Thermal and baryon density modifications to the $\sigma$-boson propagator: A road to describe the transfer of vorticity to spin in a nuclear environment in relativistic heavy-ion collisions

TL;DR

This paper calculates the $\sigma$-meson propagator at finite temperature and baryon density to understand how vortical motion in heavy-ion collisions transfers to hadron spin, focusing on medium modifications relevant for hyperon polarization.

Contribution

It provides a detailed computation of the $\sigma$-meson propagator considering thermal and baryon density effects, including dispersion relations and spectral density, for the first time in this context.

Findings

The $\sigma$-mass is significantly affected by temperature and baryon chemical potential.

Landau damping contributes to the spectral density of the $\sigma$-meson.

Approximate dispersion relations are derived for different momentum regimes.

Abstract

In the context of the description of how the vortical motion, produced in peripheral heavy-ion collisions, is transferred to the spin of hadrons, we compute the $\sigma$-meson propagator at finite temperature and baryon density. This propagator encodes the properties of a medium consisting mainly of nucleons{, and can be used to model the main interactions between hadrons} in the corona region of the reaction. We compute the one-loop $\sigma$ self-energy in an approximation that accounts for the large nucleon mass. From the real part of the self-energy, we find the dispersion relation and show that the $\sigma$-mass receives a non-negligible thermal and baryon chemical dependent {contribution}. From the imaginary part, we also compute the spectral density, which we show to contain a piece coming from the branch cut associated with Landau damping. We also present approximations for the dispersion relation and the residue at the pole in the small- and large-momentum regimes and complement the calculation, providing the sum rules satisfied by the propagator. This study aims to determine one of the elements needed to compute how the vortical motion in the corona region of the reaction is transferred to the spin of $\Lambda$ hyperons that can interact with nucleons by $\sigma$-meson exchange.