Hot QED Research Articles

Accounting for plasma constituent mass effects in heavy fermion energy loss calculations in hot QED and QCD

Accounting for plasma constituent mass effects in heavy fermion energy loss calculations in hot QED and QCD

Spin evolution of massive fermion in QED plasma

The dynamical evolution of spin of a massive probe fermion in a massless hot QED plasma at local equilibrium is investigated through the quantum kinetic theory. We consider the massive probe fermion undergoing 2-by-2 Coulomb scattering with the massless fermions in the medium. The axial kinetic equation is derived including the collision terms to the first order of gradients and leading logarithmic order of the coupling. The collision terms are vanishing at global equilibrium, around which the relaxation time can be extracted as an operator. We further decompose the axial kinetic equation into kinetic equations of axial-charge density as well as the transverse magnetic dipole moment, and illustrate the diffusion and polarization effect through preliminary numerical analysis.

Soft contribution to the damping rate of a hard photon in a weakly magnetized hot medium

We consider weakly magnetized hot QED plasma comprising electrons and positrons. There are three distinct dispersive (longitudinal and two transverse) modes of a photon in a thermo-magnetic medium. At lowest order in coupling constant, photon is damped in this medium via Compton scattering and pair creation process. We evaluate the damping rate of hard photon by calculating the imaginary part of the each transverse dispersive modes in a thermo-magnetic QED medium. We note that one of the fermions in the loop of one-loop photon self-energy is considered as soft and the other one is hard. Considering the resummed fermion propagator in a weakly magnetized medium for the soft fermion and the Schwinger propagator for hard fermion, we calculate the soft contribution to the damping rate of hard photon. In weak field approximation the thermal and thermo-magnetic contributions to damping rate get separated out for each transverse dispersive mode. The total damping rate for each dispersive mode in presence of magnetic field is found to be reduced than that of the thermal one. This formalism can easily be extended to QCD plasma.

Interaction of nonthermal muon beam with electron-positron-photon plasma: A thermal field theory approach

Interaction of a muon beam with hot dense QED plasma is investigated. Plasma system contains electrons and positrons with Fermi-Dirac distribution and Bose-Einstein distributed photons while the beam particles have nonthermal distribution. The energy loss of the beam particles during the interaction with plasma is calculated to complete leading order of interaction in terms of the QED coupling constant using thermal field theory approach. The screening effects of the plasma are computed consistently using resummation of perturbation theory with hard thermal loop approximation according to the Braaten-Pisarski method. Time evolution of the plasma characteristics and also plasma identifications during the interaction are investigated. Effects of the nonthermal parameter of the beam distribution on the energy exchange and the evolution of plasma-beam system are also explained.

Transport properties and Langevin dynamics of heavy quarks and quarkonia in the Quark Gluon Plasma

Quark Gluon Plasma transport coefficients for heavy quarks and Q Q ¯ pairs are computed through an extension of the results obtained for a hot QED plasma by describing the heavy-quark propagation in the eikonal approximation and by weighting the gauge-field configurations with the Hard Thermal Loop effective action. It is shown that such a model allows to correctly reproduce, at leading logarithmic accuracy, the results obtained by other independent approaches. The results are then inserted into a relativistic Langevin equation allowing to follow the evolution of the heavy-quark momentum spectra. Our numerical findings are also compared with the ones obtained in a strongly-coupled scenario, namely with the transport coefficients predicted (though with some limitations and ambiguities) by the AdS/CFT correspondence.

Shear Viscosity of Hot QED at Finite Chemical Potential from Kubo Formula

Within the framework of finite temperature feld theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths (damping rates) are introduced to regulate the pinch singularities and then gives a reliable estimation of the shear viscous coefficient. The finite chemical potential contributes positively compared to the pure temperature case. The result agrees with that from the kinetics theory qualitatively.

Collisional energy loss of a fast muon in a hot QED plasma

We calculate the collisional energy loss of a muon of high energy $E$ in a hot QED plasma beyond logarithmic accuracy, i.e., we determine the constant terms of order $\mathcal{O}(1)$ in $\ensuremath{-}dE/dx\ensuremath{\propto}\mathrm{ln}E+\mathcal{O}(1)$. Considering first the $t$-channel contribution to $\ensuremath{-}dE/dx$, we show that the terms $\ensuremath{\sim}\mathcal{O}(1)$ are sensitive to the full kinematic region for the momentum exchange $q$ in elastic scattering, including large values $q\ensuremath{\sim}\mathcal{O}(E)$. We thus redress a previous calculation by Braaten and Thoma, which assumed $q\ensuremath{\ll}E$ and could not find the correct constant (in the large $E$ limit). The relevance of ``very hard'' momentum transfers then requires, for consistency, that $s$ and $u$-channel contributions from Compton scattering must be included, bringing a second modification to the Braaten-Thoma result. Most importantly, Compton scattering yields an additional large logarithm in $\ensuremath{-}dE/dx$. Our results might have implications in the QCD case of parton collisional energy loss in a quark gluon plasma.

Erratum: Leading-order calculation of electric conductivity in hot quantum electrodynamics from diagrammatic methods [Phys. Rev. D75, 025014 (2007)

Using diagrammatic methods, we show how the Ward identity can be used to constrain the ladder kernel in transport coefficient calculations. More specifically, we use the Ward identity to determine the necessary diagrams that must be resummed using an integral equation. One of our main results is an equation relating the kernel of the integral equation with functional derivatives of the full self-energy; it is similar to what is obtained with 2PI effective action methods. However, since we use the Ward identity as our starting point, gauge invariance is preserved. Using power counting arguments, we also show which self-energies must be included in the resummation at leading order, including 2 to 2 scatterings and 1 to 2 collinear scatterings with the LPM effect. We show that our quantum field theory result is equivalent to the one of Arnold, Moore and Yaffe obtained using effective kinetic theory. In this paper we restrict our discussion to electrical conductivity in hot QED, but our method can in principle be generalized to other transport coefficients and other theories.

Soft fermion dispersion relation at next-to-leading order in hot QED

We study next-to-leading-order contributions to the soft static fermion dispersion relation in hot QED. We derive an expression for the complete next-to-leading-order contribution to the retarded fermion self-energy. The real and imaginary parts of this expression give the next-to-leading-order contributions to the mass and damping rate of the fermionic quasiparticle. Many of the terms that are expected to contribute according to the traditional power counting argument are actually subleading. We explain why the power counting method over estimates the contribution from these terms. For the electron damping rate in QED we obtain: ${\ensuremath{\gamma}}_{\mathrm{QED}}=\frac{{e}^{2}T}{4\ensuremath{\pi}}(2.70)$. We check our method by calculating the next-to-leading-order contribution to the damping rate for the case of QCD with two flavors and three colors. Our result agrees with the result obtained previously in the literature. The numerical evaluation of the nlo contribution to the mass is left to a future publication.

Leading-order calculation of electric conductivity in hot quantum electrodynamics from diagrammatic methods

Using diagrammatic methods, we show how the Ward identity can be used to constrain the ladder kernel in transport coefficient calculations. More specifically, we use the Ward identity to determine the necessary diagrams that must be resummed using an integral equation. One of our main results is an equation relating the kernel of the integral equation with functional derivatives of the full self-energy; it is similar to what is obtained with two-particle irreducible (2PI) effective action methods. However, since we use the Ward identity as our starting point, gauge invariance is preserved. Using power counting arguments, we also show which self-energies must be included in the resummation at leading order, including 2 to 2 scatterings and 1 to 2 collinear scatterings with the Landau-Pomeranchuk-Migdal effect. We show that our quantum field theory result is equivalent to the one of Arnold, Moore, and Yaffe obtained using effective kinetic theory. In this paper we restrict our discussion to electrical conductivity in hot QED, but our method can in principle be generalized to other transport coefficients and other theories.

Erratum: Four-point spectral functions and Ward identities in hot QED [Phys. Rev. D61, 085013 (2000)

We derive spectral representations for the different components of the 4-point function at finite temperature in the real time formalism in terms of five real spectral densities. We explicitly calculate all these functions in QED in the hard thermal loop approximation. The Ward identities obeyed by the 1-loop 3- and 4-point functions in real time and their spectral functions are derived. We compare our results with those derived previously in the imaginary-time formalism for retarded functions in hot QCD, and we discuss the generalization of our results to non-equilibrium situations.

Ward identity and electrical conductivity in hot QED

We study the Ward identity for the effective photon-electron vertex summing the ladder diagrams contributing to the electrical conductivity in hot QED at leading logarithmic order. It is shown that the Ward identity requires the inclusion of a new diagram in the integral equation for the vertex that has not been considered before. The real part of this diagram is subleading and therefore the final expressions for the electrical conductivity at leading logarithmic order are not affected.

Rates of neutrino conversion and decay in hot and dense QED plasma

Using a real-time formalism of equilibrium and nonequilibrium quantum-field theory, we derive the reaction-rate formula for neutrino-conversion ($\nu \to \nu'$) process and $\nu \bar{\nu}'$ annihilation process, which take place in a hot and dense QED plasma with background (anti)neutrinos out of equilibrium. Also derived is the formula for the inverse processes to the above ones. Using the hard-thermal-loop resummation scheme, we include the contribution from the coherent processes. The decay/production of a neutrino causes an evolution of its spatial distribution. A scheme for dealing with this evolution is presented. For the case of isotropic neutrino distribution, numerical computation is carried out for the parameter region of type-II super-nova explosion. Defferential reaction rate exhibits characteristic peak structure, which comes from the coherent processes. The contribution from the above processes to the decay or damping rate of a parent neutrino $\nu$ is also studied.

REAL-TIME NONEQUILIBRIUM DYNAMICS IN HOT QED PLASMAS

The quantum kinetics of photons in hot QED plasmas is studied directly in real time by implementing the dynamical renormalization group. In contrast to conventional approach, the dynamical renormalization group method consistently includes off-shell (energy non-conserving) effects and accounts for time-dependent collisional kernel. To lowest order we find that in the relaxation time approximation the semihard photon distribution function relaxes with a power law.

Real-time nonequilibrium dynamics in hot QED plasmas: Dynamical renormalization group approach

We study the real-time nonequilibrium dynamics in hot QED plasmas implementing a dynamical renormalization group and using the hard thermal loop (HTL) approximation. The focus is on the study of the relaxation of gauge and fermionic mean fields and on the quantum kinetics of the photon and fermion distribution functions. For semihard photons of momentum eT q \gamma and \bar{q} -> \bar{q}\gamma) at O(\alpha) grows logarithmically in time and is comparable to that produced from on-shell Compton scattering and pair annihilation at O(\alpha \alpha_s). Fermion mean fields relax as e^{-\alpha T t ln(\omega_P t)} with \omega_P=eT/3 the plasma frequency, as a consequence of the emission and absorption of soft magnetic photons. A quantum kinetic equation for hard fermions is obtained directly in real time from a field theoretical approach improved by the dynamical renormalization group. The collision kernel is time-dependent and infrared finite.

DAMPING AND REACTION RATES AND WAVE FUNCTION RENORMALIZATION OF FERMIONS IN HOT GAUGE THEORIES

We examine the relation between the damping rate of a chiral fermion mode propagating in a hot plasma and the rate at which the mode approaches equilibrium. We show how these two quantities, obtained from the imaginary part of the fermion self-energy, are equal when the reaction rate is defined using the appropriate wave function of the mode in the medium. As an application, we compute the production rate of hard axions by Compton-like scattering processes in a hot QED plasma starting from both, the axion self-energy and the electron self-energy. We show that the latter rate coincides with the former only when this is computed using the corresponding medium spinor modes.

Four-point spectral functions and Ward identities in hot QED

We derive spectral representations for the different components of the four-point function at finite temperature in the real time formalism in terms of five real spectral densities. We explicitly calculate all these functions in QED in the hard thermal loop approximation. The Ward identities obeyed by the one-loop three- and four-point functions in real time and their spectral functions are derived. We compare our results with those derived previously in the imaginary-time formalism for retarded functions in hot QCD, and we discuss the generalization of our results to non-equilibrium situations.

Right-handed neutrino production in dense and hot plasmas

For Dirac neutrinos with magnetic moment, we compute the production rate for right-handed neutrinos in a hot and dense QED plasma containing an initial population of left-handed neutrinos thermally distributed. The most important mechanisms for ν L depolarization, or production of right-handed neutrinos, are the ν L → ν R chirality flip and the plasmon decay to ν ̄ L+ν R . The rates for these processes are computed in terms of a resummed photon propagator which consistently incorporates the background effects to leading order. Applying the results to the cases of supernovae core collapse and the primordial nucleosynthesis in the early universe, we obtain upper limits on the neutrino magnetic moment.

Hot QED beyond ladder graphs

At finite temperature a breakdown of the hard thermal loop expansion arises whenever external momenta are light-like or tend to very soft scales. A resummation of ladder graphs is important in these cases where the effects of infrared or light-cone singularities are enhanced. We show that in hot QED another class of diagrams is also relevant at leading order due to long range magnetic interactions and therefore recent studies about ladder expansions need to be corrected. A general cancellation of the hard modes damping effects still occurs near the light-cone or in the infrared region. The validity of an improved version of the hard thermal loop resummation scheme is discussed.

Real-time relaxation and kinetics in hot scalar QED: Landau damping

The real time evolution of field condensates with soft length scales k^{-1}>(eT)^{-1} is solved in hot scalar electrodynamics, with a view towards understanding relaxational phenomena in the QGP and the electroweak plasma. We find that transverse gauge invariant non-equilibrium expectation values of fields relax via {\em power laws} to asymptotic amplitudes that are determined by the quasiparticle poles. The long time relaxational dynamics and relevant time scales are determined by the behaviour of the retarded self-energy not at the small frequencies, but at the Landau damping thresholds. This explains the presence of power laws and not of exponential decay. Furthermore, we derive the influence functional, the Langevin equation and the fluctuation-dissipation theorem for the soft modes, identifying the correlation functions that emerge in the classical limit. We show that a Markovian approximation fails to describe the dynamics {\em both} at short and long times. We also introduce a novel kinetic approach that goes beyond the standard Boltzmann equation and incorporates off-shell processes and find that the distribution function for soft quasiparticles relaxes with a power law through Landau damping. We also find an unusual dressing dynamics of bare particles and anomalous (logarithmic) relaxation of hard quasiparticles.