Fermionic dispersion relations at finite temperature and non-vanishing chemical potentials in the minimal standard model

TL;DR

This paper derives gauge-invariant fermionic dispersion relations at finite temperature and chemical potentials within the minimal standard model, focusing on the unbroken electroweak phase using thermal field theory.

Contribution

It provides the first analytical gauge-invariant expressions for fermionic dispersion relations considering non-zero chemical potentials in the minimal standard model.

Findings

Dispersion relations are obtained at leading order in temperature and chemical potential.

Expressions are gauge invariant and valid in the unbroken electroweak phase.

Calculations are performed in the real-time formalism at one-loop order.

Abstract

We calculate the fermionic dispersion relations in the minimal standard model at finite temperature in presence of non-vanishing chemical potentials due to the CP-asymmetric fermionic background. The dispersion relations are calculated for a vacuum expectation value of the Higgs field equal to zero (unbroken electroweak symmetry). The calculation is performed in the real time formalism of the thermal field theory at one-loop order in a general $\xi$ gauge. The fermionic self-energy is calculated at leading order in temperature and chemical potential and this fact permits us to obtain gauge invariant analytical expressions for the dispersion relations.