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

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-Gürsey $SU(4)$ 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.

💡 Research Summary

In this work the authors study the thermal behavior of two‑color quantum chromodynamics (QC₂D) by means of the functional renormalization group (FRG) applied to a linear sigma model (LSM) that respects the Pauli‑Gürsey SU(4) symmetry. The model contains the full set of low‑lying scalar and pseudoscalar mesons as well as scalar diquark baryons, which are color singlets in the SU(2) color group. The effective potential is built from the SU(4) invariants I₁ = tr