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

Gergely Fejős, Daiki Suenaga

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-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.

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

Abstract

We investigate the thermal properties of hadrons in two-color quantum chromodynamics (QCD) using the functional renormalization group (FRG) method, with particular focus on modifications of the axial anomaly effects. The hadrons are described by a linear sigma model (LSM) based on the Pauli-Gürsey symmetry, which incorporates both low-lying 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 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 QCD medium is examined.

Paper Structure

This paper contains 15 sections, 65 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Two-flavor LSM in QC$_2$D
  3. FRG approach
  4. Basics
  5. General structures
  6. Flowing couplings
  7. Numerical results
  8. Inputs
  9. Hadron masses at finite $T$
  10. Enhancement of anomaly effects at finite $T$
  11. Topological susceptibility
  12. Importance of baryonic contributions
  13. Conclusions
  14. Derivation of flow equations for $\lambda_{1k}$, $\lambda_{2k}$, $c_{1k}$, and $c_{2k}$
  15. Hadron mass formulas

Figures (8)

  • Figure 1: $T$ dependencies of the masses of $\eta$, $\pi$, $\sigma$, and $a_0$ mesons with $\mathring{M}_\eta=0.3$, $0.5$, and $0.95$ GeV.
  • Figure 2: $T$ dependencies of the mass differences $\Delta M_{(\sigma.\pi)}$ and $\Delta M_{(a_0.\eta)}$ with $\mathring{M}_\eta=0.3$, $0.5$, and $0.95$ GeV.
  • Figure 3: $T$ dependencies of the normalized anomaly coefficients $\tilde{a}$, $\tilde{c}_1$, and $\tilde{c}_2$ defined in Eq. (\ref{['AnomalyNormalized']}), with $\mathring{M}_\eta=0.3$, $0.5$ and $0.95$ GeV.
  • Figure 4: $T$ dependencies of the mean field $\sigma_0$ with $\mathring{M}_\eta=0.3$, $0.5$, and $0.95$ GeV.
  • Figure 5: $T$ dependencies of the normalized topological susceptibilities $\chi_{\rm top}$ (solid lines) and $\tilde{\chi}_{\rm top}$ (dashed lines) defined in Eqs. (\ref{['ChiTop1']}) and (\ref{['ChiTop2']}), respectively, with $\mathring{M}_\eta=0.3$, $0.5$, and $0.95$ GeV.
  • ...and 3 more figures