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

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.

35 pages, 19 figures

References in corpus (8)

• NNLO hard-thermal-loop thermodynamics for QCD
• The fermion mass at next-to-leading order in the HTL effective theory
• Real time statistical field theory
• Soft photon propagation in a hot and dense medium to next-to-leading order
• Degenerate fermionic matter at N${}^3$LO: Quantum Electrodynamics
• The soft fermion dispersion relation at next-to-leading order in hot QED
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• NLO Dispersion Laws for Slow-Moving Quarks in HTL QCD

Cited by in corpus (1)

• Hard Thermal Loop -- theory and applications