There are currently several existing and proposed experiments designed to probe sub-GeV dark matter (DM) using electron ionization in various materials. The projected signal rates for these experiments assume that this ionization yield arises only from DM scattering directly off electron targets, ignoring secondary ionization contributions from DM scattering off nuclear targets. We investigate the validity of this assumption and show that if sub-GeV DM couples with comparable strength to both protons and electrons, as would be the case for a dark photon mediator, the ionization signal from atomic scattering via the Migdal effect scales with the atomic number $Z$ and 3-momentum transfer $\mathbf{q}$ as $Z^2 \mathbf{q}^2$. The result is that the Migdal effect is always subdominant to electron scattering when the mediator is light, but that Migdal-induced ionization can dominate over electron scattering for heavy mediators and DM masses in the hundreds of MeV range. We put these two ionization processes on identical theoretical footing, address some theoretical uncertainties in the choice of atomic wavefunctions used to compute rates, and discuss the implications for DM scenarios where the Migdal process dominates, including for XENON10, XENON100, and the recent XENON1T results on light DM scattering.
Motivated by the current strong constraints on the spin-independent dark matter (DM)-nucleus scattering, we investigate the spin-dependent (SD) interactions of the light Majorana DM with the nucleus mediated by an axial-vector boson. Due to the small nucleus recoil energy, the ionization signals have now been used to probe the light dark matter particles in direct detection experiments. With the existing ionization data, we derive the exclusion limits on the SD DM-nucleus scattering through Migdal effect in the MeV-GeV DM mass range. It is found that the lower limit of the DM mass can reach ab…
The Migdal effect in Semiconductors for the Effective Field Theory of Dark Matter Direct Detection
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Walter Burke Institute for Theoretical Physics, California Institute of Technology（加州理工学院沃尔特·伯克理论物理研究所）；C.N. Yang Institute for Theoretical Physics, Stony Brook University（纽约州立大学石溪分校陈省身理论物理研究所）；Physics and Astronomy Department, Stony Brook University（纽约州立大学石溪分校物理与天文系）
The search for dark matter weakly interacting massive particles with noble liquids has probed masses down and below a GeV/c^2. The ultimate limit is represented by the experimental threshold on the energy transfer to the nuclear recoil. Currently, the experimental sensitivity has reached a threshold equivalent to a few ionization electrons. In these conditions, the contribution of a Bremsstrahlung photon or a so-called Migdal electron due to the sudden acceleration of a nucleus after a collision might be sizable. In the present work, we use a Bayesian approach to study how these effects can be…
We consider searches for the inelastic scattering of low-mass dark matter at direct detection experiments, using the Migdal effect. We find that there are degeneracies between the dark matter mass and the mass splitting that are difficult to break. Using XENON1T data we set bounds on a previously unexplored region of the inelastic dark matter parameter space. For the case of exothermic scattering, we find that the Migdal effect allows xenon-based detectors to have sensitivity to dark matter with ${\cal O}(\mathrm{MeV})$ mass, far beyond what can be obtained with nuclear recoils alone.
Due to the low nuclear recoils, sub-GeV dark matter (DM) is usually beyond the sensitivity of the conventional DM direct detection experiments. The boosted and Migdal scattering mechanisms have been proposed as two new complementary avenues to search for light DM. In this work, we consider the momentum-transfer effect in the DM-nucleus scattering to derive the new bounds on sub-GeV DM for these two scenarios. We show that such an effect is sizable so that the existing bounds on the DM-nucleus scattering cross section can be improved significantly.
Dark matter scattering off a nucleus has a small probability of inducing an observable ionization through the inelastic excitation of an electron, called the Migdal effect. We use an effective field theory to extend the computation of the Migdal effect in semiconductors to regions of small momentum transfer to the nucleus, where the final state of the nucleus is no longer well described by a plane wave. Our analytical result can be fully quantified by the measurable dynamic structure factor of the semiconductor, which accounts for the vibrational degrees of freedom (phonons) in a crystal. We s…
Large composite dark matter states source a scalar binding field that, when coupled to Standard Model nucleons, provides a potential under which nuclei recoil and accelerate to energies capable of ionization, radiation, and thermonuclear reactions. We show that these dynamics are detectable for nucleon couplings as small as $g_n \sim 10^{-17}$ at dark matter experiments, where the greatest sensitivity is attained by considering the Migdal effect. We also explore Type-Ia supernovae and planetary heating as possible means to discover this type of dark matter.
The Migdal effect has received much attention from the dark matter direct detection community, in particular due to its power in setting limits on sub-GeV particle dark matter. Currently, there is no experimental confirmation of the Migdal effect through nuclear scattering using Standard Model probes. In this work, we extend existing calculations of the Migdal effect to the case of neutron-nucleus scattering, with a particular focus on neutron scattering angle distributions in silicon. We identify kinematic regimes wherein the assumptions present in current calculations of the Migdal effect ho…
The XENON1T experiment has recently announced the observation of an excess in electron recoil events at energy range of $1-7$ keV with a $3.5~σ$ signal significance over the Standard Model prediction. In this letter we sketch the prospects of explaining such an excess from Migdal ionization events with below threshold nuclear recoil energies. Interestingly, these are expected to show signal events in the ballpark energy scale of the observed excess. We demonstrate that the observed signal can be reproduced through the Migdal effect by an $\mathcal{O}(1)$ GeV neutron-philic dark matter having a…
The Migdal effect in a dark-matter-nucleus scattering extends the direct search experiments to the sub-GeV mass region through electron ionization with sub-keV detection thresholds. In this paper, we derive a rigorous and model-independent "Migdal-photoabsorption" relation that links the sub-keV Migdal process to photoabsorption. This relation is free of theoretical uncertainties as it only requires the photoabsorption cross section as the experimental input. Validity of this relation is explicitly checked in the case of xenon with an state-of-the-arts atomic calculation that is well-benchmark…
Energy and Angular-Momentum Redistribution in Hydrogen Migdal Ionization
School of Physics, Yantai University（烟台大学物理学院）；Department of Physics and Institute of Theoretical Physics, Nanjing Normal University（南京师范大学物理科学与技术学院/理论物理研究所）；College of Science, China University of Petroleum (East China)（中国石油大学（华东）理学院）
A key strategy for the direct detection of sub-GeV dark matter is to search for small ionization signals. These can arise from dark matter-electron scattering or when the dark matter-nucleus scattering process is accompanied by a "Migdal" electron. We show that the theoretical descriptions of both processes are closely related, which allows for a principal mapping between dark matter-electron and dark matter-nucleus scattering rates once the dark matter interactions with matter are specified. We explore this parametric relationship for noble-liquid targets and, for the first time, provide an e…
When a nucleus in an atom undergoes a collision, there is a small probability to inelastically excite an electron as a result of the Migdal effect. In this Letter, we present a first complete derivation of the Migdal effect from dark matter-nucleus scattering in semiconductors, which also accounts for multiphonon production. The rate can be expressed in terms of the energy loss function of the material, which we calculate with density functional theory (DFT) methods. Because of the smaller gap for electron excitations, we find that the rate for the Migdal effect is much higher in semiconductor…
Dark matter direct detection experiments have limited sensitivity to light dark matter (below a few GeV), due to the challenges of lowering energy thresholds for the detection of nuclear recoil to below $\mathcal{O}(\mathrm{keV})$. While impressive progress has been made on this front, light dark matter remains the least constrained region of dark-matter parameter space. It has been shown that both ionization and excitation due to the Migdal effect and coherently-emitted photon bremsstrahlung from the recoiling atom can provide observable channels for light dark matter that would otherwise hav…
In recent years, dark matter direct detection experiments have spurred interest in the Migdal effect, where it is employed to extend their sensitivity to lower dark matter masses. Given the lack of observation of the Migdal effect, the calculation of the signal is subject to large theoretical uncertainties. It is therefore desirable to attempt a first measurement of the Migdal effect, and to test the theoretical predictions of the Migdal effect for the calibration of the experimental response to a potential dark matter signal. In this work, we explore the feasibility of observing the Migdal ef…
Dark Matter experiments searching for Weakly interacting massive particles (WIMPs) primarily use nuclear recoils (NRs) in their attempt to detect WIMPs. Migdal-induced electronic recoils (ERs) provide additional sensitivity to light Dark Matter with $\mathcal{O}(\text{GeV}/c^2)$ masses. In this work, we use Bayesian inference to find the parameter space where future detectors like XENONnT and SuperCDMS SNOLAB will be able to detect WIMP Dark Matter through NRs, Migdal-induced ERs or a combination thereof. We identify regions where each detector is best at constraining the Dark Matter mass and …
Recent studies have theoretically investigated the atomic excitation and ionization induced by the dark matter (DM)-nucleus scattering, and it is found that the suddenly recoiled atom is much more likely to excite or lose its electrons than expected. Such phenomenon is called the "Migdal effect". In this paper, we extend the established strategy to describe the Migdal effect in isolated atoms to the case in semiconductors under the framework of tight-binding (TB) approximation. Since the localized aspects of electrons are respected in form of the Wannier functions (WFs), the extension of the e…
Recent measurements of the germanium quenching factor deviate significantly from the predictions of the standard Lindhard model for nuclear recoil energies below a keV. This departure may be explained by the Migdal effect in neutron scattering on germanium. We show that the Migdal effect on the quenching factor can mimic the signal of a light Z' or light scalar mediator in coherent elastic neutrino nucleus scattering experiments with reactor antineutrinos. It is imperative that the quenching factor of nuclei with low recoil energy thresholds be precisely measured close to threshold to avoid su…
In this paper, we present a re-analysis of SuperCDMS data using a profile likelihood approach to search for sub-GeV dark matter particles (DM) through two inelastic scattering channels: bremsstrahlung radiation and the Migdal effect. By considering possible inelastic scattering channels, experimental sensitivity can be extended to DM masses that would otherwise be undetectable through the DM-nucleon elastic scattering channel, given the energy threshold of current experiments. We exclude DM masses down to $220~\textrm{MeV}/c^2$ at $2.7 \times 10^{-30}~\textrm{cm}^2$ via the bremsstrahlung chan…
The scattering of neutral particles by an atomic nucleus can lead to electronic ionisation and excitation through a process known as the Migdal effect. We revisit and improve upon previous calculations of the Migdal effect, using the Dirac-Hartree-Fock method to calculate the atomic wavefunctions. Our methods do not rely on the use of the dipole approximation, allowing us to present robust results for higher nuclear recoil velocities than was previously possible. Our calculations provide the theoretical foundations for future measurements of the Migdal effect using neutron sources, and searche…
The Migdal effect inside detectors provides a new possibility of probing the sub-GeV dark matter (DM) particles. While there has been well-established methods treating the Migdal effect in isolated atoms, a coherent and complete description of the valence electrons in semiconductor is still absent. The bremstrahlung-like approach is a promising attempt, but it turns invalid for DM masses below a few tens of MeV. In this paper, we lay out a framework where phonon is chosen as an effective degree of freedom to describe the Migdal effect in semiconductors. In this picture, a valence electron is e…
Nuclear scattering events with large momentum transfer in atomic, molecular, or solid-state systems may result in electronic excitations. In the context of atomic scattering by dark matter (DM), this is known as the Migdal effect, but the same effect has also been studied in molecules in the chemistry and neutron scattering literature. Here we present two distinct Migdal-like effects from DM scattering in molecules, which we collectively refer to as the molecular Migdal effect: a center-of-mass recoil, equivalent to the standard Migdal treatment, and a non-adiabatic coupling resulting from cor…
Recent theoretical studies have suggested that the suddenly recoiled atom struck by dark matter (DM) particle is much more likely to excite or lose its electrons than expected. Such Migdal effect provides a new avenue for exploring the sub-GeV DM particles. There have been various attempts to describe the Migdal effect in liquids and semiconductor targets. In this paper we incorporate the treatment of the bremsstrahlung process and the electronic many-body effects to give a full description of the Migdal effect in bulk semiconductor targets diamond and silicon. Compared with the results obtain…
Using the relativistic Hartree-Fock approximation, we calculate the rates of atomic ionization by absorption of pseudoscalar particles in the mass range from 10 to $\sim$ 50 keV. We present numerical results for atoms relevant for the direct dark matter searches (e.g. Ar, Ge, I and Xe), as well as the analytical formula which fits numerical calculations with few per cent accuracy and may be used for multi-electron atoms, molecules and condensed matter systems.
In warm dark matter scenarios structure formation is suppressed on small scales with respect to the cold dark matter case, reducing the number of low-mass halos and the fraction of ionized gas at high redshifts and thus, delaying reionization. This has an impact on the ionization history of the Universe and measurements of the optical depth to reionization, of the evolution of the global fraction of ionized gas and of the thermal history of the intergalactic medium, can be used to set constraints on the mass of the dark matter particle. However, the suppression of the fraction of ionized mediu…
We present a new public Python package, DarkHistory, for computing the effects of dark matter annihilation and decay on the temperature and ionization history of the early universe. DarkHistory simultaneously solves for the evolution of the free electron fraction and gas temperature, and for the cooling of annihilation/decay products and the secondary particles produced in the process. Consequently, we can self-consistently include the effects of both astrophysical and exotic sources of heating and ionization, and automatically take into account backreaction, where modifications to the ionizat…
We propose a new candidate of GeV scale inelastic dark matter (DM). Our construction has an anomaly-free $U(1)_X^{}$ gauge group with dark photon mediator, and can realize either scalar or fermionic inelastic DM. It is highly predictive and testable. We study the scattering rate of light inelastic DM with electrons in the XENON1T experiment and with nuclei in the XENON1T, CRESST-III, CDEX-1B and DarkSide-50 experiments. We resolve the recent XENON1T anomaly via electron recoil detection. Combining the XENON1T constraints from both electron recoils and nuclear recoils (including Migdal effect),…
We report a measurement of the ionization efficiency of silicon nuclei recoiling with sub-keV kinetic energy in the bulk silicon of a charge-coupled device (CCD). Nuclear recoils are produced by low-energy neutrons ($<$24 keV) from a $^{124}$Sb-$^{9}$Be photoneutron source, and their ionization signal is measured down to 60 eV electron equivalent. This energy range, previously unexplored, is relevant for the detection of low-mass dark matter particles. The measured efficiency is found to deviate from the extrapolation to low energies of the Lindhard model. This measurement also demonstrates th…
Direct detection strategies are proposed for dark matter particles with MeV to GeV mass. In this largely unexplored mass range, dark matter scattering with electrons can cause single-electron ionization signals, which are detectable with current technology. Ultraviolet photons, individual ions, and heat are interesting alternative signals. Focusing on ionization, we calculate the expected dark matter scattering rates and estimate the sensitivity of possible experiments. Backgrounds that may be relevant are discussed. Theoretically interesting models can be probed with existing technologies, an…
We estimate dark matter density for the Universe with a reheating temperature smaller than the mass of dark matter, assuming dark matter to be a weakly interacting massive particle. During the reheating process, an inflaton decays and releases high-energy particles, which are scattered inelastically by the thermal plasma and emit many particles. Dark matters are produced through these inelastic scattering processes and pair creation processes by high-energy particles. We properly take account of the Landau-Pomeranchuk-Migdal effect on inelastic processes and show that the resultant energy dens…
The ionization yield in the two-phase liquid xenon dark-matter detector has been studied in keV nuclear-recoil energy region. The newly-obtained nuclear quenching as well as the recently-measured average energy required to produce an electron-ion pair are used to calculate the total electric charges produced. To estimate the fraction of the electron charges collected, the Thomas-Imel model is generalized to describing the field dependence for nuclear recoils in liquid xenon. With free parameters fitted to experiment measured 56.5 keV nuclear recoils, the energy dependence of ionization yield f…
In this paper we estimate the event rates of neutralino-nucleus scattering leading to electron emission by the atomic ionization. We find that the branching ratio for detecting electrons vis a vis the traditional neutralino nucleus elastic scattering sensitively depends on the threshold energy. In the case of a light target and a neutralino mass of 100 GeV we estimate it to be around 10 percent assuming a reasonable threshold energy of 250 eV.
Any injection of electromagnetically interacting particles during the cosmic dark ages will lead to increased ionization, heating, production of Lyman-alpha photons and distortions to the energy spectrum of the cosmic microwave background, with potentially observable consequences. In this note we describe numerical results for the low-energy electrons and photons produced by the cooling of particles injected at energies from keV to multi-TeV scales, at arbitrary injection redshifts (but focusing on the post-recombination epoch). We use these data, combined with existing calculations modeling t…
The precision measurements of the cosmic microwave background power spectrum put a strong constraint on the dark matter annihilation cross section since the electromagnetic energy injection by the dark matter annihilation affects the ionization history of the universe. In this paper, we update our previous simulation code for calculating the ionization history with the effect of dark matter annihilation by including Helium interactions and improving the precision of calculations. We give an updated constraint on the annihilation cross section and mass of dark matter using the modified RECFAST …
