Direct Detection of sub-GeV Dark Matter with Electrons from Nuclear Scattering1footnote 11footnote 1This article is registered under preprint number: KCL-PH-TH/2017-54, TTK-17-43

Direct Detection of sub-GeV Dark Matter
with Electrons from Nuclear Scattering111This article is registered under preprint number: KCL-PH-TH/2017-54, TTK-17-43

Matthew J. Dolan Felix Kahlhoefer Christopher McCabe ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, University of Melbourne, 3010, Australia Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, D-52056 Aachen, Germany Department of Physics, King’s College London, Strand, London, WC2R 2LS, United Kingdom

Dark matter (DM) particles with mass in the MeV to GeV range are an attractive alternative to heavier weakly-interacting massive particles. Direct detection of such light particles is challenging because the energy transfer in DM-nucleus interactions is small. If the recoiling atom is ionised, however, the resulting electron may be detected even if the nuclear recoil is unobservable. Considering the case of dual-phase xenon detectors, we demonstrate that including electron emission from nuclear recoils significantly enhances their sensitivity to sub-GeV DM particles. Existing experiments like LUX set world-leading limits on the DM-nucleon scattering cross section, and future experiments like LZ may probe the cross section relevant for thermal freeze-out. The proposed strategy is complementary to experiments looking for DM-electron scattering in scenarios where the DM particles couple with similar strength to protons and electrons.

Beyond Standard Model, sub-GeV dark matter, direct detection, Migdal effect

1 Introduction

In spite of spectacular improvements in sensitivity over recent years, dark matter (DM) direct detection experiments have so far failed to observe conclusive evidence of a DM signal. While this may be interpreted as a failure of the paradigm of weakly-interacting massive particles (WIMPs) Duerr et al. (2016); Escudero et al. (2016); Arcadi et al. (2017), an alternative explanation is that WIMPs are somewhat lighter than usually assumed and that the energy they can deposit in a detector is below current experimental thresholds (see ref. Battaglieri et al. (2017) for a recent review). This consideration has led to increasing interest in experiments with lower thresholds for nuclear recoils, such as CRESST Angloher et al. (2016, 2015, 2017); Petricca et al. (2017), DAMIC Aguilar-Arevalo et al. (2016), EDELWEISS Arnaud et al. (2017), NEWS-G Arnaud et al. (2018) or SuperCDMS Agnese et al. (2017), in experiments sensitive for electron recoils Essig et al. (2012); Graham et al. (2012); Essig et al. (2016, 2017a), or indeed in the development of completely novel types of detectors Guo and McKinsey (2013); Hochberg et al. (2016a, b, c); Schutz and Zurek (2016); Carter et al. (2017); Hochberg et al. (2017a); Derenzo et al. (2017); Hochberg et al. (2017b); Essig et al. (2017b); Knapen et al. (2017a); Bunting et al. (2017); Budnik et al. (2017); Tiffenberg et al. (2017); Maris et al. (2017); Hochberg et al. (2017c).

Direct detection experiments based on liquid xenon, on the other hand, are usually believed to be insensitive to nuclear recoils with sub-keV energy, corresponding to sub-GeV DM particles. This conclusion is based on the implicit assumption that the electron cloud of the recoiling atom instantly follows the nucleus, so that ionisations and excitations are only produced subsequently, as the recoiling atom collides with surrounding xenon atoms. The resulting primary scintillation (S1) signal is then too small to be observable.

Figure 1: Illustration of electron emission from nuclear recoils. If a DM particle scatters off a nucleus (panel 1), we can assume that immediately after the collision the nucleus moves relative to the surrounding electron cloud (panel 2). The electrons eventually catch up with the nucleus, but individual electrons may be left behind and are emitted, leading to ionisation of the recoiling atom (panel 3).

From neutron-nucleus scattering experiments it is however well-known that the sudden acceleration of a nucleus after a collision can lead to excitations and ionisation of atomic electrons (see e.g. refs. Ruijgrok et al. (1983); Vegh (1983); Baur et al. (1983); Pindzola et al. (2014)). This effect, which is illustrated in figure 1, can lead to both highly-energetic -rays and ionisation electrons being produced from the primary interaction. In this case, the S1 signal is much larger and the sensitivity of dual-phase xenon detectors is significantly enhanced. The case of -ray emission was investigated in detail in ref. Kouvaris and Pradler (2017). Ref. McCabe (2017) furthermore showed that dual-phase xenon detectors such as LUX Akerib et al. (2017a), XENON1T Aprile et al. (2017) or PandaX Cui et al. (2017) can distinguish such events from the bulk of electron recoil events, which constitute the main background.

Recently, ref. Ibe et al. (2017) pointed out that the probability to ionise a recoiling atom is in fact orders of magnitude larger than the probability to obtain a -ray, since in contrast to photons there is no momentum suppression for the emission of low-energy electrons. This effect has been named “Migdal effect” in the DM literature Vergados and Ejiri (2005); Moustakidis et al. (2005); Bernabei et al. (2007), as the calculation makes use of the Migdal approximation Landau and Lifshitz (1965) that the electron cloud of the incident atom does not change during the nuclear recoil induced by the DM interaction (see figure 1). In the frame of the atom, this results in a simultaneous boost for all electrons, which can lead to excitation or ionisation of electrons.

In this letter, we further explore the formalism developed in ref. Ibe et al. (2017) and apply it to the case of dual-phase xenon detectors. We find that the sensitivity of this type of experiment in the sub-GeV mass range is significantly enhanced. By reinterpreting existing data from the LUX experiment, we obtain the strongest limit on DM with mass between  GeV and comparable limits to CRESST-III Petricca et al. (2017) between  GeV. A second central observation of our letter is that in scenarios where the DM couples with equal strength to electrons and protons (as in the case of interactions mediated by a dark photon with kinetic mixing Foot (2004); Feng et al. (2009)), experiments may be more sensitive to ionisation electrons resulting from nuclear recoils than from electron recoils. As we will demonstrate, the search strategy considered in this paper can therefore probe unexplored parameter regions of dark photon models and future experiments may be sensitive to parameter space compatible with thermal freeze-out.

This letter is structured as follows. In section 2 we review the central aspects of the Migdal effect and collect the relevant formulae from the literature. In section 3 we discuss the resulting signatures in dual-phase xenon detectors, considering the LUX experiment for concreteness. In section 4 we present the resulting bounds on the parameter space of two interesting models of low-mass DM. We first consider the case of a scalar mediator, which couples to Standard Model (SM) particles proportional to their mass, and then focus on the case of a vector mediator, which has couplings to SM particles proportional to their electric charge. Our conclusions are presented in section 5.

2 Ionisation electrons from nuclear recoils

In this section we summarize the key results from ref. Ibe et al. (2017), which are needed for calculating the signatures of low-mass DM scattering on nuclei in direct detection experiments. The differential event rate for DM-nucleus scattering with respect to the nuclear recoil energy and the DM velocity is given by


where denotes the local DM density, the DM-nucleus scattering cross section222We have absorbed the coherent enhancement factor into our definition of ., the DM mass, the DM-nucleus reduced mass and the DM speed distribution in the laboratory frame McCabe (2014). We neglect nuclear form factors since we are only interested in small momentum transfers. The differential event rate for a nuclear recoil of energy to be accompanied by an ionisation electron with energy is


where the transition rate is given by


In this expression and denote the initial quantum numbers of the electron that is being emitted, is the momentum of each electron in the rest frame of the nucleus immediately after the scattering process, and the function quantifies the probability to emit an electron with final kinetic energy . We can make the dependence of on explicit by writing


where is a fixed reference velocity. The functions depend on the target material under consideration and have been calculated for a range of elements relevant for direct detection experiments in ref. Ibe et al. (2017) taking .

If the emitted electron comes from an inner orbital, the remaining ion will be in an excited state. To return to the ground state, further electronic energy will be released in the form of photons or additional ionisation electrons. The total electronic energy deposited in the detector is hence approximately given by


where is the (positive) binding energy of the electron before emission and we assume that the binding energy of the electrons in the outermost orbitals are negligible. The nuclear recoil can also lead to the atom being in double or higher states of ionisation. Existing results for the helium atom show that double ionisation is less likely than single ionisation Feist et al. (2008); Liertzer et al. (2012). Accordingly, we neglect this possibility in this work.

We integrate eq. (2) over both the nuclear recoil energy and the DM velocity to calculate the energy spectrum. In doing so, we need to ensure that we include only those combinations of , and that satisfy energy and momentum conservation. The resulting calculation is identical to the case of inelastic DM Tucker-Smith and Weiner (2001), with the DM mass splitting being replaced by the total electronic energy .333We neglect the difference in mass between the original atom and the recoiling excited state. We therefore find


The maximum electronic and nuclear recoil energy for a given DM mass are given by


For , (and hence ), we generically find . For concreteness, for and (the approximate xenon atom mass), we find while . The electronic energy is therefore much easier to detect than the nuclear recoil energy.

3 Sensitivity of dual-phase xenon detectors

Having obtained the relevant formulae for the distribution of electronic and nuclear recoil energy at the interaction point where the DM-nucleus scattering occurs, we now convert these energies into observables accessible for direct detection experiments. The focus of this discussion will be on dual-phase xenon detectors, but we note that the dominance of the electronic energy  resulting from the Migdal effect is not limited to xenon. These detectors convert the atomic excitations and ionisations at the interaction point into a primary (S1) and a secondary (S2) scintillation signal Chepel and Araujo (2013). A specific detector can be characterized by two functions: quantifies the probability to obtain specific S1 and S2 values for given and ; and quantifies the probability that a signal with given S1 and S2 will be detected and will satisfy all selection cuts. Using these two functions, we can write


where we have now expressed the differential event rate from eq. (2) in terms of .

As we have seen above, for sub-GeV DM particles, nuclear recoil energies are below  keV. The scintillation and ionisation yield for such small energies have not yet been measured in liquid xenon, but theoretical arguments predict the resulting signals to be very small Sorensen (2015). We conservatively neglect this contribution and assume that only electronic energy contributes to the S1 and S2 signals, such that and the integration over in eq. (8) can be immediately performed.

Refs. McCabe (2016, 2017) discuss how we determine and for dual-phase xenon experiments using a Monte Carlo simulation of the detector based on the Noble Element Simulation Technique (NEST) Szydagis et al. (2011, 2013); Lenardo et al. (2015). For given , the mean S1 and S2 signals can be written as and , respectively, where are detector-dependent gain factors and and are properties of liquid xenon determined from calibration data Akerib et al. (2016a); Goetzke et al. (2017); Boulton et al. (2017); Akerib et al. (2017b). The Monte Carlo simulation then determines the probability for fluctuations in the number of excited and ionised atoms produced initially, recombination fluctuations as well as finite extraction and detection efficiencies Akerib et al. (2017c).

As pointed out in ref. McCabe (2017), these fluctuations play a crucial role for the sensitivity of dual-phase xenon detectors to sub-GeV DM particles. The reason is that the mean S1 signal expected from the scattering of such light DM particles lies below the detection threshold of typical detectors. Thus, the signal can only be observed in the case of an upward fluctuation of the S1 signal. Moreover, events with unusually large S1 signal have the advantage that they do not look like typical electronic recoils, which are the dominant source of background in these detectors. Instead, they look more similar to nuclear recoils, which have a smaller ratio of S2/S1 than electron recoils. This feature makes it possible to distinguish between the expected signal and the main sources of backgrounds.

We focus on the LUX experiment Akerib et al. (2016b, 2017a) and, following ref. McCabe (2017), implement two different approaches to estimate the sensitivity of the full LUX data set to sub-GeV DM, adopting the astrophysical parameters used in ref. McCabe (2017) for our analysis.444Although XENON1T and PandaX have larger exposures than LUX, the analysis cuts and thresholds mean that LUX is marginally more sensitive at low energies. For the cut-and-count (CC) approach we determine the region in S1-S2 space that contains 90% of the DM events passing all cuts and count the number of observed events in this region. A limit can then be set by assuming all these events to be signal events and calculating a Poisson upper bound on the expected number of events (at 90% confidence level). A more powerful approach is the profile likelihood method (PLR), which takes into account the likelihood for signal and background at each observed event Barlow (1990); Cowan et al. (2011). In contrast to the CC approach, the PLR method requires a background model. Our model consists of two components: a component flat in energy from electronic recoils and a component from the decays of Xe. Further details are given in ref. McCabe (2017).

We also estimate the expected sensitivity of the LZ experiment Mount et al. (2017), and note that a similar sensitivity should be expected with XENONnT Aprile et al. (2016a). We show results assuming 1000 days of data taking and a 5.6 tonne target volume for the ‘baseline’ and ‘goal’ parameter sets discussed in Mount et al. (2017). The ‘goal’ parameter set results in a higher sensitivity primarily owing to a higher value of , a lower trigger threshold and a lower radon background rate.

4 Results

Figure 2: Exclusion limits (solid lines) and projected sensitivities (dotted lines) for sub-GeV DM. The bounds resulting from our analysis of electron emission after nuclear recoils in the LUX detector are shown in blue (using two different statistical methods). The left panel considers the case of a scalar mediator (couplings proportional to mass), the right panel considers the case of a vector mediator (couplings proportional to charge). In the latter case, there are constraints both from experiments looking for nuclear recoils (NR) and from experiments looking for electron recoils (ER). The bounds from the CRESST surface run, LUX NR+ and LUX 2013 (CC) as well as the projection for LZ (baseline) have been omitted in the right panel for clarity. We also show the parameter combinations that yield the observed DM relic abundance for one specific model (complex scalar DM). See text for details.

We present the results of our analysis for DM particles interacting with nuclei via two different types of mediators: scalars and vectors. The difference between these two cases is the way in which the mediator couples to SM particles Kaplinghat et al. (2014). For a scalar mediator these couplings generically arise from mixing with the SM Higgs boson, so that the mediator couples to SM particles proportional to their mass. This means in particular that the DM-nucleus cross section for nuclei with mass number  is enhanced by a coherence factor, , where and are the DM-proton cross section and reduced mass, respectively. Furthermore, couplings to electrons are negligible. Models with sub-GeV DM particles and (light) scalar mediators have for example been considered recently in the context of self-interacting DM Kahlhoefer et al. (2017a, b).

For a vector mediator, on the other hand, couplings to SM particles arise from kinetic mixing with the SM photon. As a result, couplings to SM particles are expected to be proportional to their electromagnetic charge, leading to a enhancement for scattering on nuclei with charge number , i.e. , and comparable couplings to protons and electrons. These so-called dark photon models have been studied extensively in the literature, and there has been much work on the possibility to search for them in direct detection experiments An et al. (2015); Essig et al. (2016, 2017a), at low-energy colliders Essig et al. (2013); Lees et al. (2017) and at beam-dump experiments Andreas et al. (2012); Izaguirre et al. (2013); Batell et al. (2014).

We emphasize that even if the couplings of the DM particle to protons and electrons are comparable, the corresponding scattering cross sections are not. The reason is that the scattering cross section is proportional not only to the coupling squared, but also to the reduced mass squared Essig et al. (2012). For sub-GeV DM particles, one finds and , so scattering on nucleons is enhanced by a factor . For heavy atoms, the coherence factor for the nucleus leads to an additional enhancement in spite of the larger number density of electrons. Thus, the probability for DM particles in the mass range 0.1–1 GeV to scatter on nuclei is many orders of magnitude larger than the probability to scatter on electrons. Most of these scattering processes will be unobserved, but even a small fraction of events with ionisation electrons are sufficient to obtain strong constraints.

Our results are summarized in figure 2, focusing on the mass range . The left panel shows the case of a scalar mediator (Higgs mixing), the right panel the case of a vector mediator (kinetic mixing). An additional assumption in both plots is that the mediator is sufficiently heavy that the scattering can be described by contact interactions, which is the case for  Kahlhoefer et al. (2017b). No further assumptions are needed to compare the constraints from different direct detection experiments looking for nuclear or electron recoils.555We do not show constraints from hidden photon searches at BaBar Lees et al. (2017), which require the assumption of a specific ratio between the DM mass and the mediator mass. Projected sensitivities are taken from ref. Agnese et al. (2017) for SuperCDMS-Ge, from ref. Kahlhoefer et al. (2017b) for CRESST-III and from ref. Battaglieri et al. (2017) for SENSEI, DAMIC and SuperCDMS-Si.

We find that in both of the cases considered, the sensitivity of current dual-phase xenon detectors for sub-GeV DM can compete with other existing and proposed strategies. In the case of a scalar mediator, only experiments sensitive to nuclear recoils give relevant constraints. We find that in this case the exclusion limit obtained from LUX is comparable to the one from the first analysis of CRESST-III Petricca et al. (2017) for while for smaller masses, LUX gives the world-leading limit. In particular, we significantly improve the LUX bound obtained from -rays emitted in nuclear scattering processes McCabe (2017), and from the CRESST 2017 surface run Angloher et al. (2017).

In the case of vector mediators, LUX constraints are slightly weakened relative to the ones from CRESST due to a smaller difference in the enhancement factors. In addition, there are now strong constraints from searches for electron scattering in XENON100 Aprile et al. (2016b); Essig et al. (2017a). Nevertheless, we observe that searches for electrons emitted for nuclear recoils in LUX set competitive bounds for DM masses around 200-300 MeV. LZ can significantly improve upon these bounds in the future and provide complementary constraints to alternative electron-recoil strategies proposed to search for sub-GeV DM Battaglieri et al. (2017).

Lastly, to put our results into context, it is instructive to compare the sensitivity of direct detection experiments to the parameter regions where the DM particle can be a thermal relic that obtains its abundance via the freeze-out mechanism. Such a comparison is necessarily model dependent, but the number of possibilities is limited by strong constraints on sub-GeV WIMPs Boehm et al. (2013); Knapen et al. (2017b). Here we focus on one viable scenario, namely a vector mediator and complex scalar DM Essig et al. (2016). If the mediator mass is sufficiently large, , the DM relic abundance probes the same combination of parameters as direct detection experiments. In other words, for each value of there is a unique value of  corresponding to the observed relic abundance Ade et al. (2016). The scattering cross sections obtained in this way are indicated by the grey band in the right panel of figure 2. We observe that current bounds exclude the simplest realization of thermal freeze-out in the model that we consider for , while the next generation of direct detection experiments is expected to probe the relevant cross sections across the entire mass range of interest.

5 Conclusions

The sub-GeV mass range represents a new frontier in the search for particle DM. While direct detection experiments are often considered insensitive to nuclear recoils induced by scattering of light DM particles, we have shown that electrons emitted from recoiling atoms significantly boost the signal, leading to an enhanced sensitivity for, and new bounds on, the DM-nucleus scattering cross-section. In dual-phase xenon detectors the sensitivity to these signals is further enhanced by the possibility of upward fluctuations in the S1 signal, leading to the possibility to distinguish between signal and background.

In the present work we have focused on the LUX experiment as an example of existing technology and the LZ experiment as illustration of the power of next-generation experiments. Nevertheless, the same physics will be relevant for other direct detection experiments sensitive to electronic recoils. Moreover, our results may also be applied to coherent neutrino-nucleus scattering Akimov et al. (2017); Ibe et al. (2017) and to the interpretation of calibration data based on neutron-nucleus scattering Verbus et al. (2017); Barbeau et al. (2007).

In conclusion, we emphasize that direct detection experiments are only just beginning to probe the interesting parameter space for sub-GeV WIMPs. Significant improvements of sensitivity are required in order to probe the cross sections favoured by the freeze-out mechanism. To achieve this goal we need both a dedicated experimental effort to build new types of direct detection experiments with very low thresholds, and further theoretical developments to better understand the ways in which DM particles can lead to observable signals in conventional direct detection experiments.


We thank Josef Pradler and Tien-Tien Yu for discussions and Florian Reindl for correspondence. MJD is supported by the Australian Research Council and thanks King’s College London for hospitality during the commencement of this project. FK is supported by the DFG Emmy Noether Grant No. KA 4662/1-1. CM is supported by the Science and Technology Facilities Council (STFC) Grant ST/N004663/1.



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