Chiral symmetry and axial U(1) symmetry in finite temperature QCD with domain-wall fermion

摘要

We study the restoration of the spontaneously broken chiral symmetry and theanomalously broken axial U(1) symmetry in finite temperature QCD at zerochemical potential. We use 2 flavors lattice QCD with optimal domain-wallfermion on the $ 16^3 \times 6 $ lattice, with the extent $ N_s = 16 $ in thefifth dimension, in the temperature range $ T = 130-230 $ MeV. To examine therestoration of the chiral symmetry and the axial $ U(1) $ symmetry, we usediluted $ Z_2 $ noises to calculate the chiral condensate, and the chiralsusceptibilities in the scalar and pseudoscalar meson channels, for flavorsinglet and non-singlet respectively. From the degeneracy of the chiralsusceptibilities around $ T_c $, it suggests that the axial $ U(1) $ symmetryis restored in the chirally symmetric phase. Moreover, we examine the spectraldensity $ \rho(\lambda_c) $ of the 4D effective Dirac operator with exactchiral symmetry, which is obtained by computing zero modes plus (180+180)conjugate pairs of low-lying modes for each gauge configuration. Thesuppression of low modes in the spectral density provides a consistency checkof the restoration of axial $ U(1) $ symmetry in the chirally symmetric phase.