PHYSICAL REVIEW LETTERS 125, 131806 (2020)

Reexamining the Solar Explanation for the XENON1T Excess

† ‡ ∥ Christina Gao ,1,* Jia Liu ,2,7, Lian-Tao Wang,2,3, Xiao-Ping Wang,4,8,§ Wei Xue,5, and Yi-Ming Zhong6,¶ 1Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 2Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA 3Department of Physics, University of Chicago, Chicago, Illinois 60637, USA 4HEP Division, Argonne National Laboratory, 9700 Cass Ave., Argonne, Illinois 60439, USA 5Department of Physics, University of Florida, Gainesville, Florida 32611, USA 6Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637, USA 7School of Physics and State Key Laboratory of Nuclear Physics and Technology, , Beijing 100871, China 8School of Physics, Beihang University, Beijing 100083, China (Received 7 July 2020; accepted 28 August 2020; published 24 September 2020)

The XENON1T collaboration has observed an excess in electronic recoil events below 5 keV over the known background, which could originate from beyond-the-standard-model physics. The solar axion is a well-motivated model that has been proposed to explain the excess, though it has tension with astrophysical observations. The traveling from the Sun can be absorbed by the electrons in the atoms via the axion-electron coupling. Meanwhile, they can also scatter with the atoms through the inverse Primakoff process via the axion-photon coupling, which emits a photon and mimics the electronic recoil signals. We found that the latter process cannot be neglected. After including the keV photon produced via the inverse Primakoff process in the detection, the tension with the astrophysical constraints can be significantly reduced. We also explore scenarios involving additional new physics to further alleviate the tension with the astrophysical bounds.

DOI: 10.1103/PhysRevLett.125.131806

Axions are pseudogoldstone bosons which naturally It is tempting to explain the XENON1T excess using the arise from the beyond-the-standard-model (BSM) physics solar axions since the axion energy spectrum naturally scenarios [1–3]. Because of an approximate shift symmetry, matches the excess. The axions are produced in the Sun they can be naturally light. Typically, they are very weakly from several processes, including the Primakoff process coupled to other particles, which makes them a good γ þ Ze → Ze þ a; the atomic axion-recombination and candidate of or dark sector particles [4–6]. deexcitation, bremsstrahlung, and Compton (ABC) scatter- The phenomenology of the axions is rich, and they give ing processes; and the nuclear transitions. Hence, the axion- unique signals in cosmology, astrophysics, and particle photon gaγ, axion-electron gae, and axion-nucleon gan physics [7–11]. couplings enter the production. With their tiny coupling XENON1T, a dual-phase liquid xenon detector, is one of to photons, the keVaxions have a long lifetime and can travel the leading experiments looking for dark matter (DM). from the Sun to the XENON1T. For the processes in the Because of its large volume and low backgrounds, the detector which can give the signal, XENON1T [12] con- XENON1T is also sensitive to other rare processes poten- sidered only the axion-electron coupling. In this case, the tially related to BSM physics. Recently, the XENON1T axions could be absorbed by the electrons in xenon atoms. collaboration reported their searches for the low-energy The relevant axion couplings can be summarized in the electronic recoil, with an excess in the range of 1–5 keV, following Lagrangian: which cannot be accounted for by the known backgrounds [12]. The XENON1T collaboration has also performed a fit ∂μa 1 to the excess using the solar axion model [13]. Since this L ⊃− ¯γμγ − ˜ μν ð Þ gae 2 e 5e 4 gaγaFμνF : 1 report, there have been active speculations about the me explanation of the excess [14–43]. Fμν is the field strength of the photon, and its dual ˜ μν 1 μναβ F ¼ 2 ϵ Fαβ. However, the parameter space of the Published by the American Physical Society under the terms of solar axion interpretation of the excess is in tension with he the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to astrophysical observations of stellar evolution including the the author(s) and the published article’s title, journal citation, white dwarfs (WDs) and the horizontal branch (HB) stars in and DOI. Funded by SCOAP3. the globular clusters (GCs) [12,25].

0031-9007=20=125(13)=131806(8) 131806-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 125, 131806 (2020)

numerically. We take the expression above and fit the form 2 2 factor by the relation Fa ¼ k =q ðZ − FγÞ [44], and the atomic form factor Fγ is reported in Ref. [54]. The fit gives −1 −1 r0 ¼ 4.04 keV ¼ð49 pmÞ , which is close to the recip- rocal of the xenon atomic radii 108 pm [55]. This screening length corresponds to a screened charge of Zsc ¼ 5.3 for xenon at jqj¼3 keV. Next, we calculate the event rate from solar axions with both the inverse Primakoff process and the axioelectric effect. The cross section of the latter process is given by [56,57] FIG. 1. The solar axion induced photon signal through the inverse Primakoff process. 2 3 2 β2=3 σ ¼ σ gae Ea 1 − a ð Þ ae pe β 2 3 ; 3 a 16παme In this Letter, we take into account the fact that, at the σ β keV energy range, the current XENON1T experiment can where pe is the photoelectric cross section [58] and a is the axion velocity. We will focus on the low energy excess hardly distinguish the detector response of photons from ≲5 that of electronic recoils. Hence, instead of electronic ( keV) throughout this Letter, hence, only consider the contributions to solar axion flux from the ABC process, recoil, the low-energy photons generated through the ABC Prim Φa , and the Primakoff process, Φa , and neglect that inverse Primakoff scattering between the solar axion and 57 the xenon atoms in the detector can mimic the electronic from the nuclear transition of Fe. The ABC flux originates ΦABC ∝ signal, as shown in Fig. 1. Using the inverse Primakoff from the axion-electron coupling and is given by a 2 process to detect axions was proposed in the cryogenic gae [59]. The Primakoff flux is given by [60] experiments via Bragg scattering [44–46] and was dΦPrim applied by the SOLAX, COSME, CUORE, CDMS, and a ¼ 6 × 1010 cm−2 s−1 keV−1 – dE EDELWEISS collaborations [47 52]. However, it was not a 2 2.481 included in the liquid type of gaγ Ea − ð1 205 Þ × e Ea= . keV : ð4Þ experiments previously. We show that, after including both 10−10 GeV keV the electronic recoil and the inverse Primakoff process, the tension between the solar axion explanation and the Given the solar axion flux Φa, the differential event rate astrophysical constraints is significantly reduced. after including both axioelectric and inverse Primakoff The Letter is structured as follows: first, we describe the processes in the detection is given by detection using the inverse Primakoff process, and after ΦABC ΦPrim considering the astrophysics and terrestrial constraints, we dR NA d a d a ¼ ðErÞþ ðErÞ present the fit to the data of XENON1T. Then, we discuss dEr A dE dE the possible extensions of new physics to further alleviate invPrim × ½σ →γ ðE Þþσ ðE Þ; ð5Þ the tension between the constraints and the XENON1T fit. a r ae r We conclude in the end. where NA is the Avogadro constant, A ¼ 131 is the atomic Detection from the inverse Primakoff process.—In this weight of xenon, and Er represents the electronic recoil section, we compute the contribution to the electronic recoil energy, which is faked by photons in the inverse Primakoff þ → γ þ from the inverse Primakoff process a Xe Xe, process. where Xe represents the xenon nucleus. The differential To compare with the results reported by the XENON1T cross section is given by [44,46,53] collaboration, we further smear the differential event rate σ ¼ invPrim 2 with a Gaussian with its variance satisfying =Er dσ →γ α q pffiffiffiffiffi a ¼ g2 ð4 − q2=k2ÞF2ðq2Þ; ð Þ ða= E þ bÞ%. A numerical fit to the data of XENON1T Ω 16π aγ k2 a 2 r d energy resolution [61] yields a ¼ 35.9929 keV1=2 and where α is the fine structure constant, k is the momentum of b ¼ −0.2084. After the smearing, we apply the detector the incoming axion and q is the momentum transfer. In the efficiency [12]. limit of small axion mass, ma ≪ jkj, the energy of the Figure 2 shows two examples of the differential event outgoing photon is also approximately jkj. Fa is the form rate of the electronic recoils given different values of gae factor characterizing the screening effect of the electric and gaγ. In the case that gae ¼ 0, the spectrum is only ðq2Þ¼ k2 ð −2 þ q2Þ Prim charge of the nucleus, given by Fa Z = r0 , determined by the detection of Φa through the inverse where Z ¼ 54 is the atomic number of xenon and r0 is Primakoff process. It is clear that, with gae switched off, the screening length [44], that can be determined solar axions can still account for the low energy excess,

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FIG. 3. he 2D axion couplings parameter fit for the XENON1T excess after including the inverse Primakoff process. Our best fit (90% C.L.) to the XENON1T excess is shown in the red shaded region with the solid boundary. In comparison, a “XENON-like” analysis with only the electron recoil included as the signal yields is shown in the region with the dashed boundary. The main difference is that the inclusion of the inverse Primakoff process allows for a region in which gaγ is relatively large while gae can be FIG. 2. Fit to electronic recoil energy spectrum with gaγ only small, reducing the tension with the astrophysical data. Also (top) and both gaγ and gae allowed (bottom). included are the constraints (95% C.L.) from astrophysical observables including WDLF [68], the tip of RGB [69] and the R parameter (with two models) [64], as well as the constraints from although the fit is not as good as that allowing both g and ae the global fit of the solar data [70], LUX [73], and PandaX [74], gaγ to be nonzero. with arrows denoting excluded regions. We do not show con- Constraints from astrophysics and terrestrial experi- straints from CAST [75] and magnetic WDs [71] by assuming the ments.—The most severe constraints on the solar axion axion mass ≳1 eV. The shaded green region contains 1σ to 4σ explanation of the XENON1T excess are from the stellar contours favored by the anomalous stellar cooling [25,72]. cooling in the HB and red-giant branch (RGB) stars, which −10 −1 we review below. gaγ < 4.1 × 10 GeV [70]. Other constraints such as Axions with sizable gaγ and gae couplings speed up the x-ray observations on magnetic WDs [71] get significantly burning of the He-core (H-core) for HB (RGB). The weakened for axion mass ≳1 meV. In Fig. 3, we also show lifetime of the stars in the two phases is proportional to 1σ to 4σgae − gaγ contours favored by the anomalous stellar their observed numbers. Therefore, one can use the R cooling [25,72]. parameter, the ratio of the number of HB stars to that of On the terrestrial experiments side, the axion searches RGB stars, to constrain the axion couplings. Reference [62] from LUX [73] suggest g < 3.5 × 10−12. Similar constraint ¼ 1 39 0 03 ae obtained a weighted average Rav . . from the is also shown by PandaX [74]. The CAST experiment [75] −11 −1 R parameters of 39 low-metallicity galactic GCs reported constrains light axions with g γ < 6.6 × 10 GeV . ¼ 0 a by [63]. Assuming gae , gaγ is constrained to be gaγ < This bound gets significantly weakened for axions with 6 6 10−11 −1 . × GeV . For nonzero gae, Ref. [64] presented mass ≳1 eV. two stellar evolution models which give slightly different Results.—In Fig. 3, we present our fit to the XENON1T predictions of the R parameter. In Fig. 3, we adopted the excess and compare it with the bounds from the previous resulting 95% C.L. constraints on the g − g γ plane for ae a section. We scan two parameters gae, gaγ, and apply the both models from Fig. 4 of [64]. In the Supplemental method of least squares to the XENON1T data to find the Material [65], we further discuss the bound dependence on 90% C.L. contours with (solid red) and without (dashed the He abundance of GCs. The bremsstrahlung energy loss red) including the inverse Primakoff process. In compari- from the axion-electron coupling affects the white dwarf son, we also show the constraints (95% C.L.) from luminosity function (WDLF) and constrains gae ≲ 2.8 × astrophysical observables including WDLF, the tip of −13 10 [68]. The same argument on RGB constrains gae ≲ RGB, and the R parameter (with two models), as well 4.3 × 10−13 [69]. The global fit of the solar data constrains as the constraints from the global fit of the solar data and

131806-3 PHYSICAL REVIEW LETTERS 125, 131806 (2020) the direct search at LUX and PandaX. The constraints from approximately 1 for a momentum transfer of a few keV. We CAST and magnetic WDs can be evaded by the axion with follow Ref. [53] to calculate the Primakoff energy loss due 0 a mass ≳1 eV and we do not show them in Fig. 3. to Eq. (6) for A with mA0 ¼ 0.1ð1Þ keV. The resulting solar From Fig. 3, we see that the inclusion of the inverse- energy loss rate per unit volume is Primakoff process has a significant impact on the parameter 2 α g 0 region preferred by the XENON1T data. In particular, it A0Primð Þ ≈ Primð Þ 16 9ð4 3Þ B aγA ð Þ Qa Sun Qa Sun × . . × α 2 ; 8 opens up a parameter region in which gaγ ≫ gae=GeV and gaγ the inverse Primakoff process gives rise to the observed −13 and that for HB is signal. Moreover, for gae ∼ 10 , it prefers a gaγ which is a 10−10 −1 2 few × GeV , 1 order of magnitude smaller than the 0 α g γ 0 QA PrimðHBÞ¼QPrimðHBÞ × 15.6ð8.0Þ × B a A ; ð9Þ preferred gaγ without the inclusion of the inverse Primakoff a a α 2 gaγ process, satisfying the constraints from the global fit of the Prim solar data, and significantly reducing the tension with the where Qa is the energy loss rate per unit volume stellar cooling bounds. Future terrestrial axion experiments, from Eq. (1). The cross section for inverse Primakoff A0invPrim A0Prim such as the International Axion Observatory [76] and the detection at XENON1T is given by σa→γ ¼ 2σγ→a . Multilayer Optical Haloscope [77], can complement the For mA0 ¼ 0.1ð1Þ keV, astrophysical probes and cover the relevant g γ coupling a 2 α g 0 region for axions with mass of several eV. σA0invPrim ¼ σinvPrim 400ð90Þ B aγA ð Þ — a→γ a→γ × × α 2 : 10 Possible extensions. Even though the inclusion of the gaγ inverse Primakoff process can significantly improve the prospect of explaining the XENON1T excess with the solar Combining the solar axion flux and the detection cross 0 ¼ 0 1ð1Þ axions, it is still in tension with the stellar cooling bounds, section, we find that for mA . keV, it requires with a discrepancy as large as 8σ, as claimed by [25]. g γ 0 g ≈ 0.11ð0.23Þg γe; ð11Þ Indeed, if the excess is completely due to new physics, a A B a there remains three possibilities. It could certainly come to explain the XENON1T excess. Moreover, this choice of from other new physics instead of the solar axion, in which parameter helps to alleviate the HB cooling tension, such case a new explanation of the keV scale needs to be found. that its energy loss is reduced to 19% (40%) of that solely It is also possible that there is additional uncertainty in the due to axion from Eq. (1). ð1Þ stellar cooling bound which still has not been appreciated However, there are severe constraints for U B cou- (see, e.g., [78,79] and the discussion in the Supplemental plings from astrophysics and collider physics. The stars Material [65]). Instead of pursuing these avenues, we will (the Sun, HB, and supernova) can be cooled by directly explore a third possibility, with new physics in addition to emitting A0 through bremsstrahlung and Compton scatter- ð1Þ ≲ the solar axion. In particular, we focus on the parameter ing. The constraint from SN1987 A for U B is gB −10 space given by gaγ ≫ gae=GeV, where the most relevant 2.5 × 10 [80]. For solar and HB cooling, the emission of 0 2 2 constraint is from the R parameter, the cooling from HB. A from the ion leg is suppressed by Oðme=mnÞ and, thus, ð1Þ −10 We introduce a U B gauge boson and discuss its effects. requires gB ≲ 10 [81,82]. For collider physics, the UV Consider an axion coupling to both photon and dark anomaly cancellation of Uð1Þ leads to Wess-Zumino 0 B gauge boson A carrying the Uð1Þ Baryon charge, 0 B operators at low energy, which constrains gB=mA < 3 × 1 10−10 keV−1 [83] from the invisible decays of the Z boson 0 ˜ μν 0 μ L ⊃− g γ 0 aFμνF þ g AμJ : ð Þ 2 a A B B 6 or mesons. Therefore, both sets of constraints suggest that g ≲ 10−10 for keV A0. ð1Þ 0 B The U B A couples to the baryonic current JB, but not 0 0 To explain the XENON1T excess, the coupling gaγA directly to electrons. Hence, processes mediated by A do should be larger than ∼0.1 GeV−1, meaning a cutoff scale not suffer the screening effect. Therefore, the Primakoff 0 of 10 GeV. Such an energy scale may arise from integrating production in the Sun is increased if A is lighter than the out new light particles [31]. However, the thermal photon in thermal photon in the plasma, and the detection cross 0 the plasma can decay via γ → a þ A , thus, a large g γ 0 is 2 2 ∼ 600 0 a A section is enhanced by A =Zsc for light A with 0 −1 not desirable. In summary, both gB and gaγA are highly 0 ∼ 4 mA

131806-4 PHYSICAL REVIEW LETTERS 125, 131806 (2020) to electrons via one-loop induced kinetic mixing, which is difference in the value of couplings, both scenarios are ð − 2Þ ≲ 10−5 constrained by the g e measurement to be ge marginally allowed given the astrophysical constraints. [84]. The loop induced coupling to electron is on the order Conclusions.—Solar axion is an appealing explanation of ge ∼ gBα. However, there can also be a UV contribution for the XENON1T excess, with its energy naturally in the to the kinetic mixing as well. With fine tuning, the total keV range. In this Letter, we have emphasized the impor- coupling to the electron can be made to be consistent with tance of including photons with a similar recoil spectrum the constraint. The resulting scenario could have interesting as a possible explanation for the XENON1T excess. In implications which deserve further study. particular, it can significantly reduce the tension between the solar axion explanation and the astrophysical data, We also consider using the environment effect to weaken especially the stellar cooling bound. Introducing additional the HB cooling bound while keeping the solar axion flux new physics can further alleviate the remaining tension. intact. The core temperature of HB and the Sun are 10 and ω We conclude, here, by briefly discussing future prospects. 1 keV, and the corresponding photon plasma mass p are 2 We expect that further sharpening the stellar cooling bound and 0.3 keV, respectively. Consider axions coupling to both 0 will certainly help to clarify the situation. Indeed, if there is photon and Uð1Þ , additional new physics that helps to relieve the tension with 1 1 the astrophysical bound, it would be interesting in exploring ˜ μν 0 ˜ μν L ⊃− g γaFμνF − g γ 0 aFμνF : ð12Þ other possible signals of these new physics. For example, a 4 a 2 a A ð1Þ more sensitive search for the U B can have the potential of shedding new light on this scenario. We also note that it is The resulting Primakoff production of axions contains possible to have new physics models in which the photon γ 0 diagrams with t-channel or A . One can choose the sign comes from completely different sources. For example, it of gaγA0 to have destructive interference among the two can come from a different dark matter scattering process [31] diagrams and make them cancel for HB with a particular or from decaying from an excited state of the dark matter combination of gaγA0 gB. However, a complete cancellation [26,41], or the dark photon conversion process considered in only works for particular momentum transfer and, thus, this Letter. In these cases, the spectrum of the photon would does not apply to the entire phase space. In addition, the be different from the one from the inverse Primakoff process. core temperature for HB is not a constant, thus, the Future data can be used to distinguish these scenarios. cancellation may only happen within a restricted volume. We would like thank Luca Grandi, Tarek Saab, Evan Therefore, it is difficult to have a significant environment- Shockley for discussing in detail the response to the dependent suppression. electron and photon in the XENON1T detector, Fei Gao, Above, we focused on the solar axions, where the origin Jingqiang Ye for the details of fit and the analysis, Aaron of the keV scale of the excess can be naturally explained. Pierce and Sergey Sibiryakov for the axion models and Nevertheless, it is hard to accommodate the stellar cooling constraints, and Maurizio Giannotti, Andreas Ringwald, bounds. Dropping the relation between the keV scale and the and Oscar Straniero for clarifying the weighted average for solar axion energy, one may consider a broader range of the the R parameter and the theoretical prediction formula. ð1Þ signal sources. For example, the U B dark photon could be C. G. is supported by Fermi Research Alliance, LLC under the dark matter, with mass mA0 ≃ 2.8 keV. In this case, the Contract No. DE-AC02-07CH11359, J. L. acknowledges detection at XENON1T is through the dark photon con- support by an Oehme Fellowship, L. T. W. is supported by version A0 þ Xe → γ þ Xe with the cross-section given by the DOE Grant No. DE-SC0013642, X. P. W. is supported by the DOE Grant No. DE-AC02-06CH11357, W. X. is 2 2 supported by the DOE Grant No. DE-SC0010296, and 2 2 e gB σv ¼ A Zsc ; ð13Þ Y. Z. is supported by the Kavli Institute for Cosmological 6πm2 Xe Physics at the University of Chicago through an endow- 0 ment from the Kavli Foundation and its founder Fred Kavli. where A ¼ 131, Z ∼ 5.3. Since A is much lighter than the sc J. L. and X. P. W. have moved to Peking University and nucleus, the photon energy is about m 0 . The total number A Beihang University respectively, during the review and ð Þσ ðρ 0 Þ of events is given by exposure=mXe v DM=mA , where revision processes. ρ ¼ 0 3 3 DM . GeV=cm is the local DM density. The excess ≈ 5 10−11 can be explained with gB × . Such a value is Note added.—Shortly after this work appeared on arXiv, a marginally below that from the astrophysical and collider study [85] appeared that also investigated the inverse ≲ 10−10 bounds gB . References [12,42] studied kinetic Primakoff effect on the solar axion detection. mixing dark photon dark matter as a solution for the excess and requires the mixing parameter ϵ ≈ 7 × 10−16. The difference between those models and ours comes *Corresponding author. from the dark photon coupling to electrons. The [email protected] † resulting dark-photoelectric cross section is approximately Corresponding author. ð 2 2Þðϵ2 2 Þ mN=me =gB times of Eq. (13). Though there is a large [email protected]

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