# Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group

## TL;DR

This study uses the functional renormalization group to analyze meson spectral functions at finite temperature and isospin density, revealing phase transitions and crossover behaviors in a two-flavor quark-meson model.

## Contribution

It introduces a comprehensive FRG approach to compute spectral functions and critical temperatures, capturing the transition from meson gas to quark gas and BEC-BCS crossover.

## Key findings

- Critical temperature increases when including meson two-point functions.
- Spectral functions show a transition from meson gas to quark gas with temperature.
- Crossover from BEC to BCS pairing occurs with increasing isospin density.

## Abstract

The pion superfluid and the corresponding Goldstone and soft modes are investigated in two-flavor quark-meson model with functional renormalization group. By solving the flow equations for the effective potential and the meson two-point functions at finite temperature and isospin density, the critical temperature for the superfluid increases sizeably in comparison with solving the flow equation for the potential only. The spectral function for the soft mode shows clearly a transition from meson gas to quark gas with increasing temperature and a crossover from BEC to BCS pairing of quarks with increasing isospin density.