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 semiconductors than in atomic targets. Accounting for the Migdal effect in semiconductors can therefore significantly improve the sensitivity of experiments such as DAMIC, SENSEI and SuperCDMS to sub-GeV 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 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 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…
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…
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…
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…
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…
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…
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…
I demonstrate that the Baier-Katkov approach to the Landau-Pomeranchuk-Migdal effect based on their quasiclassical operator method is conceptually wrong in quantum regime of interaction of the charged particles with the medium constituents which takes place for electrons and positrons in real media.
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 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 soft behavior of the bremsstrahlung from a source is discussed in terms of classical transport models and within a non--equilibrium quantum field theory (Schwinger - Kadanoff - Baym - Keldysh) formulation.
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 ato…
The Landau, Pomeranchuk, Migdal (LPM) effect (suppression of the bremsstrahlung from high energy electron due to a multiple scattering of an emitting electron in dense media) is considered for the case when thickness of a target is of the order or less than the formation length of radiation. The effects of the polarization of a medium and transition radiation are taken into account as well. Qualitative picture of the phenomenon is discussed in detail. Comparison with recent experimental data is carried out.
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…
We analyze within the light-cone path integral approach [4] the recent CERN SPS data [19] on the Landau-Pomeranchuk-Migdal effect for photon bremsstrahlung in quantum regime from 149, 207, and 287 GeV electrons. Calculations have been carried out treating accurately the Coulomb effects and including the inelastic processes. Comparison with experiment is performed accounting for multi-photon emission. Our results are in good agreement with the data.
The calculation of the radiative energy loss encountered by a fast charged particle which undergoes multiple scattering is being investigated. A detailed derivation of the Landau-Pomeranchuk-Migdal coherent effect in QED is given, focusing on the specific feature of the Coulomb interaction. As a result the radiation intensity per unit length in the coherent regime is shown to be proportional to $\sqrt ω$ for a photon energy $ω$ times a logarithmic enhancement which is determined exactly.
Soft photon and gluon radiation off a fast quark propagating through nuclear matter is discussed. The close anology between the Landau - Pomeranchuk - Migdal (LPM) effect in QED and the emission of soft gluons, suggested in ref. \cite{BDPS} for ``hot" plasma, is confirmed and the relation between Mueller's approach and traditional calculations is established. It is shown that perturbative QCD can be applied to take into account the LPM coherent suppression both for photon and gluon induced radiation. The formulae for the photon and gluon radiation densities are presented.
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 recent data of the SLAC E-146 collaboration on the Landau-Pomeranchuk-Migdal effect for bremsstrahlung from 8 and 25 GeV electrons are analyzed within a rigorous light-cone path integral approach. Numerical calculations have been carried out treating rigorously the Coulomb effects and including the inelastic processes. Comparison with the experimental data is performed taking into account multi-photon emission and photon absorption. For most of the targets the theoretical predictions are in excellent agreement with the experimental data.
For the first time a rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given. The rate of photon (gluon) radiation by an electron (quark) in medium is expressed through the Green's function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of $e^{+}e^{-}$ pair off an atom, in QCD it is proportional to the cross section of interaction with color centre of the color singlet quark-antiquark-gluon system.
Using the Coulomb correction to the screening angular parameter of the Moliere multiple scattering theory, we obtained analytically and numerically the Coulomb corrections to the parameters of the Migdal LPM effect theory. We showed that these corrections allow to eliminate the discrepancy between the predictions of the LPM effect theory and its measurement at least for high Z targets and also to further improve the agreement between the predictions of the LPM effect theory analogue for a thin layer of matter and experimental data.
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…
I discuss in this lecture how to make a connection between effective chiral Lagrangians -- low-energy effective theory of QCD -- and Landau Fermi liquid theory extended by Migdal to nuclear matter. The practical purpose of such a connection is to provide a link between certain observables in relativistic heavy-ion processes and those in low-energy spectroscopy, giving a new insight into how chiral dynamics manifests itself in nuclear systems.
High-energy Coulomb corrections (CCs) to some quantities of the quantum Migdal theory of the Landau-Pomeranchuk-Migdal (LPM) effect are obtained analytically and numerically for the regimes of small and strong LPM suppression on the basis of a refined Moliere multiple scattering theory. Numerical calculations are presented in the ranges of the nuclear charge number Z of a scatterer from 6 to 92 and the expansion parameter B of Moliere from 4.5 to 8.5. It is shown that the relative CC to the spectral bremsstrahlung rate can reach a value of the order of -19% in the ranges considered and must be…
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…
The cross section of bremsstrahlung from high-energy electron suppressed due to the multiple scattering of an emitting electron in a dense media (the LPM effect) is discussed. Development of the LPM effect theory is outlined. For the target of finite thickness one has to include boundary photon radiation as well as the interference effects. The importance of multiphoton effects is emphasized. Comparison of theory with SLAC data is presented.
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.
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…
A rigorous evaluation of the Landau-Pomeranchuk-Migdal effect for finite-size targets is performed within the path integral approach previously developed in ref. [4]. The bremsstrahlung rate in QED is expressed through a solution of a two-dimensional Schrödinger equation with an imaginary potential. The boundary condition for this solution is formulated in terms of a product of the light-cone electron--photon wave function and the dipole cross section for scattering of $e^{+}e^{-}$ pair off an atom. Numerical calculations are performed for homogeneous and structured targets. Our predictions fo…
The radiation from high-energy electrons is investigated for the case when a target consists of several separated plates. The spectrum of radiation is considered in the region in which the bremsstrahlung is under influence of the multiple scattering of a projectile (the LPM effect), the polarization of a medium and the hard part of the boundary radiation contribute. In this region the general expression for the radiation spectrum is obtained for the $N$-plate target. A qualitative description of the arising interference pattern is given.
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…
It is shown that the high-energy expansion of the scattering amplitude calculated from Feynman diagrams factorizes in such a way that it can be reduced to the eikonalized form up to the terms of inverse power in energy in accordance with results obtained by solving the Klein-Gordon equation. Therefore the two approaches when applied to the suppression of the emission of soft photons by fast charged particles in dense matter should give rise to the same results. A particular limit of thin targets is briefly discussed.
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.
The non-abelian Landau-Pomeranschuk-Migdal (LPM) effect arises from the quantum interference between spatially separated, inelastic radiation processes in matter. A consistent probabilistic implementation of this LPM effect is a prerequisite for extending the use of Monte Carlo (MC) event generators to the simulation of jet-like multi-particle final states in nuclear collisions. Here, we propose a local MC algorithm, which is based solely on relating the LPM effect to the probabilistic concept of formation time for virtual quanta. We demonstrate that this implementation of formation time physi…
Bremsstrahlung of photons from highly relativistic electrons is investigated. The cross section of the processes, which is suppressed due to a multiple scattering of an emitting electron in dense media (LPM effect) and due to photon interaction with electrons of a medium, is calculated with an accuracy up to "next to leading logarithm" and with the Coulomb corrections taken into account. Making allowances for a multiple scattering and a polarization of a medium an analysis of radiation on a target boundary is carried out. The method of consideration of radiation in a thin target under influenc…
We reinterpret Landau-Migdal Fermi-liquid theory of nuclear matter as an effective chiral field theory with a Fermi surface. The effective field theory is formulated in terms of a chiral Lagrangian with its {\it mass and coupling parameters} scaling a la Brown-Rho and with the Landau-Migdal parameters identified as the fixed points of the field theory. We show how this mapping works out for response functions to the EM vector current and then using the same reasoning, make prediction on nuclear axial current, in particular on the enhanced axial-charge transitions in heavy nuclei. We speculate …
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…
A new rigorous light-cone path integral approach to the Landau-Pomeranchuk-Migdal effect in QED and QCD is discussed. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed through the Green's function of a two-dimensional Schrodinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of e+e- pair off an atom, in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a medium constituent. In QED our predictions agree well with the photon s…
In recent studies, the production rate of photons or lepton pairs by a quark gluon plasma has been found to be enhanced due to collinear singularities. This enhancement pattern is very dependent on rather strict collinearity conditions between the photon and the quark momenta. It was estimated by neglecting the collisional width of quasi-particles. In this paper, we study the modifications of this collinear enhancement when we take into account the possibility for the quarks to have a finite mean free path. Assuming a mean free path of order $(g^2T\ln(1/g))^{-1}$, we find that only low invaria…
