Impact of chirality imbalance and nonlocal interactions on the QCD biased axionic domainwall interpretation of NANOGrav 15 year data

Abstract

We investigate the influence of the chirality imbalance with local CP-breaking in hot QCD on the generation of a stochastic gravitational wave background (SGWB) sourced by the axion-like particle (ALP) domain-wall annihilation, induced by the QCD bias. Such a bias is quantified by the QCD topological susceptibility $\chi_t$, and its dependence on the $\theta$ angle and the chiral chemical potential $\mu_5$ is investigated at temperatures near the QCD scale within a nonlocal Nambu-Jona-Lasinio (NJL) model. We find that, besides the small-$\theta$ range, the axionic domain-wall interpretation of NANOGrav 15-year data on the nHz gravitational waves is still possible for a certain large-$\theta$ range if $\mu_5$ is large enough. We confirm that the peak of $|\chi_t|$ at the critical temperature $T_c$ for the CP restoration at $\theta=\pi$ exhibits a pronounced width compared to the local NJL result. Thus, for $\theta$ at and around $\pi$, the QCD bias near $T_c$ can also produce a GW signal strength compatible with the NANOGrav 15-year data.