Hard Thermal Loop Research Articles

Plasmon properties in classical lattice gauge theory

In order to investigate the features of the classical approximation at high temperatures for real time correlation functions, the plasmon frequencies and damping rates were recently computed numerically in the SU(2)+Higgs model and in the pure SU(2) theory. We compare the lattice results with leading order hard thermal loop resummed perturbation theory. In the broken phase of the SU(2)+Higgs model, we show that the lattice results can be reproduced and that the lattices used are too coarse to observe some important plasmon effects. In the symmetric phase, the main qualitative features of the lattice results can also be understood. In the pure SU(2) theory, on the other hand, there are discrepancies which might point to larger Landau and plasmon damping effects than indicated by perturbation theory.

Three-point spectral density in QED and the ward identity at finite temperature

We derive the spectral representations of QED 3-point functions and then explicitly calculate the 3-point spectral densities in hard thermal loop approximation within the real time formalism. The Ward identities obeyed by the retarded and advanced 2- and 3-point functions are discussed. We compare our results with those for hot QCD .

On Finite-Temperature and Finite-Density Radiative Corrections to the Neutrino Effective Potential in the Early Universe

Finite-temperature and finite-density radiative corrections to the neutrino effective potential in the otherwise CP-symmetric early Universe are considered in the real-time approach of thermal field theory. A consistent perturbation theory endowed with the hard thermal loop resummation techniques developed by Braaten and Pisarski is applied. Special attention is focused on the question whether such corrections can generate any nonzero contribution to the CP-symmetric part of the neutrino potential, if the contact approximation for the W-propagator is used.

Classical lattice gauge fields with hard thermal loops

We propose a formulation of the long-distance dynamics of gauge theories at finite temperature on a lattice in Minkowski space, including the effects of hard thermal loops on the dynamics of the long wavelength modes. Our approach is based on the dual classical limits of quantum fields as waves and particles in the infrared and ultraviolet limits, respectively. It exhibits manifest invariance under space-dependent lattice gauge transformations and conserves Gauss' law.

Resummation and the MSW effect inside a supernova core

Abstract The electron-neutrino ( v e ) charged-current self-energy, in an ultra-degenerate medium of ultra-relativistic electrons, is examined in the real-time approach of Thermal Field Theory. The starting point are the hard thermal loop resummation techniques developed by Braaten and Pisarski and others. In such a way, an order α correction to the standard MSW potential is found. In addition, the absence of electron-mass singularities at O ( α ) is confirmed in a coherent process.

Equilibrium and non-equilibrium hard thermal loop resummation in the real time formalism

We investigate the use of the hard thermal loop (HTL) resummation technique in non-equilibrium field theory. We use the Keldysh representation of the real time formalism (RTF). We derive the HTL photon self energy and the resummed photon propagator. We show that no pinch singularities appear in the non-equilibrium HTL effective propagator. We discuss a possible regularization mechanism for these singularities at higher orders. As an example of the application of the HTL resummation method within the RTF we discuss the damping rate of a hard electron.

Batalin–Fradkin Approach to (1 + 1)-Dimensional Massive Vector Fields and the Gluonic Effective Action for Hard Thermal Loops

The Lagrangian of (1 + 1)-dimensional massive vector fields is studied. Since this system has second class constraints, the method of Batalin–Fradkin, which introduces new fields to convert second class constraints into first class ones, is applied in an extended manner. Instead of the usual treatment, which uses the Stueckelberg field as a new field, we can use a pseudoscalar field. We will show there are at least two ways to introduce a pseudoscalar. At the quantum level, one way leads to the system that is equivalent to the original system, and the other way gives an inequivalent system. The relation of these two ways is clarified. As an application of the latter way, we consider QCD at finite temperature and the gluonic effective action for hard thermal loops is constructed.

Breakdown of the hard thermal loop expansion for quasi-real photons production

We discuss the bremsstrahlung production of soft real and virtual photons in a quark-gluon plasma at thermal equilibrium beyond the Hard Thermal Loop (HTL) resummation. The physics is controlled by the ratio $Q^{2}/q_{0}^{2}$ of the virtuality to the energy. When $Q^{2}/q_{0}^{2} ⌈ g^{2}$ where g is the strong coupling constant, the emission rate is enhanced by a factor 1/g2 over the HTL results due to light-cone singularities and the bremsstrahlung is induced by scattering of the quark via both transverse and longitudinal soft gluon exchanges. When $Q^{2}/q_{0}^{2}$ increases, the enhancement factor is given by $q_{0}^{2}/Q^{2}$. When this ratio is near unity, the bremsstrahlung contribution is of the same order as the rate predicted by the HTL resummation. In that case, the bremsstrahlung is induced by both soft and hard gluon exchanges.

HotBviolation, the lattice, and hard thermal loops

It has recently been argued that the rate per unit volume of baryon number violation (topological transitions) in the hot, symmetric phase of electroweak theory is of the form $\eta \alpha_w^5 T^4$ in the weak-coupling limit, where $\eta$ is a non-perturbative numerical coefficient. Over the past several years, there have been attempts to extract the rate of baryon number violation from real-time simulations of classical thermal field theory on a spatial lattice. Unfortunately, the coefficient $\eta$ will not be the same for classical lattice theories and the real quantum theory. However, by analyzing the appropriate effective theory on the lattice using the method of hard thermal loops, I show that the only obstruction to precisely relating the rates in the real and lattice theories is the fact that the long-distance physics on the lattice is not rotationally invariant. (This is unlike Euclidean-time measurements, where rotational invariance is always recovered in the continuum limit.) I then propose how this violation of rotational invariance can be eliminated - and the real B violation rate measured - by choosing an appropriate lattice Hamiltonian. I also propose a rough measure of the systematic error to be expected from using simpler, unimproved Hamiltonians. As a byproduct of my investigation, the plasma frequency and Debye mass are computed for classical thermal field theory on the lattice.

Scattering of Soft, Cool Pions

Consider the effective lagrangian for pions in the chiral limit, computed to leading order in an expansion about zero temperature. To describe the scattering of pions with small momenta, it is necessary to include not just the usual shift in the pion decay constant, but also a new, nonlocal term, which is precisely analogous to the hard thermal loops of hot gauge theories.

Hard thermal loops in a magnetic field and the chiral anomaly

The fermionic dispersion relation in the presence of a background magnetic field and a high temperature QED plasma is calculated exactly in the external field, using the Hard Thermal Loop effective action. As the field strength increases there is a smooth transition from the weak-field ( qB ⪡ q 2 T 2) thermal dispersion relations to the vacuum Landau levels when the backgroun field is much stronger than any thermal effects ( qB ⪢ q 2 T 2). The self-energy at finite field strength acquires an imaginary part. The spectral width becomes important for critical field strengths ( qB ≈ q 2 T 2), necessitating the use of the full spectral function. It is shown that the spectral function satisfies the usual condition of normalization and causality. Using the exact spectral function I also show that the production of chirality in an external electromagnetic field at high temperature is unaffected by the presence of the thermal masses of the fermions.

Enhanced photon production near the light—cone by a hot plasma

Strong collinear divergences, although regularized by a thermal mass, result in a breakdown of the standard hard thermal loop expansion in the calculation of the production rate of photons by a plasma of quarks and gluons using thermal field theory techniques.

On the thermal effective expansion of a scalar theory

We consider a scalar massless quantum field model, at finite temperature T, both renormalizable and asymptotically free. Focusing on the thermal equilibration process of some Higgs particle, several new aspects are brought out, regarding the hard thermal loop resummation program.

On non-Abelian Thomas-Fermi screening

The Thomas-Fermi screening of non-Abelian gauge fields by fermions or screening of gluon fields in quark matter is discussed. It is described by an effective mass term which is, as with hard thermal loops, related to the eikonal for a Chern-Simons theory and the Wess-Zumino-Witten action.

Motion of Chern-Simons number at high temperatures under a chemical potential

I investigate the evolution of finite temperature, classical Yang-Mills field equations under the influence of a chemical potential for Chern-Simons number N cs. The rate of N cs diffusion,, Γ d , and the linear response of N cs to a chemical potential, Γ μ , are both computed; the relation Γ d = 2 Γ μ is satisfied numerically and the results agree with the recent measurement of Γ d by Ambjørn and Krasnitz. The response of N cs under chemical potential remains linear at least to μ = 6 T, which is impossible if there is a free energy barrier to the motion of N cs. The possibility that the result depends on lattice artefacts via hard thermal loops is investigated by changing the lattice action and by examining elongated rectangular lattices; provided that the lattice is fine enough, the result is weakly if at all dependent on the specifics of the cutoff. I also compare SU(2) with SU(3) and find Γ SU(3)∼ 7( α s/ α w ) 4 Γ SU(2) .

Relaxation and kinetics in scalar field theories.

A new approach to the dynamics of relaxation and kinetics of thermalization in a scalar field theory is presented that incorporates the relevant time scales through the resummation of hard thermal loops. An alternative derivation of the kinetic equations for the ``quasiparticle'' distribution functions is obtained that allows a clear understanding of the different ``coarse graining'' approximations usually involved in a kinetic description. This method leads to a systematic perturbative expansion to obtain the kinetic equations including hard-thermal loop resummation and to an improvement including renormalization, off-shell effects and contributions that change chemical equilibrium on short time scales. As a byproduct of these methods we establish the relation between the relaxation time scale in the linearized equation of motion of the quasiparticles and the thermalization time scale of the quasiparticle distribution function in the ``relaxation time approximation''. Hard thermal loop resummation dramatically modifies the scattering rate for long wavelength modes as compared to the usual (semi) classical estimate. Relaxation and kinetics are studied both in the unbroken and broken symmetry phases of the theory. The broken symmetry phase also provides the setting to obtain the contribution to the kinetic equations from processes that involve decay of a heavy scalar into light scalar particles in the medium.

Massive hard thermal loops in curved space-time

The effective actions generating the hard thermal loops with massive internal fields are derived, in the presence of a background space-time, for theories with various external fields.

THERMAL TWO-POINT FUNCTION OF A HEAVY MUON IN HOT QED PLASMA WITHIN BLOCH NORDSIECK APPROXIMATION

The thermal propagator of a heavy muon propagating in a hot QED plasma is examined within the Bloch–Nordsieck approximation, which is valid in the infrared region. Hard thermal loop resummation á la Arnold and Espinosa is taken into account for the photon line. It is shown that the heavy muon damping rate is finite.

Improved hard-thermal-loop effective action for hot QED and QCD

The conventional results for hard thermal loops, which are the building blocks of resummed perturbation theory in thermal field theories, have collinear singularities when external momenta are light-like. It is shown that by taking into account asymptotic thermal masses these singularities are removed. The thus improved hard thermal loops can be summarized by compact gauge-invariant effective actions, generalizing the ones found by Taylor and Wong, and by Braaten and Pisarski.

Really computing nonperturbative real time correlation functions.

It has been argued by Grigoriev and Rubakov that one can simulate real time processes involving baryon number nonconservation at high temperature using real time evolution of classical equations, and summing over initial conditions with a classical thermal weight. It is known that such a naive algorithm is plagued by ultraviolet divergences. In quantum theory the divergences are regularized, but the corresponding graphs involve the contributions from the hard momentum region and also the new scale \ensuremath{\sim}gT comes into play. We propose a modified algorithm which involves solving the classical equations of motion for the effective hard thermal loop Hamiltonian with an ultraviolet cutoff \ensuremath{\mu}\ensuremath{\gg}gT and integrating over initial conditions with a proper thermal weight. Such an algorithm should provide a determination of the infrared behavior of the real time correlation function 〈Q(t)Q(0)${\mathrm{〉}}_{\mathit{T}}$ determining the baryon violation rate. Hopefully, the results obtained in this modified algorithm will be cutoff independent.