Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology

Vicente Azcoiti

doi:10.1051/epjconf/201817504007

Abstract

The axion is one of the more interesting candidates to make the dark matter of the universe, and the axion potential plays a fundamental role in the determination of the dynamics of the axion field. Moreover, the way in which the U(1)A anomaly manifests itself in the chiral symmetry restored phase of QCD at high temperature could be tested when probing the QCD phase transition in relativistic heavy ion collisions. With these motivations, we investigate the physical consequences of the survival of the effects of the U(1)A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the σ and π susceptibilities diverge in this limit at any T ≥ Tc. We also show that the difference between the π and δ susceptibilities diverges in the chiral limit at any T ≥ Tc, a result that can be contrasted with the existing lattice calculations; and discuss on the generalization of these results to the Nf ≥ 3 model.

Highlights

We report the results of an investigation on the physical consequences of the survival of the topological effects of the axial anomaly in the high temperature phase of QCD
We investigate the physical consequences of the survival of the effects of the U(1)A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the σ and πsusceptibilities diverge in this limit at any T ≥ Tc
The main conclusion obtained from this hypothesis was that all the topological effects of the axial anomaly should disappear in this phase, the topological susceptibility and all θ-derivatives of the free energy density vanish, and the theory becomes θ-independent at any T > T c in the infinite-volume limit

Summary

Introduction

To summarize the main results, our starting hypothesis in [1] was to assume that the perturbative expansion of the free energy density in powers of the quark mass, m, has a non-vanishing convergence radius in the high temperature chiral symmetric phase of QCD. The free energy density should be a singular function of the quark mass, in the chiral limit, if the topological effects of the U(1)A anomaly survive in the chiral symmetry restored phase of QCD at finite temperature, and the main purpose of reference [2] was to investigate this issue.

Results

Conclusion