Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model

TL;DR

This study uses the FRG method within a linear sigma model to explore how the $U(1)$ axial anomaly effects are enhanced in hot two-color QCD, revealing small mass differences among chiral partners and the impact of baryonic fluctuations.

Contribution

It introduces a FRG-based analysis of the axial anomaly effects in hot two-color QCD using a linear sigma model with $SU(4)$ symmetry, highlighting anomaly enhancement at finite temperature.

Findings

Mass differences among chiral partners remain small at finite temperature.

Couplings related to the $U(1)$ axial anomaly are enhanced in hot medium.

Baryonic fluctuations significantly contribute to anomaly enhancement.

Abstract

We investigate the thermal properties of hadrons in two-color quantum chromodynamics (QC$_2$D) using the functional renormalization group (FRG) method, with particular focus on modifications of the $U(1)$ axial anomaly effects. The hadrons are described by a linear sigma model (LSM) based on the Pauli-G\"{u}rsey $SU(4)$ symmetry, which incorporates both low-lying $0^\pm$ mesons and diquark baryons. We find that all quartic couplings are comparably suppressed when physical values of the pion mass and decay constant are taken as inputs, for which a reasonably smooth chiral symmetry restoration at finite temperature is reproduced. Consequently, mass differences among chiral partners remain small. Despite these tiny mass differences, mass degeneracies of chiral partners in the hot medium are clearly demonstrated, consistent with chiral symmetry restoration. Moreover, we find that the couplings responsible for the $U(1)$ axial anomaly are enhanced upon entering the finite temperature regime. Baryonic fluctuations also provide sizable contributions to these enhancements. Finally, the fate of the topological susceptibility in the hot QC$_2$D medium is examined.