R. V. Popov, V. M. Shabaev, D. A. Telnov, I. I. Tupitsyn, I. A. Maltsev, Y. S. Kozhedub, A. I. Bondarev, N. V. Kozin, X. Ma, G. Plunien, T. Stöhlker, D. A. Tumakov, V. A. Zaytsev
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18 pages, 22 figures, 1 table Minor corrections, results unchanged
In slow collisions of two bare nuclei with the total charge number larger than the critical value, $Z_{\rm cr} \approx 173$, the initially neutral vacuum can spontaneously decay into the charged vacuum and two positrons. Detection of the spontaneous emission of positrons would be the direct evidence of this fundamental phenomenon. However, the spontaneous emission is generally masked by the dynamical positron emission, which is induced by a strong time-dependent electric field created by the colliding nuclei. In our recent paper [I.A. Maltsev et al., Phys. Rev. Lett. 123, 113401 (2019)] it has been shown that the spontaneous pair production can be observed via measurements of the pair-production probabilities for a given set of nuclear trajectories. In the present paper, we have significantly advanced this study by exploring additional aspects of the process we are interested in. We calculate the positron energy spectra and find that these spectra can give a clear signature of the transition from the subcritical to the supercritical regime. It is found that focusing on a part of the positron spectrum, which accounts for the energy region where the spontaneously created positrons can contribute, allows to get a much stronger evidence of the transition to the supercritical mode, making it very well pronounced in collisions, for example, of two uranium nuclei. The possibility of extending this study to collisions of bare nuclei with neutral atoms is also considered. The probability of a vacancy in the lowest-energy state of a quasimolecule which is formed in collisions of a bare U nucleus with neutral U and Cm atoms has been calculated. The relatively large values of this probability make such collisions suitable for observing the vacuum decay.
When dense high-energy lepton bunches collide, the beam particles can experience rest-frame electromagnetic fields which greatly exceed the QED critical one. Here it is demonstrated that beamstrahlung efficiently converts lepton energy to high-energy photons in this so-called supercritical QED regime, as the single-photon emission spectrum exhibits a pronounced peak close to the initial lepton energy. It is also shown that the observation of this high-energy peak in the photon spectrum requires one to mitigate multiple photon emissions during the interaction. Otherwise, the photon recoil induc…
The scenario of spontaneous positron emission, caused by the supercritical Coulomb source with charge $Z$ and size $R$, is explored in essentially non-perturbative approach with emphasis on the vacuum energy $\mathcal{E}_{VP}$\footnote{Throughout the paper the abbreviation "VP"\, stands for "vacuum polarization"\,.}, considered as a function of $R$ with fixed $Z>Z_{cr,1}\simeq 170$. It is shown that in the supercritical region the behavior of $\mathcal{E}_{VP}(R)$ turns out to be quite different in dependence on the value of the Coulomb charge $Z$. In particular, spontaneous emission becomes a…
We discuss properties of photons in extremely strong magnetic fields induced by the relativistic heavy-ion collisions. We investigate the vacuum birefringence, the real-photon decay, and the photon splitting which are all forbidden in the ordinary vacuum, but become possible in strong magnetic fields. These effects potentially give rise to anisotropies in photon and dilepton spectra.
We calculate the total scattering cross-section of a dynamical quantum electrically neutral dipole in QED of the infinitely heavy charge and of the infinitely heavy dipole in the leading order in electromagnetic coupling constant.
We compare the use of the Coulomb gauge in finite temperature QED with a recently proposed prescription for covariant gauges, in which only the transverse photon degrees of freedom are thermalized. Using the Landau rule as a guide, we clarify the relation between the retarded electron self-energy and the elements of the self-energy matrix in the real-time formulation of . The general results are illustrated by means of the one-loop expressions for the electron self-energy in a QED plasma.
Creation of charged fermion pair from a vacuum in the so-called supercritical Coulomb potential is examined for the case when created pair moves in one plane. In which case the quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with a Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states…
The potential energy of a static charge distribution on a lattice is rigorously computed in the standard compact quantum electrodynamic model. The method used follows closely that of Weyl for ordinary quantum electrodynamics in continuous space-time. The potential energy of the static charge distribution is independent of temperature and can be calculated from the lattice version of Poisson's equation. It is the usual Coulomb potential.
An expression for the density of a planar induced vacuum charge is obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in this potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. The behavior of the obtained vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulo…
We study the vacuum polarization of planar charged Dirac fermions by a strong Coulomb potential. Induced vacuum charge density is calculated and analyzed at the subcritical and supercritical Coulomb potentials for massless and massive fermions. For the massless case the induced vacuum charge density is localized at the origin when the Coulomb center charge is subcritical while it has a power-law tail when the Coulomb center charge is supercritical. The finite mass contribution into the induced charge due to the vacuum polarization is small and insignificantly distorts the Coulomb potential onl…
It is conjectured that all perturbative approaches to quantum electrodynamics (QED) break down in the collision of a high-energy electron beam with an intense laser, when the laser fields are boosted to `supercritical' strengths far greater than the critical field of QED. As field strengths increase toward this regime, cascades of photon emission and electron-positron pair creation are expected, as well as the onset of substantial radiative corrections. Here we identify the important role played by the collision angle in mitigating energy losses to photon emission that would otherwise prevent …
We argue that calculations in QED at finite temperature are more conveniently carried out in the Coulomb gauge, in which only the physical photon degrees of freedom play a rol and are thermalized. We derive the photon propagator in this gauge for real-time finite temperature calculations and show that the four-fermion static Coulomb interaction that appears in the Lagrangian can be accounted for by suitably modifying the photon propagator. The Feynman rules of the theory are written in a manifestly covariant form, although they depend on the velocity 4-vector $u_μ$ of the background medium. As…
It is well known that there are resonant states with complex energy for the supercritical Coulomb impurity in graphene. We show that opening of a quasiparticle gap decreases the imaginary part of energy, |ImE|, of these states and stabilizes the system. For gapless quasiparticles with strong Coulomb interaction in graphene, we solve the Bethe-Salpeter equation for the electron - hole bound state and show that it has a tachyonic solution for strong enough coupling α=e^2/κ\hbar v_F leading to instability of the system. In the random-phase approximation, the critical coupling is estimated to be α…
In noncommutative QED photons present self-interactions in the form of triple and quartic interactions. The triple interaction implies that, even though the photon is electrically neutral, it will deflect when in the presence of an electromagnetic field. If detected, such deflection would be an undoubted signal of noncommutative space-time. In this work we derive the general expression for the deflection of a photon by any electromagnetic field. As an application we consider the case of the deflection of a photon by an external static Coulomb field.
We study the spontaneous emission of charged bosons from supercritical Coulomb potentials and charged black holes. We find the exact emission rate from the Bogoliubov transformation by applying the tunneling boundary condition on the Jost functions at the asymptotic boundaries. The emission rate for charged bosons in the supercritical Coulomb potential increases as the charge $Zα> 1/2$ of the superatom and the energy of the bosons increase but is suppressed for large angular momenta. We discuss physical implications of the emission of charged bosons from superatoms and charged black holes.
The Coulomb scattering between three charged pions is shown to be perturbatively calculable using scalar QED for the relative momenta accessible to high-energy experiments of particle collisions. For the triplet relative momenta, $Q_3 \gtrsim 50$ MeV/$c$, the calculated three-pion correlation function at $O(α^2)$ is very similar to the commonly-used triple-product of pair factors -- Riverside approximation. At lower $Q_3$, but above the lowest existing experimental measurement of $\sim15$ MeV/$c$, terms of $O(α^3)$ or higher are needed to obtain a convincing description of three-pion Coulomb i…
We consider QED in five dimensions in a configuration where matter is localized on a 3-brane while foton propagates in the bulk. The idea is to investigate the effects of the Kaluza-Klein modes of the photon in the relativistic regime, but in low energy, and in the nonrelativistic regime. In the relativistic regime, we calculate the cross section for the reaction $e^+ + e^- \to μ^+ + μ^-$. We compare our theoretical result with a precise measurement of this cross section at $\sqrt{s}=57.77$ GeV. As result, we extract a lower bound on the size of the extra dimension. In the nonrelativistic regi…
The process $\ee \to \W^+\W^- \to \f_1 \fbar_2 \, \f_3 \fbar_4$ contains charges in the initial, intermediate and final stages. This gives a rich selection of possible QED interconnection effects. Coulomb interaction is the simplest of these, and can thus be used to explore consequences. We study a number of experimental observables, with emphasis on those related to the W momentum distribution. Second-order Coulomb effects are shown to be practically negligible. The limited LEP~2 statistics will not allow detailed tests, so any theory uncertainty will be reflected in the systematic error on t…
The vast majority of QED results are obtained in relatively weak fields and so in the framework of perturbation theory. However, forthcoming laser facilities providing extremely high fields can be used to enter not-yet-studied regimes. Here, a scheme is proposed that might be used to reach a supercritical regime of radiation reaction or even the fully non-perturbative regime of quantum electrodynamics. The scheme considers the collision of a 100 GeV-class electron beam with a counterpropagating ultraintense electromagnetic pulse. To reach these supercritical regimes, it is unavoidable to use a…
Since the invention of chirped pulse amplification, which was recognized by a Nobel prize in physics in 2018, there has been a continuing increase in available laser intensity. Combined with advances in our understanding of the kinetics of relativistic plasma, studies of laser-plasma interactions are entering a new regime where the physics of relativistic plasmas is strongly affected by strong-field quantum electrodynamics (QED) processes, including hard photon emission and electron-positron ($e^+$-$e^-$) pair production. This coupling of quantum emission processes and relativistic collective …
The lowest order QED radiative corrections to the cross-section of the recharged process of transition of two charged pions to two neutral ones and to the pionium life time are calculated in frames of scalar QED. It is argued that the ultraviolet cut--off of the loop momentum is to be chosen of order of $ρ$ meson mass. This fact permits to perform the calculation in frames of Effective Chiral Lagrangian theory with vector-meson dominance. The Coulomb factor corresponding to interaction in the initial state, shown, is to be removed to avoid the double counting. Resulting value of the radiative …
The QED Coulomb correction is one of the most important corrections to the e+ e- --> W+ W- total cross section near threshold. We calculate these corrections through second order, and discuss the implications for extracting M_W from a threshold cross section measurement at LEP2. Analytic expressions are derived in various kinematic limits.
A strong electromagnetic field polarizes the vacuum and in the presence of an electric field creates pairs of a charged particle and its anti-particle. Magnetars, highly magnetized neutron stars with magnetic field comparable to or greater than the Schwinger field, give a significant amount of the vacuum polarization and vacuum birefringence and the induced electric field can create the electron-positron pairs, which are strong field quantum electrodynamics (QED) processes. In this paper, we use a closed formula for the one-loop effective action in the presence of a supercritical magnetic fiel…
We show that QED in the Coulomb gauge can be considered as a low energy linear approximation of a non-linear $σ$-type model where the photon emerges as a vector Goldstone boson related to the spontaneous breakdown of Lorentz symmetry down to its spatial rotation subgroup at some high scale $M$. Starting with a general massive vector field theory one naturally arrives at this model if the pure spin-1 value for the vector field $A_μ(x)$ provided by the Lorentz condition $\partial_μA_μ(x)=0$ is required. The model coincides with conventional QED in the Coulomb gauge in the limit of M going to inf…
I calculate the 1-loop vacuum polarization $Π_{μν}(k,B,a)$ for a photon of momentum $k=(\hat k,k_3)$ interacting with the electrons of a thin medium of thickness $2a$ simulating graphene, in the presence of a constant and uniform external magnetic field $B$ orthogonal to it (parallel to $k_3$). Calculations are done with the techniques of Schwinger, adapted to the geometry and Hamiltonian under scrutiny. The situation gets more involved than for the electron self-energy because the photon is now allowed to also propagate outside the medium. This makes $Π_{μν}$ factorize into a quantum, "reduce…
Systems with the quantum numbers of up to twelve charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and quantum electrodynamics (QCD+QED) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the quark masses to remove strong isospin breaking effects. A non-relativistic effective field theory, which perturbatively includes finite-volume Coulomb effects, is analyzed for systems of multiple charg…
The properties of the QED-vacuum energy $\hbox{$\cal E $}_{VP}$ under Coulomb super-criticality condition $Z>Z_{cr,1}$ are explored in essentially non-perturbative approach. It is shown that in the supercritical region $\hbox{$\cal E $}_{VP}$ is the decreasing function of the Coulomb source parameters, resulting in decay into the negative range as $\sim - Z^4/R$. The conditions, under which the emission of vacuum positrons can be unambiguously detected on the nuclear conversion pairs background, are also discussed. In particular, for a super-critical dummy nucleus with charge $Z$ and $R(Z) \si…
The Coulomb problem for charged massive vector bosons is known to be unstable, the boson falls on the Coulomb center. It is shown that when the charge of the Coulomb center is smeared over a small but finite volume, then instead of the fall there appears a large series of bound states localized inside the volume containing the Coulomb charge. It is shown also that the fall on the Coulomb center is completely suppressed, when the conventional QED vacuum polarization is taken into account.In gauge theories (SU(2), Standard Model) the renormalizability of a theory may be insufficient to guarantee…
We re-examine the physics of supercritical nuclei, specially focusing on the scattering phase $δ_{\varkappa}$ and its dependence on the energy $\varepsilon$ of the diving electronic level, for which we give both exact and approximate formulas. The Coulomb potential $Zα/r$ is rounded to the constant $Zα/R$ for $r < R$. We confirm the resonant behavior of $δ_{\varkappa}$ that we investigate in details. In addition to solving the Dirac equation for an electron, we solve it for a positron, in the field of the same nucleus. This clarifies the interpretation of the resonances. Our results are compar…
Within an explicit scalar QED model we compare, at fixed x << 1, the leading-twist K_T-dependent `quark' distribution f_q(x, K_T) probed in deep inelastic scattering and Drell-Yan production, and show that the model is consistent with the universality of f_q(x, K_T). The extension of the model from the aligned-jet to the 'symmetric' kinematical regime reveals interesting properties of the physics of Coulomb rescatterings when comparing DIS and DY processes. At small x the transverse momentum <k_T^2> induced by multiple scattering on a single centre is process dependent, as well as the transver…
Properties and different representations of the Uehling potential are investigated. Based on these properties and by using our formulas for the Fourier transform of the Uehling potential we have developed the new analytical, logically closed and physically transparent procedure which can be used to evaluate the lowest-order vacuum polarization correction to the cross sections of a number of QED processes, including the Mott electron scattering, bremsstrahlung, creation and/or annihilation of the $(e^{-}, e^{+})-$pair in the field of a heavy Coulomb center, e.g., atomic nucleus.
We discuss the status of atomic physics in strong field. We focus on the problem of electron-positron lines observed in heavy-ion collisions and on QED effects, calculated in strong Coulomb fields, especially Delbrück-scattering. We discuss the similarities and differences between these effects and channeling respectively beamstrahlung. We investigated the prospects for photon-channeling, calculated channeling from first principles on the basis of the Dirac equation, and determined the rate for electron-positron pair production in the collision of two high-energy particle pulses.
The photon polarization operator in superstrong magnetic fields induces the dynamical photon "mass" which leads to screening of Coulomb potential at small distances $z\ll 1/m$, $m$ is the mass of an electron. We demonstrate that this behaviour is qualitatively different from the case of D=2 QED, where the same formula for a polarization operator leads to screening at large distances as well. Because of screening the ground state energy of the hydrogen atom at the magnetic fields $B \gg m^2/e^3$ has the finite value $E_0 = -me^4/2 \ln^2(1/e^6)$.
In this work we review various findings in the planar quantum physics with the special emphasis on the two-component quantum electrodynamics in three-dimensional spacetime (QED_{3}) with the Chern-Simons (CS) term. First the classical electrodynamics is briefly outlined. Then we construct and classify the unitary irreducible representations of the Poincare group and connect them to various covariant fields. Subtleties with discrete symmetries arising in QED_{3} are also discussed. Quantization of the free gauge field with and without the CS term is performed in Coulomb gauge. Subsequently we d…
In this paper we investigate the photoproduction of QED bound states in proton -- proton, proton -- nucleus and nucleus -- nucleus collisions at RHIC, LHC and FCC energies considering an accurate treatment of the absorptive corrections and for the nuclear form factor. The total cross sections for the production of singlet and triplet $(l^+ l^-)$ states, with $l = e,\, μ, \, τ$, are estimated and a detailed analysis of the photoproduction of singlet QED bound states is performed considering the rapidity ranges covered by central and forward detectors. The impact of the Coulomb corrections on th…
Potential non-relativistic Quantum Electrodynamics and the Keldysh-Schwinger formalism is used to derive Kadanoff-Baym-like equations for two-body field correlators. These cover the out-off-equilibrium dynamics and spectrum of heavy particle-antiparticle pairs under ultra-soft transitions inside a plasma background, whose temperature is much smaller compared to the typical relative pair momentum. It is shown that the dynamical equation for the pair phase-space distribution function, containing recombination and dissociation via the electric dipole interactions, is consistent with the previous …
The non-perturbative effects of QED-vacuum reconstruction under influence of a supercritical EM-source ($Z>Z_{cr,1}$) are considered in view of lepton number conservation. The question is here that if the vacuum shells formation and spontaneous positron emission, associated with discrete levels diving into the lower continuum, exist in reality, then it by no means should be a signal of new physics. The reason is that the emitted positrons carry away the lepton number equal to $(-1)\times$their total number, and so the corresponding amount of positive lepton number should be shared by VP-densit…
The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas fo…
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativ…
