Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation

Abstract

We examine the axial U (1) symmetry near and above the finite temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U (1) symmetry is always violated by quantization, i.e. the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a 16 3 × 8 lattice with two flavors of dynamical quarks represented by the overlap fermion formalism. Chiral symmetry and its violation due to the axial anomaly is manifestly realized with this formulation, which is a prerequisite for the study of the effective restoration of the axial U (1) symmetry. In order to avoid discontinuity in the gauge configuration space, which occurs for the exactly chiral lattice fermions, the simulation is confined in a fixed topological sector. It induces finite volume effect, which is well described by a formula based on the Fourier transform from the θ-vacua. We confirm this formula at finite temperature by calculating the topological susceptibility in the quenched theory. Our two flavor simulations show degeneracy of the meson correlators and a gap in the Dirac operator spectral density, which implies that the axial U (1) symmetry is effectively restored in the chirally symmetric phase.PACS numbers:

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

“…Another lattice analysis based on meson screening masses pointing towards Uð1Þ A restoration taking place above T c is [41], for two flavors and two colors. On the other hand, the lattice results in [42][43][44] are consistent with Uð1Þ A restoration taking place at the chiral transition or very close above it. These simulations are performed in the chiral limit for two flavors.…”

Thermodynamics of strong-interaction matter from lattice QCD

“…Moreover, results obtained with chiral fermions are still controversial. Calculations performed with dynamical overlap fermions 60,110 and so-called optimal domain wall fermions 111 at present suggest that U A (1) does get restored already at T c , which would still allow for the occurrence of a first order transition when approaching the chiral limit. The procedure to calculate bulk thermodynamic observables in lattice QCD is well established.…”

“…However, with increasing speed of super-computers calculations with physical light quark masses become feasible and chiral fermions have been used recently also for QCD thermodynamics studies. [59][60][61][62] In particular in the analysis of subtle aspects of the QCD transition related to the temperature dependence of the axial anomaly, calculations with fermions obeying exact chiral symmetry already at non-zero values of the cut-off are mandatory.…”

Topology in QCD and the axion abundance

“…Meanwhile, the analysis in ref. [21] suggests the effective restoration of U A (1) symmetry right above the critical temperature, indicating the disappearance of the instanton effects. The presence or absence of the U A (1) symmetry at the critical temperature T c can also be inferred through the nature of the chiral phase transition of massless two flavor QCD as attempted in, e.g., ref.…”