Chiral transition andU(1)Asymmetry restoration from lattice QCD using domain wall fermions

Abstract

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U (1) A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N τ = 8 and spatial extent N σ = 16 in a temperature range of T = 139 − 195 MeV, corresponding to lattice spacings of a ≈ 0.12 − 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m π = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U (1) A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U (1) A and chiral symmetry restoration via Banks-Casher relations.

Thermodynamics of strong-interaction matter from lattice QCD

“…The temperature dependence of the U A (1) breaking measure, χ π − χ δ , has been extensively studied using the DWF formalism for several volumes as well as quark masses. 59,61,109 As depicted in Fig. 8, calculations with DWF clearly show that χ π − χ δ does not vanish around the chiral crossover temperature T c and remains non-vanishing for 165 MeV T 195 MeV, independent of the light quark masses.…”

Relevance of the axial anomaly at the finite-temperature chiral transition in QCD

“…For N c = 3 and N f = 2 we have κ = 23/3. Although χ vanishes in the massless limit, the Dirac zero modes associated with the instantons induce a residual contribution to the U(1) A symmetry breaking, giving rise to a difference between the susceptibilities of the so-called π and δ channels at high T [17,18], which behaves as χ π − χ δ ∼ T −κ in the chiral massless limit.…”

“…The breaking of the U(1) A symmetry at finite T , and its role at the chiral transition, has been much investigated [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Monte Carlo (MC) simulations of lattice QCD [17][18][19][20][21][22][23][24][25] find a substantial suppression of the U(1) A anomaly effects at large T , as predicted by the DIG model.…”

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

“…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.…”