S-parameter at Non-Zero Temperature and Chemical Potential

TL;DR

This paper calculates how finite temperature and chemical potential affect the S-parameter, revealing a reduction at small momenta and implications for lattice simulations in high-energy physics.

Contribution

It introduces a generalized S-parameter at non-zero temperature and density, accounting for Lorentz symmetry breaking and plasma corrections.

Findings

S-parameter decreases at small external momenta with non-zero T and chemical potential

S-parameter vanishes at small m/T due to finite temporal extent

Results applicable to lattice simulations with anti-periodic boundary conditions

Abstract

We compute the finite-temperature and matter density corrections to the S-parameter at the one loop level. At non-zero temperature T and matter density Lorentz symmetry breaks and therefore we suggest a suitable generalization of the S-parameter. By computing the plasma correction, we discover a reduction of the S-parameter in the physically relevant region of small external momenta for any non-zero chemical potential and T. In particular, the S-parameter vanishes at small m/T, where m is the mass of the fermions, due to the finite extent of the temporal direction. Our results are directly applicable to the determination of the S-parameter via first principle lattice simulations performed with anti-periodic boundary conditions in the temporal direction.