from [18] and includes the relativistic ity particles. Their velocities have to be so high that corrections, relevant at large momentum exchange. For these particles cannot be gravitationally bound to the ER ∼ keV recoil energies, the excitation factor is domi- DM halo of our Galaxy. Here we will speculate about nated by the n = 3 and n = 4 atomic shells, the former possible physical origins of such flux of fast DM-like par- starting at ER > 1:17 keV. The differential rate is given ticles. One needs to consider non-trivial DM dynamics, by that must be consistent with all constraints. For exam- dR dσv ple, DM up-scattering by cosmic rays [20, 21] seems not = nT nDM ; (5) to be consistent with other experiments. dER dER One possibility is that the Earth is currently passing 27 where nT ' 4:2 × 10 =ton is the number density of through a DM (sub-)halo that moves with a very high Xenon atoms, and nDM is the number density of the speed relative to us. The origin of such halo is, however, fast DM component. The rate depends on the product unclear, as the required velocities v >∼ 0:05 are an order of nDMσe, which we fit to the Xenon1T excess. To com- magnitude larger than the velocity dispersions in nearby pare the spectra with the Xenon1T data, we smear them rich galaxy clusters. by a detector resolution σdet = 0:45 keV [19], approxi- Another possibility is that a flux of fast DM is pro- mated as constant, multiply by the efficiency given in [1] duced by semi-annihilation processes (see e.g. [22{28]) and bin them as the available data in [1].