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

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.2 of 23 mass-eigenstate basis, one diagonalizes the mass matrix, and the corresponding chiral transformation changes θ by arg det M. Hence, in the Standard Model the coefficient of the Q ∝ FF term is in fact. Therefore, to be precise, we change our notation toθ-term, L θ → Lθ.Since CP is not a symmetry of the Standard Model, there is no a priori reasonθ, which results from the contributions from both the strong and weak interactions, should vanish. And yet, the experimental bound on it is extremely low, θ < 10 −10 [9], and in fact consistent with zero. Therefore, the mystery of the vanishing strong CP violation is: why isθ so small?The most satisfactory answer till this very day has been provided by axions, even though the original variant has been ruled out [1]. In the meantime, they turned out to be very important also for cosmology, as promising candidates for dark matter-see from relatively recent references such as [10,11] to the earliest papers [12][13][14]. (For an example of a broader review of axion physics, see [15].) It is thus no wonder that ever since the original proposal of the axion mechanism [2-5] in 1977-1978, many theorists kept developing various ideas on this theoretically much needed object, trying to pinpoint the properties of this elusive particle and increase chances of finding it.However, to no avail. There have even been some speculations that the axion is hidden in plain sight, by being experimentally found, paradoxically, already years before it was conjectured theoretically: namely, that the axion should in fact be identified with the well-known η ′ meson with a minuscule admixture of a pseudoscalar composite of neutrinos [16]. Nevertheless, while an intimate relation between the axion and η ′ doubtlessly exists, reformulations of the axion theory, let alone so drastic ones, are in fact not needed to exploit this axion-η ′ relationship: thanks to the fact that both of their masses stem from the axial anomaly...

T-dependence of the axion mass when the U_A(1) and chiral symmetry breaking are tied

“…Hence, the (partial) U A (1) restoration observed in Ref. [11] must also be a crossover, which in the present work, as well as in its longer counterpart [30] containing a detailed analysis of the model parameter dependence, translates into the corresponding smooth T -dependence of the axion mass.…”

Perturbative RG Analysis of the Condensate Dependence of the Axial Anomaly in the Three-Flavor Linear Sigma Model

“…One, therefore, repeats the calculations starting from (16), but this time expands only in terms of s 8 so that the ρ dependence of the parameters can be traced via s 0 . A long but straightforward calculation leads once again to the possibility of identifying the invariants appear in (17), whose coefficients now read as…”

“…For example, earlier renormalization group studies indicate that when considering a fielddependent anomaly coefficient, it decreases as a function of the chiral condensate [11,14], and this profile function can also depend explicitly on the tempereture (though the former effect is more dominant). Effective restoration of the anomaly has, e.g., a consequence regarding the order of the chiral transition [15], the axion mass [16], and the fate of η meson, whose mass if substantially drops [17][18][19][20][21][22], in a nuclear medium could lead to the formation of an η -nucleon bound state.…”

Perturbative RG analysis of the condensate dependence of the axial anomaly in the three flavor linear sigma model

“…There are also several arguments and results that indicate that it might be reasonable to assume that it is visible even beyond T C [8,9,10,11,12]. Effective restoration of the anomaly has, e.g., a consequence regarding the order of the chiral transition [13], the axion mass [14], and the fate of η ′ meson, whose mass if substantially drops [15,16,17,18,19,20], in a nuclear medium could lead to the formation of an η ′ -nucleon bound state.…”