Roles of $U(1)$ axial anomaly effects in cold and dense two-color QCD with $2+2$ flavors

TL;DR

This work investigates flavor-symmetry violation and $U(1)_A$ anomaly effects in cold, dense $QC_2D$ with $2+2$ flavors using a Pauli-Gürsey–inspired $SU(8)$ linear sigma model, complemented by an NJL analysis. The anomaly term $c$ induces flavor mixing between light and heavy sectors, and diquark condensation in the light sector leads to a baryon superfluid phase in which heavy quark physics is significantly modified, including enhancement of the heavy chiral condensate $\langle\bar{Q}Q\rangle$ and potential heavy-diquark condensation. The study finds that topological susceptibility $\chi_{top}$ is suppressed with increasing density, largely independent of the anomaly strength, and reports a possible complete inverse mass hierarchy for negative-parity diquarks when the anomaly is strong. A heavy-diquark–driven superfluid phase and anomaly-enhanced heavy-quark dynamics are corroborated by an NJL treatment, providing a coherent framework for lattice QC$_2D$ checks of flavor-symmetry violation and heavy-flavor effects in dense matter. The results offer concrete predictions for lattice simulations and deepen understanding of how the $U(1)_A$ anomaly shapes hadron spectra and phase structure in two-color QCD.

Abstract

We explore phase structures and hadron mass spectra in cold and dense two-color QCD with $2+2$ flavors where the sign problem disappears. We particularly focus on $U(1)$ axial anomaly effects. We employ an $N_f=2+2$ linear sigma model based on the $SU(8)$ Pauli-Gürsey symmetry to describe negative-parity as well as positive-parity hadrons, for which low-energy excitations are appropriately described particularly in the baryon superfluid phase with light diquark condensates. As a result, the strange chiral condensate is found to be enhanced in the superfluid phase owing to the flavor-mixing structure of $U(1)$ axial anomaly effects. We also confirm this enhancement by means of the Nambu--Jona-Lasinio model. Besides, our present analysis predicts the existence of a novel superfluid phase where heavy diquarks condense in dense regime. The topological susceptibility with $2+2$ flavors from the viewpoints of the anomaly effects and chiral-symmetry restoration is investigated. Furthermore, we derive a complete inverse mass hierarchy for negative-parity diquarks with sufficient anomaly effects. Our findings are expected to provide future lattice simulations with useful information on flavor-symmetry violation from the $U(1)$ axial anomaly aspects in cold and dense two-color QCD medium.

Figures (14)

• Figure 1: Top: the eight-point interaction generated by the anomalous $c$ term. Bottom: two types of the anomalous contributions to the potential $V_{\rm LSM}$.
• Figure 2: $\mu_q$ dependences of $\phi_Q$ with several values of $c$ (top). We also present those of $\phi_q$ (middle) and $\Delta_q$ (bottom) for completeness. The vertical dotted line indicated $\mu_q^{\rm cr} = m_{\pi_{qq}}^{\rm vac}/2$.
• Figure 3: $\mu_q$ dependences of $\sqrt{\phi_q^2+\Delta_q^2}$ with several values of $c$.
• Figure 4: Mass spectra of light $0^+$ (left) and $0^-$ (right) hadrons at finite $\mu_q$ ($\mu_q=\mu_Q$), with the parameter set I with $c=1$ (top) and set II with $c=0$ (bottom) in Table \ref{['tab:Parameters']}. The masses are normalized by $m_{\pi_{qq}}^{\rm vac}$. The masses of $\sigma_{h}$ and $\eta_{h}$ are also exhibited in these panels owing to the mixings.
• Figure 5: Mass spectra of heavy-light $0^+$ (left) and $0^-$ (right) hadrons at finite $\mu_q$ ($\mu_q=\mu_Q$). The same parameters as in Fig. \ref{['fig:MassLLHH']} are adopted.