Akira Niégawa

Temperature dependence of the non-abelian gauge couplings at finite temperature

Abstract The temperature dependence of the non-abelian gauge couplings at finite temperature is calculated using the momentum-space subtraction method. The inverse of the coupling, a ( μ , ξ ≡ T / μ ) −1 ∼ b ln[ μ / Λ ( ξ )], shows essentially a power-like ξ (≡ T / μ ) dependence in sharp contrast with the usual logarithmic dependence on the renormalization scale μ. The strong vertex dependence of the coupling is clarified.

Quantum field theories in nonextensive Tsallis statistics

Within the framework of Tsallis statistics with q ≃ 1, we construct a perturbation theory for treating relativistic quantum field systems. We find that there appear initial correlations, which do not exist in the Boltzmann-Gibbs statistics. Applying this framework to a quark-gluon plasma, we find that the so-called thermal masses of quarks and gluons are smaller than in the case of Boltzmann-Gibbs statistics.

Leading T3-behavior and vertex-configuration dependence of real-time thermal QCD coupling

Abstract The properties of effective coupling in real-time thermal QCD are investigated at one-loop order in the large-T regime, focusing on its strong dependence on the momentum configuration of a vertex. A striking observation is that the leading large-T behavior in a general vertex-configuration is cubic in T, a−1 ∼ T3, which is solely controlled by those contributions that have been overlooked so far. The relation with the coupling defined in the imaginary time formalism is also discussed.

Calculational rules for finite temperature reaction rates

Abstract Systematic calculational rules are found for evaluating the reaction rate of a generic process taking place in a thermal reservoir in equilibrium. The rules are formulated in a diagrammatic representation within the framework of a real-time thermal field theory. It becomes clear how each “forward” diagram can be cut; thus the finite temperature generalization of the Cutkosky (or cutting) rules is settled. The relationship is clarified between our diagrammatic rules and those for finding the imaginary part of the relevant “forward” amplitude established by Kobes and Semenoff; the latter is shown to contain different reaction rates.

How to resolve the factorization- and the renormalization-scheme ambiguities simultaneously?☆

Abstract A combined investigation of both the factorization- and renormalization-scheme dependences of perturbative QCD calculations is reported. Applyong Stevensons optimization method, we get a remarkable result, which forces us to exponentiate “everything” with uncorrected subprocess cross sections.

Analytic continuation of thermal N-point functions from imaginary to real energies

Thermal [ital n]-point Green functions in the framework of quantum field theory at finite temperature are considered. We reanalyze how analytic continuations from imaginary to real energies relate these functions originally defined in the imaginary-time formalism to retarded and advanced realtime ones. We described a new and rather simple method which is valid to all orders of perturbation theory and which has the further advantage that it is independent of approximations often applied in actual finite-order calculations.

A Slavnov-Taylor identity and equality of damping rates for static transverse and longitudinal gluons in hot QCD

Abstract A Slavnov-Taylor identity is derived for the gluon polarization tensor in hot QCD. We evaluate its implications for damping of gluonic modes in the plasma. Applying the identity to next to the leading order in hard-thermal-loop resummed perturbation theory, we derive the expected equality of damping rates for static transverse and longitudinal (soft) gluons. This is of interest also in view of deviating recent reports of γ t ( p =0)≠ γ l ( p =0) based on a direct calculation of γ l ( p =0).

On the gauge dependence problem of the fermion damping rate in hot gauge theories

Abstract The gauge-dependence problem of the damping rate of a fermionic mode in hot gauge theories is carefully examined to the effective one-loop order using recently proposed resummation methods in terms of “hard thermal loops”. We study the case of a heavy fermion ( M ⪢ T ), which enables us to investigate the essential point of controversy in great detail. Explicit calculation in general covariant gauges shows which calculation procedure should be employed to get a gauge-parameter independent result.

Screening of mass singularities and finite soft-photon production rate in hot QCD

The production rate of a soft photon from a hot quark-gluon plasma is computed to leading order at logarithmic accuracy. The canonical hard-thermal-loop resummation scheme leads to a logarithmically divergent production rate due to mass singularities. We show that these mass singularities are screened by employing the effective hard-quark propagator, which is obtained through resummation of the one-loop self-energy part in a self-consistent manner. The damping-rate part of the effective hard-quark propagator, rather than the thermal-mass part, plays the dominant role of screening mass singularities. Diagrams including photon{endash} (hard-)quark vertex corrections also yield the leading contribution to the production rate. {copyright} {ital 1997} {ital The American Physical Society}

Cancellation of energy divergences and renormalizability in Coulomb gauge QCD within the Lagrangian formalism

In Coulomb gauge QCD in the Lagrangian formalism, energy divergences arise in individual diagrams. We give a proof on cancellation of these divergences to all orders of perturbation theory without obstructing the algebraic renormalizability of the theory.