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

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 ≥ T c. We also show that the difference between theπ andδ susceptibilities diverges in the chiral limit at any T ≥ T c , a result that can be contrasted with the existing lattice calculations; and discuss on the generalization of these results to the N f ≥ 3 model. ⋆ Acknowledges financial support by Ministerio de Economía y Competitividad under Grant No. FPA2015-65745-P (MINECO/FEDER).

Patterns and partners for chiral symmetry restoration

“…Therefore, our results here are fully consistent with [39]. Let us remark that in the light chiral limitm → 0 þ , neithermχ 5;disc nor χ 8A P in (19) vanishes at T ¼ 0.…”

“…The same conclusion about the vanishing of χ top for any temperature above chiral restoration has been reached in [39]. Note that the main argument in that work actually relies on the identity,…”

“…Although χ top is particularly difficult to measure in the lattice [5,29,30], its vanishing or asymptotic reduction indicates Uð1Þ A restoration, as the system becomes less sensitive to the P-breaking anomaly contribution parametrized in the θ term [39].…”

Chiral and U(1)A restoration for the scalar and pseudoscalar meson nonets

“…Namely, at T ¼ 0 the results in [50] show that χ 8A P has a finite limit form → 0 þ , which together with (25) imply χ 5;disc ∼ 1=m and χ top ∼m away from T c . The latter behavior for χ top is actually supported in the recent work [31], where it is argued that χ top ∼mhqqi l in the chiral limit. More discussion about the chiral limit of the different susceptibilities will be carried out within ChPT in Sec.…”

“…In addition, screening and pole masses at Uð1Þ A restoration within the NJL model are studied in [29,30]. A recent work intimately connected with our present analysis is [31], where the Oð4Þ and Uð1Þ A transitions are studied in terms of the topological susceptibility.…”