NLO quark self-energy and dispersion relation using the hard thermal loop resummation

TL;DR

This paper computes the next-to-leading order quark self-energy and dispersion relations in a quark-gluon plasma using the hard-thermal-loop resummation in real-time formalism, providing detailed numerical results.

Contribution

It introduces a method to calculate NLO quark self-energy and dispersion laws incorporating HTL-effective vertices and four-point functions.

Findings

Numerical evaluation of NLO quark self-energy as a function of momentum and energy ratio.

Plots showing NLO corrections to quark dispersion relations.

Explicit expressions for NLO self-energy in terms of HTL-effective vertices.

Abstract

Using the hard-thermal-loop (HTL) resummation in real-time formalism, we study the next-to-leading order (NLO) quark self-energy and corresponding NLO dispersion laws. In NLO, we have replaced all the propagators and vertices with the HTL-effective ones in the usual quark self-energy diagram. Additionally, a four-point vertex diagram also contributes to the quark NLO self-energy. We calculate the usual quark self-energy diagram and the four-point vertex diagram separately. Using those, we express the NLO quark self-energy in terms of the three- and four-point HTL-effective vertex functions. Using the Feynman parametrization, we express the integrals containing the three- and four-point HTL effective vertex functions in terms of the solid angles. After completing the solid angle integrals, we numerically calculate the momentum integrals in the NLO quark self-energy and plot them as a function of the ratio of momentum and energy. Using the NLO quark self-energy, we plot the NLO correction to dispersion laws.