[Paper Review] Fermion damping rate in a hot medium

Peter A. Henning, R. Sollacher+1 more|ArXiv.org|Sep 12, 1994

Physics of Superconductivity and Magnetism1 references3 citations

TL;DR

This paper calculates the self-consistent damping rate of massive fermions in a hot medium, coupled to massless scalar, vector, and pseudoscalar bosons. Using a resummation of Fock diagrams, it eliminates infrared divergences without requiring boson screening, yielding analytical results in the coupling constant but non-analytic behavior in temperature near T=0.

ABSTRACT

In principle every excitation acquires a finite lifetime in a hot system. This nonzero spectral width is calculated self-consistently for massive fermions coupled to massless scalar, vector and pseudoscalar bosons. It is shown that the self-consistent summation of the corresponding Fock diagram for fermions eliminates all infrared divergences although the bosons are not screened at all. Our solutions for the fermion damping rate are analytical in the coupling constant, but not analytical in the temperature parameter around T=0.

Motivation & Objective

• To determine the damping rate of massive fermions in a finite-temperature medium.
• To resolve infrared divergences in fermion self-energy calculations without assuming boson screening.
• To provide a self-consistent, non-perturbative resummation of Fock diagrams for fermion damping.
• To analyze the analytic structure of the damping rate in the coupling constant and temperature, particularly near T=0.

Proposed method

• Employing a self-consistent resummation of Fock diagrams in finite-temperature field theory.
• Using real-time formalism to compute the imaginary part of the fermion self-energy, related to the damping rate.
• Considering coupling to massless scalar, vector, and pseudoscalar bosons in a hot medium.
• Applying a non-perturbative resummation technique that removes infrared divergences even when bosons are unscreened.
• Deriving analytical expressions for the damping rate in terms of the coupling constant.
• Analyzing the temperature dependence, especially the non-analytic behavior at T=0.

Experimental results

Research questions

• RQ1 How does the fermion damping rate behave in a hot medium when bosons are not screened?
• RQ2 Can infrared divergences in the fermion self-energy be removed through self-consistent resummation of Fock diagrams?
• RQ3 What is the analytic structure of the damping rate in the coupling constant and temperature, particularly near T=0?
• RQ4 How do different types of massless bosons (scalar, vector, pseudoscalar) contribute to the damping rate?
• RQ5 Is the damping rate expressible in closed analytical form without perturbative assumptions?

Key findings

• The self-consistent resummation of Fock diagrams successfully removes all infrared divergences, even without screening of the bosons.
• The resulting damping rate is analytical in the coupling constant, indicating a well-defined perturbative expansion in this parameter.
• The damping rate exhibits non-analytic behavior in the temperature parameter around T=0, signaling a breakdown of naive perturbation theory at low temperatures.
• The method applies uniformly to scalar, vector, and pseudoscalar boson couplings, showing robustness across different interaction types.
• The results are exact within the framework of the resummation approach and provide a consistent description of fermion width in thermal field theory.