Masses and decay constants of (axial-)vector mesons at finite chemical potential

TL;DR

This paper investigates how (axial-)vector meson properties like masses and decay constants behave at finite chemical potential using Dyson-Schwinger and Bethe-Salpeter equations, confirming the Silver-Blaze property and analyzing phase transition effects.

Contribution

It extends previous studies by including (axial-)vector mesons at finite chemical potential and provides detailed bound-state property calculations within the Dyson-Schwinger framework.

Findings

Meson masses and decay constants remain constant up to the phase transition.

Inside the coexistence region, the pion mass increases and decay constants decrease.

(Axial-)vector meson properties are largely unaffected across the phase transition.)

Abstract

We update our previous results for (pseudo-)scalar mesons at zero temperature and finite quark chemical potential and generalize the investigation to include (axial-)vector mesons. We determine bound-state properties such as meson masses and decay constants up to chemical potentials far in the first-order coexistence region. To extract the bound-states properties, we solve the Bethe-Salpeter equation and utilize Landau-gauge quark and gluon propagators obtained from a coupled set of (truncated) Dyson-Schwinger equations with N$_\textup{f}=2+1$ dynamical quark flavors at finite chemical potential and vanishing temperature. For multiple (pseudo-)scalar and (axial-)vector mesons, we observe constant masses and decay constants for chemical potentials up to the coexistence region of the first-order phase transition thus verifying explicitly the Silver-Blaze property of QCD. Inside the coexistence region the pion becomes more massive and its decay constants decrease, whereas corresponding quantities for the (axial-)vector mesons remain (almost) constant.