Thermal field theory at next-to-leading order in the hard thermal loop expansion

Abstract

In this paper we study the hard-thermal-loop effective theory at next-to-leading order. Standard power-counting predicts that a large number of diagrams, including 2-loop diagrams, may need to be calculated. In all of the calculations that have been done however, with the exception of the photon self-energy, the full next-to-leading order contribution can be obtained by calculating only soft 1-loop diagrams with effective lines and vertices. It is of interest to know if the photon self-energy is the only exception to this rule, or if there are others, and which ones. In this paper we perform a refined power-counting analysis using real-time finite temperature field theory which is particularly well suited to the task. We show that the standard power-counting rules obtained from the imaginary time formalism usually over-estimate the size of the 2-loop diagrams. We argue that the only exceptions to the rule that the 1-loop soft diagrams give the next-to-leading order contribution are $2n$-photon vertices.

arXiv comment20 pages, 13 figures

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Cited by in corpus (9)

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• The HTL Lagrangian at NLO: the photon case
• Soft photon propagation in a hot and dense medium to next-to-leading order
• Ultrasoft fermion mode and off-diagonal Boltzmann equation in quark-gluon plasma at high temperature
• Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge
• NLO quark self-energy and dispersion relation using the hard thermal loop resummation
• NLO Dispersion Laws for Slow-Moving Quarks in HTL QCD