J.C. Taylor

High-temperature limit of thermal QCD

Abstract We study the high-temperature behaviour of the n -point function to one-loop order in thermal QCD. We employ an analytic continuation of the imaginary-time formalism. The leading terms are all of order T 2 . They are totally symmetric in their Lorentz indices and traceless. They are gauge independent and obey simple, QED-like, Ward identities. The n -point functions for n >3 can be expressed as linear combinations with rational coefficients of the 2- and 3-point functions - a fact which follows from the symmetry, tracelessness and Ward identities.

Non-abelian eikonal exponentiation

Abstract Recently, Gatheral [1] has generalized the well-known exponentiation properties of soft photons in QED to the case of soft gluons in QCD in the eikonal approximation. We add three things to his work. (i) We clarify the definition of the colour weight factors which appear in the exponent. (ii) We show how the eikonal approximation can be renormalized, consistently with the exponentiation. (iii) We derive a differential equation obeyed by the cross section for emission of soft gluons with given maximum total energy. We also discuss the relationship between the exponentiation theorem and expectation values of Wilson loops.

The effective action of hard thermal loops in QCD

In thermal QCD, the order-T2 contributions to one-loop diagrams have some striking simple properties, including gauge invariance. We present a generating function for these contributions in a simple closed form.

Hard thermal QCD, forward scattering and effective actions

Abstract We study the high-temperature behaviour of the n-point function to one-loop order in thermal QCD, in the analytic continuation of the imaginary-time formalism. Using ideas of Barton, we relate these functions to angular integrals of the forward-scattering amplitudes (for the thermal particles) in the high-energy limit. These amplitudes are Lorentz and gauge invariant, and the Ward identities determine all of them uniquely in terms of the two-point one. We are thus able, by gauge invariance, to write down a generating function for all n-point functions. Its relationship to a previous one (with a Lorentz and gauge non-invariant integrand) is explained.

Ghosts and Renormalization in the Planar Gauge

We make two points about the planar gauge in non-abelian gauge theories: (a) Although ghosts are absent from S-matrix elements they ar necessary to formulate Slavnov identities. (b) The Slavnov identities by themselves are insufficient to control the field renormalization-a supplementary argument is necessary.

Are Axial Gauges Useful in Perturbative {QCD}?

Abstract The general source of the problems with the time-like and space-like axial gauges is analysed. These problems are avoided in the light-like case, using the Leibbrandt-Mandelstam prescription. However, this does not satisfy graph-by-graph unitarity, and so its usefulness in typical perturbative QCD arguments is open to question.

High-temperature QCD and the classical Boltzmann equation in curved spacetime

Abstract It has been shown that the high-temperature limit of perturbative thermal QCD is easily obtained from the Boltzmann transport equation for “classical” coloured particles [P.F. Kelly et al., Phys. Rev. D 50 (1994) 4209]. We generalize this treatment to curved space-time. We are thus able to construct the effective stress-energy tensor. We give a construction for an effective action. As an example of the convenience of the Boltzmann method, we derive the high-temperature 3-graviton function. We discuss the static case.

Quark-antiquark annihilation is infrared safe at high energy to all orders

In perturbative QCD, the Bloch-Nordsieck cross section for quark-antiquark annihilation is known, to order g4, to be infrared finite, except for terms which are power-suppressed at high energies. We give a fairly simple explanation of this fact, using analyticity, unitarity and an analysis of mass singularities is both Feynman and axial gauges. The arguments applies fairly easily to order g6. Assuming a generalized unitarity principle, the argument can be extended to all orders.

Asymptotic states and infrared divergences in non-abelian theories

We give a general definition of a class of asymptotic states in non-abelian gauge theories. We argue, using unitarity, that they give infrared-finite S-matrix elements. We discuss the energy of the soft gluons in these states.

Metric dependence of partition function at high temperature

Abstract This paper is about thermal field theory in a background gravitational field (in space-time which is asymptotically minkowskian). We use the analytically continued imaginary-time formalism in one-loop order, and restrict ourselves to high temperatures. An all-orders, but implicit, expression is given for the partition function.