Partial $U(1)_A$ Restoration and $\eta$ Enhancement in High-Energy Heavy-Ion Collisions

Abstract

We calculate the thermally averaged rates for the $\eta$-$\pi$ conversion and $\eta$ scattering using the Di Vecchia-Veneziano model and t' Hooft model, which incorporate explicitly the $U(1)_A$ anomaly. Assuming an exponential suppression of the $U(1)_A$ anomaly, we also take into account the partial restoration of $U(1)_A$ symmetry at high temperatures. We find that the chemical equilibrium between $\eta$ and $\pi$ breaks up considerably earlier than the thermal equilibrium. Two distinct scenarios for the $\eta$ freeze-out are discussed and the corresponding chemical potentials are calculated. We predict an enhancement of the thermal $\eta$-production as a possible signal of the partial $U(1)_A$ restoration in high-energy heavy-ion collisions.