Abstract
We compute the effect of the chiral phase transition of QCD on the axion mass and self-coupling; the coupling of the axion to the quarks at finite temperature is described within the Nambu--Jona-Lasinio model. We find that the axion mass decreases with temperature, following the response of the topological susceptibility, in agreement with previous results obtained within chiral perturbation theory at low and intermediate temperatures. As expected, the comparison with lattice data shows that chiral perturbation theory fails to reproduce the topological susceptibility around the chiral critical temperature, while the Nambu--Jona-Lasinio model offers a better qualitative agreement with these data, hence a more reliable estimate of the temperature dependence of the axion mass in the presence of a hot quark medium. We complete our study by computing the temperature dependence of the self-coupling of the axion, finding that this coupling decreases at and above the phase transition. The model used in our work as well as the results presented here pave the way to the computation of the in-medium effects of hot and/or dense quark-gluon plasma on the axion properties.
Highlights
The current theory used to describe the strong interactions is QCD, which possesses the Uð1ÞA anomaly as well as the spontaneous breaking of chiral symmetry as some of its main features
We find that the axion mass decreases with temperature, following the response of the topological susceptibility, in agreement with previous results obtained within chiral perturbation theory at low and intermediate temperatures
We summarize the results for the axion mass and its self-coupling obtained within the NJL model around and above the QCD critical temperature, and we compare these with the same quantities computed within χPT
Summary
The current theory used to describe the strong interactions is QCD, which possesses the Uð1ÞA anomaly as well as the spontaneous breaking of chiral symmetry as some of its main features. Fð2Þ to the NJL Lagrangian, in which, according to the PQ mechanism, ha=fa þ θi 1⁄4 0; introducing the quantum fluctuation a 1⁄4 hai þ δa, renaming δa → a where a on denotes the axion field; and performing a chiral rotation that transfers the interaction of a with F · Fto the interaction of the a with the quarks After this chiral rotation is performed, we are left with an effective theory of the axion interacting with a thermal bath of quarks, the latter being capable of describing the important chiral crossover of QCD at finite temperature, which instead lacks in χPT.
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