Search for Light Dark Matter Interactions Enhanced by the Migdal effect or Bremsstrahlung in XENON1T

TL;DR

This paper reports on a novel analysis of XENON1T data that searches for low-mass dark matter particles by detecting electronic recoils caused by the Migdal effect and Bremsstrahlung, extending sensitivity down to about 85 MeV/c^2.

Contribution

It introduces a new method using ionization signals alone to improve sensitivity to light dark matter in liquid xenon detectors.

Findings

Enhanced sensitivity to dark matter masses down to 85 MeV/c^2.

First application of Migdal effect and Bremsstrahlung in XENON1T data.

No significant dark matter signal observed.

Abstract

Direct dark matter detection experiments based on a liquid xenon target are leading the search for dark matter particles with masses above $\sim$ 5 GeV/c$^2$, but have limited sensitivity to lighter masses because of the small momentum transfer in dark matter-nucleus elastic scattering. However, there is an irreducible contribution from inelastic processes accompanying the elastic scattering, which leads to the excitation and ionization of the recoiling atom (the Migdal effect) or the emission of a Bremsstrahlung photon. In this letter, we report on a probe of low-mass dark matter with masses down to about 85 MeV/c$^2$ by looking for electronic recoils induced by the Migdal effect and Bremsstrahlung, using data from the XENON1T experiment. Besides the approach of detecting both scintillation and ionization signals, we exploit an approach that uses ionization signals only, which allows for a lower detection threshold. This analysis significantly enhances the sensitivity of XENON1T to light dark matter previously beyond its reach.

Equations

$$\frac{d^{2}R}{d{E}_{\mathrm{ER}}dv}\propto \frac{{\left|f(E_{\mathrm{ER}})\right|}^2}{E_{\mathrm{ER}}}\sqrt{1-\frac{2E_{\mathrm{ER}}}{{\mu }_N{v}^2}}\left(1-\frac{E_{\mathrm{ER}}}{{\mu }_N{v}^2}\right),$$

$$\large\begin{array}[]{lll}\frac{dR}{dE_{\mathrm{ER}}}&\simeq&\int dE_{\mathrm{NR}}dv\frac{d^{2}R}{dE_{\mathrm{NR}}dv}\\ &&\times\frac{1}{2\pi}\sum_{n,l}\frac{d}{dE_{\mathrm{ER}}}p^{c}_{q_{e}}(n,l\rightarrow E_{\mathrm{ER}}-E_{n,l}),\end{array}$$

Full text

Dark Matter, Direct Detection, Xenon, Migdal effect, Bremsstrahlung

The existence of dark matter (DM) is supported by various astronomical and cosmological observations Clowe et al. (2004); Rubin et al. (1980); Aghanim et al. (2018) but its nature remains unknown. The most promising DM candidate is the so-called weakly interacting massive particle (WIMP) Jungman et al. (1996), which explains the current abundance of dark matter as a thermal relic of the Big Bang Lee and Weinberg (1977). In the last three decades, numerous terrestrial experiments have been built to detect the faint interactions between WIMPs and ordinary matter. Among them, experiments using dual-phase (liquid/gas) xenon time projection chambers (TPCs)  Akerib et al. (2016); Cui et al. (2017); Aprile et al. (2018) are leading the search for WIMPs with masses from a few GeV/c2 to TeV/c2. The mass of the WIMP is expected to be larger than about 2 GeV/c2 from the Lee-Weinberg limit Lee and Weinberg (1977) assuming a weak scale interaction. On the other hand, DM in the sub-GeV/c2 mass range has been proposed in several models Battaglieri et al. (2017); Boehm et al. (2004); Boehm and Fayet (2004). In this letter, we report on a probe of light DM-nucleon elastic interactions by looking for electronic recoils (ERs) in XENON1T, induced by secondary radiation (Bremsstrahlung Kouvaris and Pradler (2017) and the Migdal effect Migdal (1941); Ibe et al. (2018)) that can accompany a nuclear recoil (NR). ER signals induced by the Migdal effect and Bremsstrahlung (BREM) can go well below 1 keV, where the detection efficiency for scintillation signal is low. Therefore, in addition to the analysis utilizing both ionization and scintillation signals, we performed analysis using the ionization signal only, which improves the detection efficiency for sub-keV ER events. We present results from a proble of light DM (LDM) with masses as low as 85 MeV/c2.

The XENON1T direct dark matter detection experiment Aprile et al. (2017a) uses a dual-phase TPC containing 2 tonnes of ultra-pure liquid xenon (LXe) as the active target material. It is located at the INFN Laboratori Nazionali del Gran Sasso (LNGS) in Italy, which has an average rock overburden of 3600 m water-equivalent. The prompt primary scintillation (S1) and secondary electroluminescence of ionized electrons (S2) signals are detected by top and bottom arrays of 248 Hamamatsu R11410-21 3*′′* photomultiplier tubes (PMTs) Aprile et al. (2015, 2017b). They are used to reconstruct the deposited energy and the event interaction position in three dimensions, which allows for fiducialization of the active volume Aprile et al. (2019a, b). The XENON1T experiment has published WIMP search results by looking for NRs from WIMP-nucleus elastic scattering using data from a one-tonne-year exposure, achieving the lowest ER background in a DM search experiment Aprile et al. (2018). The excellent sensitivity of LXe experiments to heavy WIMPs comes from the heavy xenon nucleus which gives a coherent enhancement of the interaction cross-section and from the large NR energy. The sensitivity to sub-GeV/c2 LDM, on the other hand, decreases rapidly with lowering DM mass since detectable scintillation and ionization signals produced by these NRs become too small. The energy threshold (defined here as the energy at which the efficiency is 10%) in a LXe TPC is mainly limited by the amount of detectable S1 signals. A significant fraction of deposited NR energy is transferred into heat due to the Lindhard quenching effect Lindhard et al. (1963). Thus the detection efficiency for these NRs becomes extremely low, with less than 10% for NRs below 3.5 keV in XENON1T Aprile et al. (2018). It is challenging to detect the NR signals from LDM interactions.

Unlike NRs, ERs lose negligible energy as heat because recoil electrons have small masses compared with xenon nuclei. This leads to a lower energy threshold for ER signals. Probing the ER signals induced by the Migdal effect and BREM enables a significant boost of XENON1T’s sensitivity to LDMs, thanks to the lowered threshold.

When a particle elastically scatters off a xenon nucleus, the nucleus undergoes a sudden momentum change with respect to the orbital atomic electrons, resulting in the polarization of the recoiling atom and a kinematic boost of the electrons. The de-polarization process can lead to BREM emission Kouvaris and Pradler (2017), and the kinematic boost of atomic electrons can result in ionization and/or excitation of the atom, which eventually causes secondary radiation, known as the Migdal effect (MIGD) Migdal (1941); Ibe et al. (2018).

The differential rate of BREM emission with photon energy EER is given by

[TABLE]

where $v$, $\mu_{N}$, and $f(E_{\mathrm{ER}})$ are the velocity of DM, the reduced mass of the xenon nucleus and DM, and the atomic scattering factor, respectively Kouvaris and Pradler (2017).

The differential rate of MIGD process giving an NR of energy ENR accompanied by an ER of energy EER is given by

[TABLE]

where $p^{c}_{q_{e}}$ is the probability for an atomic electron, with quantum numbers ($n$, $l$) and binding energy $E_{n,l}$, to be ionized and receive a kinetic energy $E_{\mathrm{ER}}-E_{n,l}$ Ibe et al. (2018). $p^{c}_{q_{e}}$ is related to $q_{e}$ which is the momentum of each electron in the rest frame of the nucleus after the scattering. The shell vacancy is immediately refilled, and an X-ray or an Auger electron with energy $E_{n,l}$ is emitted. $E_{n,l}$ is measured simultaneously with the energy deposited by the ionized electron, since the typical timescale of the de-excitation process is $\mathcal{O}$(10) fs. Atomic electrons can also undergo excitation instead of ionization, in which case an X-ray is emitted during de-excitation Ibe et al. (2018). Excitation, however, is sub-dominant compared to the ionization process, and thus is not considered in this analysis. Only the contributions from the ionization of M-shell ($n$=3) and N-shell ($n$=4) electrons are considered in this work, as inner electrons (n$$\leq2) are too strongly bound to the nucleus to contribute significantly. The contribution from the ionization of valence electrons ($n$=5) is neglected because it is subdominant in region of interest compared to the ones from M- and N-shell electrons, and the calculation of it has large uncertainty since the assumption of isolated atom is used for LXe Ibe et al. (2018). An illustration of MIGD and BREM is given in Fig. 1. The radiation from MIGD is typically 3-4 orders of magnitude more likely to occur than BREM. Although only a very small fraction (about 3$\times 10^{-8}$ and 8$\times 10^{-6}$ for DM masses of 0.1 and 1.0 GeV/c2, respectively) of NRs accompanies MIGD radiations, the larger energy and ER nature make them easier to be detected than the pure NRs.

The data used in previous analyses Aprile et al. (2018) consists of two science runs with a livetime of 32.1 days (SR0) and 246.7 days (SR1), respectively. The two runs were taken under slightly different detector conditions. To maximize the amount of data acquired under stable detector conditions we decided to use SR1 only. The same event selection, fiducial mass, correction, and background models as described in Aprile et al. (2018) are used for the SR1 data, which we refer to as the S1-S2 data in later text. The exposure of the S1-S2 data is about 320 tonne-days. The interpretation of such S1-S2 analysis is based on the corrected S1 (cS1) signal and the corrected S2 signal from the PMTs at the bottom of the TPC (cS2b).

The region of interest in the S1-S2 data is from 3 to 70 photoelectrons (PEs) in cS1, which corresponds to median ER energies from 1.4 to 10.6 keV in the 1.3-tonne fiducial volume (FV) of XENON1T. The lower value is dictated by the requirement of the 3-fold PMT coincidence for defining a valid S1 signal Aprile et al. (2019a). A detailed signal response model Aprile et al. (2019b) is used to derive the influence of various detector features, including the requirement of the 3-fold PMT coincidence, on the reconstructed signals. The effective exposure, which is defined as exposure times detection efficiency, and its uncertainty as a function of deposited ER energy for the S1-S2 data are shown in Fig. 2, with the signal spectra from MIGD and BREM induced by 0.1 GeV/c2 and 1 GeV/c2 DM masses overlaid. The (cS2b, cS1) distribution of S1-S2 data are shown in Fig. 3. The rise of the event rate at around 0.85 keV for DM mass of 1.0 GeV/c2 is contributed by the ionization of M-shell electrons Ibe et al. (2018); Kouvaris and Pradler (2017). In our signal models, deposited energy below 1 keV, at which the median detection efficiency in 1.3-tonne FV is 10%, from MIGD and BREM is neglected for the S1-S2 data in the following analysis. There are only two sub-keV measurement of ionization yield for ER in LXe Akerib et al. (2017); Boulton et al. (2017).

The S1-S2 data selections Aprile et al. (2019a) provide excellent rejection of noise and backgrounds, and are characterized as well by the well-established background models Aprile et al. (2019b) and a fully blind analysis Aprile et al. (2018). However they also limit the detection efficiency of $\mathcal{O}$(1) keV energy depositions. We therefore consider also the events with no specific requirement on S1 (S2-only data) in this work. Although the reduction of available information in the S2-only data implies less background discrimination, the increased detection efficiency in the $<$ 1 keV ER energy region, shown in Fig. 2, enables a more sensitive search for LDM-nucleus interactions through MIGD and BREM. The interpretation of such S2-only data is based on the uncorrected S2 signal, combining both signals from top and bottom PMT arrays.

We analyze the S2-only data as in Aprile et al. (2019c), using the LDM signal models appropriate for MIGD and BREM. As detailed in Aprile et al. (2019c), 30% of the data was used for choosing regions of interest (ROIs) in S2 and event selections. A different S2 ROI is chosen for each dark matter model and mass to maximize the signal-to-noise ratio, based on the training data. The event selections used for this work are the same as in Aprile et al. (2019c), and mainly based on the width of each S2 waveform, reconstructed radius, and PMT hit-pattern of the S2. Fig. 4 shows the observed S2 spectra for the S2-only data, along with the expected DM signal distributions by MIGD with masses of 0.1, 0.5, and 1.0 GeV/c2, respectively. The S2 ROIs for these three DM models shown in Fig. 4 are indicated by the colored arrows. Conservative estimates of the background from 214Pb-induced $\beta$ decays, solar-neutrino induced NRs, and surface backgrounds from the cathode electrode are used in the inference Aprile et al. (2019c). The background model is shown in Fig. 4 as shaded gray region.

The detector response to ERs from MIGD and BREM in (cS2b, cS1) space (for the S1-S2 data) and in reconstructed number of electrons (for the S2-only data) is derived using the signal response model described in Aprile et al. (2019b). Note that the ionization yield used for the S2-only data is more conservative than the Noble Element Simulation Technique (NEST) v2 model Szydagis et al. (2018). Fig. 3 shows the comparison between the expectation from our signal response model and the S1-S2 data, as well as the (cS2b, cS1) distribution of ERs from MIGD. Signal contours for different DM masses are similar since the energy spectra from MIGD and BREM are not sensitive to incident dark matter velocity as long as it is kinematically allowed. We have ignored the contribution of NRs in the signal model of MIGD and BREM, since it is small compared with ERs from MIGD and BREM in this analysis and there is no measurement of scintillation and ionization yields in LXe for simultaneous ER and NR energy depositions. We use the inference only for DM mass below 2 GeV/c2, above which the contribution of an NR in the signal rate becomes comparable with or exceeds the signal model uncertainty.

The S1-S2 data are interpreted using an unbinned profile likelihood ratio as the test statistic, as detailed in Aprile et al. (2019b). The unbinned profile likelihood is calculated using background models defined in cS2b, cS1, and spatial coordinates. The uncertainties from the scintillation and ionization yields of ER backgrounds, along with the uncertainties in the estimated rates of each background component, are taken into account in the inference Aprile et al. (2019b). The inference procedure for the S2-only data is detailed in Aprile et al. (2019c), which is based on simple Poisson statistics using the number of events in the S2 ROI. The event rates of spin-independent (SI) and -dependent (SD) DM-nucleon elastic scattering are calculated following the approaches described in Lewin and Smith (1996); Aprile et al. (2018) and Aprile et al. (2019d), respectively.

The results are also interpreted in a scenario where LDM interacts with the nucleon through a scalar force mediator $\phi$ with equal effective couplings to the proton and neutron as in the SI DM-nucleon elastic scattering. In this scenario, the differential event rates are corrected by ${m_{\phi}}^{4}/({m_{\phi}}^{2}+q^{2}/c^{2})^{2}$  Del Nobile et al. (2015); Ren et al. (2018), where $q=\sqrt{2m_{N}E_{R}}$ and $m_{N}$ are the momentum transfer and the nuclear mass, respectively. We take the light mediator (LM) regime where the momentum transfer is much larger than ${m_{\phi}}$ and thus the interaction cross section scales with $m_{\phi}^{4}$. In this regime, the contribution of NRs is largely suppressed compared with SI DM-nucleon elastic scattering due to the long-range nature of the interaction. Therefore, the results are interpreted for DM mass up to 5 GeV/c2 for SI-LM DM-nucleon elastic scattering.

In addition, we also take into account the fact that DM particle may be stopped or scatter multiple times when passing through Earth’s atmosphere, mantle, and core before reaching the detector (Earth-shielding effect) Emken and Kouvaris (2018); Mahdawi and Farrar (2017); Emken and Kouvaris (2017). If the DM-matter interaction is sufficiently strong, the sensitivity for detecting such DM particles in terrestrial detectors, especially in underground laboratory, can be reduced or even lost totally. Following Armengaud et al. (2019), verne code Kavanagh (2017) is used to calculate the Earth-shielding effect for SI DM-nucleon interaction. A modification of the verne code based on the methodology in Kavanagh (2018) is applied for the calculations of SD and SD-LM DM-nucleon interactions. To account for the Earth-shielding effect for SD DM-nucleon interaction, 14N in the atmosphere and 29Si in Earth’s mantle and core are considered, and their spin expectation values, $\langle S_{n}\rangle$ and $\langle S_{p}\rangle$, are taken from Hooper and McDermott (2018). Both the lower and upper boundaries of excluded parameter space are reported in this work. The lower boundaries are conventionally referred to as upper limits in later context, and are the primary interest of this work. The upper boundaries are dominated by the overburden configuration of the Gran Sasso laboratory which hosts the detector.

No significant excess is observed above the background expectation in the search using the S1-S2 data. Fig. 5 shows the 90% confidence-level (C.L.) limits on the SI and SD (proton-only and neutron-only cases) DM-nucleon interaction cross-section using signal models from MIGD and BREM with masses from about 85 MeV/c2 to 2 GeV/c2, and Fig. 6 shows the 90% C.L. limits on the SI-LM DM-nucleon interaction cross-section with masses from about 100 MeV/c2 to 5 GeV/c2. The sensitivity contours for the results derived using S2-only data are not shown because of the conservativeness of the background model. The upper limits derived using the S1-S2 data deviate from the median sensitivity by about 1-2 $\sigma$ due to the under-fluctuation of the ER background in the low energy region. As described in Aprile et al. (2019c), the jumps in the S2-only limits are originating from the changes in the observed number of events due to the mass-dependent S2 ROIs. The results, by searching for ER signals induced by MIGD, give the best lower exclusion boundaries on SI, SD proton-only, SD neutron-only, and SI-LM DM-nucleon interaction cross-section for mass below about 1.8, 2.0, 2.0, and 4.0 GeV/c2, respectively as compared to previous experiments Akerib et al. (2019); Armengaud et al. (2019); Liu et al. (2019); Abdelhameed et al. (2017); Arnaud et al. (2018); Agnese et al. (2016); Agnes et al. (2018); Abdelhameed et al. (2019); Agnese et al. (2018). The upper limits derived from the S1-S2 data become comparable with those from the S2-only data at $\sim$ GeV/c2 since the efficiency of the S1-S2 data to DM signals with mass of $\sim$ GeV/c2 becomes sufficiently high. However, the upper limits derived from the S1-S2 data do not provide significantly better constraints than those from the S2-only data for DM masses larger than 1 GeV/c2, because both data are dominated by the ER background, which is very similar to the expected DM signal.

In summary, we performed a search for LDM by probing ER signals induced by MIGD and BREM, using data from the XENON1T experiment. These new detection channels significantly enhance the sensitivity of LXe experiments to masses unreachable in the standard NR searches. We set the most stringent upper limits on the SI and SD DM-nucleon interaction cross-sections for masses below 1.8 GeV/c2 and 2 GeV/c2, respectively. Together with the standard NR search Aprile et al. (2018), XENON1T results have reached unprecedented sensitivities to both low-mass (sub-GeV/c2) and high-mass (GeV/c2 - TeV/c2) DM. With the upgrade to XENONnT, we expect to further improve the sensitivity to DM with masses ranging from about 85 MeV/c2 to beyond a TeV/c2.

The authors would like to thank Masahiro Ibe and Yutaro Shoji for helpful discussions on MIGD and for providing us with the code for calculating the rate of MIGD radiation in xenon. We would like to thank Bradley Kavanagh for helpful discussion on the Earth-shielding effect. We gratefully acknowledge support from the National Science Foundation, Swiss National Science Foundation, German Ministry for Education and Research, Max Planck Gesellschaft, Deutsche Forschungsgemeinschaft, Netherlands Organisation for Scientific Research (NWO), Netherlands eScience Center (NLeSC) with the support of the SURF Cooperative, Weizmann Institute of Science, Israeli Centers Of Research Excellence (I-CORE), Pazy-Vatat, Fundacao para a Ciencia e a Tecnologia, Region des Pays de la Loire, Knut and Alice Wallenberg Foundation, Kavli Foundation, and Istituto Nazionale di Fisica Nucleare. This project has received funding or support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreements No. 690575 and No. 674896, respectively. Data processing is performed using infrastructures from the Open Science Grid and European Grid Initiative. We are grateful to Laboratori Nazionali del Gran Sasso for hosting and supporting the XENON project.