# Quarks and light (pseudo-)scalar mesons at finite chemical potential

## TL;DR

This paper studies how light scalar and pseudoscalar mesons behave at finite quark chemical potential using Dyson-Schwinger equations, revealing constant meson properties up to the phase transition and confirming the Silver-Blaze property.

## Contribution

It extends Dyson-Schwinger equation analysis to finite chemical potential for light mesons, including charge-parity breaking and Silver-Blaze property validation.

## Key findings

- Meson masses and decay constants remain constant below the phase transition.
- Charge-conjugation parity breaking occurs with increasing chemical potential.
- The Silver-Blaze property is confirmed for colored quantities.

## Abstract

We investigate the properties of light scalar and pseudoscalar mesons at finite (light) quark chemical potential. To this end we solve a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators in Landau-gauge QCD and extent earlier results for $N_f=2+1$ dynamical quark flavors to finite chemical potential at zero temperature. We then determine the meson bound state masses, wave functions, and decay constants for chemical potentials below the first-order phase transition from their homogeneous Bethe-Salpeter equation. We study the changes in the quark dressing functions and Bethe-Salpeter wave functions with chemical potential. In particular, we trace charge-conjugation parity breaking. Furthermore, we confirm the validity of the Silver-Blaze property: all dependencies of colored quantities on chemical potential cancel out in observables and we observe constant masses and decay constants up to and into the coexistence region of the first-order chiral phase transition.