Functional renormalization for chiral andUA(1)symmetries at finite temperature

Abstract

We investigated the chiral symmetry and UA(1) anomaly at finite temperature by applying the functional renormalization group to the SU (3) linear sigma model. Expanding the local potential around the classical fields, we derived the flow equations for the renormalization parameters. In chiral limit, the flow equation for the chiral condensate is decoupled from the others and can be analytically solved. The Goldstone theorem is guaranteed in vacuum and at finite temperature, and the two phase transitions for the chiral and UA(1) symmetry restoration happen at the same critical temperature. In general case with explicit chiral symmetry breaking, the two symmetries are partially and slowly restored, and the scalar and pseudoscalar meson masses are controlled by the restoration in the limit of high temperature.

AUA(1)symmetry restoration scenario supported by the generalized Witten–Veneziano relation and its analytic solution

“…The present paper stresses it is important that such experiments look for signatures (primarily related to the η -η complex) that would test the scenario of Ref. [14] (and related ideas [19,20,[40][41][42]) on the relationship between the U A (1) and SU A (3) chiral symmetry breaking and restoration.…”

QCD phase structure at finite temperature and density

“…In the present Euclidean setup we are restricted to p 2 0 ≥ 0. The approximation Z π (im π,pol , 0) ≈ Z π (0, 0) ≡ Z π (0) is therefore the optimal choice for the wave function renormalisation in (87), as it is closest to the pion pole. Since this pole, in turn, is close to the origin in the region where mesons are dynamically relevant, this approximation is even quantitative if Z π (p) is only mildly momentum dependent in the small region |p 2 | m 2 π .…”

Updated study of the η−η′ mixing and the thermal properties of light pseudoscalar mesons at low temperatures

“…The pion-mass dependences of the averages of the mixing angles θ q and θ s are shown, where θ q and θ s are mixing angles defined in the quark-flavor basis in Eq. (9). The lattice data are taken from Ref.…”

“…The thermal behaviors of the topological and chiral susceptibilities serve as useful theoretical objects to discriminate different patterns of the U A ð1Þ and chiral symmetry restoration and have been extensively investigated by many lattice simulations [18][19][20][21] and effective theory studies [8][9][10][11][12][13][14][15][16][17]. The masses of the light flavor pseudoscalar mesons π, K, η and η 0 will be definitely affected by the restoration of the U A ð1Þ and chiral symmetries.…”

“…[7,10,19] show that there is no obvious drop of the η 0 mass even in the relatively high temperature region above T c . The puzzling problem has intrigued many studies in both lattice simulations and phenomenological discussions [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”