Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the UA(1) Symmetry

Davor Horvatić,Dalibor Kekez,Dubravko Klabučar

doi:10.3390/universe5100208

Davor Horvatić, Dalibor Kekez + Show 1 more

Open Access

https://doi.org/10.3390/universe5100208

Copy DOI

Journal: Universe	Publication Date: Oct 8, 2019
Citations: 4	License type: CC BY 4.0

Affiliation: University of Zagreb, Rudjer Boskovic Institute

Abstract

The temperature (T) dependence of the axion mass is predicted for T ′ s up to ∼ 2 . 3 × the chiral restoration temperature of QCD. The axion is related to the U A ( 1 ) anomaly. The squared axion mass m a ( T ) 2 is, modulo the presently undetermined scale of spontaneous breaking of Peccei–Quinn symmetry f a (squared), equal to QCD topological susceptibility χ ( T ) for all T. We obtain χ ( T ) by using quark condensates calculated in two effective Dyson–Schwinger models of nonperturbative QCD. They exhibit the correct chiral behavior, including the dynamical breaking of chiral symmetry and its restoration at high T. This is reflected in the U A ( 1 ) symmetry breaking and restoration through χ ( T ) . In our previous studies, such χ ( T ) yields the T-dependence of the U A ( 1 ) -anomaly-influenced masses of η ′ and η mesons consistent with experiment. This in turn supports our prediction for the T-dependence of the axion mass. Another support is a rather good agreement with the pertinent lattice results. This agreement is not spoiled by our varying u and d quark mass parameters out of the isospin limit.

Highlights

The axion, one of the oldest hypothetical particles beyond the Standard Model, intensely sought for by many experimentalists already for 40 years still escapes detection [1]
While an intimate relation between the axion and η ′ doubtlessly exists, reformulations of the axion theory, let alone so drastic ones, are not needed to exploit this axion-η ′ relationship: thanks to the fact that both of their masses stem from the axial anomaly and are determined by the topological susceptibility of QCD, in the present paper we show how our previous study [17] of the temperature (T) dependence of the η ′ and η mesons give us a spin-off in the form of the T-dependence of the axion mass, ma (T)
Peccei and Quinn (PQ) introduced [2,3] a new global symmetry U(1)PQ which is broken spontaneously at some very large, but otherwise still unknown scale fa > 108 GeV [1,73], which determines the absolute value of the axion mass ma

Summary

Introduction

The axion, one of the oldest hypothetical particles beyond the Standard Model, intensely sought for by many experimentalists already for 40 years still escapes detection [1]. Tc. Here Figure 2 illustrates this generic behavior by displaying the results obtained in Section 3 for a specific DSE model: the higher current quark mass, the smoother the crossover behavior, which results in the crossover behavior of other quantities, like the presently all-important quantity, the QCD topological susceptibility χ(T). This comes about as follows: the quantity which in Shore’s mass relations [69] has the role of χYM in the Witten–Veneziano relation, is called the full-QCD topological charge parameter A. Will suffice to yield the crossover behavior found on lattice ( e.g., in Refs. [70,71,72])

The Axion Mass from the Non-Abelian Axial Anomaly of QCD

The Axion as the Almost-Goldstone Boson of the Peccei–Quinn Symmetry

Summary and Discussion