Scattering amplitudes approach to hard thermal loops

Leonardo De La Cruz

doi:10.1103/physrevd.104.014013

Abstract

Inspired by recent progress on classical limits of scattering amplitudes, we show that hard thermal loops can be obtained from classical limits of off-shell currents. The classicality of hard thermal loops is made manifest by associating classical wavenumbers to soft particles. We compute the classical limit of these currents in QED, QCD and gravity. Our proposal does not involve the introduction of ghosts.

Highlights

In past decades progress in the field of scattering amplitudes has improved our ability to make predictions in scattering experiments [1]
Inspired by the KMOC approach to classical observables, we propose a map between classical limits of off-shell currents at zero temperature and hard thermal loop (HTL) currents
In this paper we have shown that HTLs arise from classical limits of off-shell currents

Summary

INTRODUCTION

In past decades progress in the field of scattering amplitudes has improved our ability to make predictions in scattering experiments [1]. The limit of high temperature T in perturbative thermal QCD is useful for the description of collective phenomena in plasmas This limit can be consistently incorporated into an effective theory known as hard thermal loop (HTL) effective theory [46,47,48,49,50]. Inspired by the KMOC approach to classical observables, we propose a map between classical limits of off-shell currents at zero temperature and HTL currents This map is based on the simple observation that to extract classical limits of scattering amplitudes one should distinguish between the momentum p of a particle and its wavenumber pp ≡ ħp ; ð1Þ which we interpret as the distinction between soft and hard in HTL currents. We will mostly use the KMOC approach but other strategies to obtain the classical limit may be used as well. e.g., [12,20,54]

FROM KINETIC THEORY TO CLASSICAL LIMITS OF OFF-SHELL CURRENTS

QCD AND GRAVITY

DISCUSSION