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Register a new userAxial $U(1)$ symmetry at high temperature in 2-flavor lattice QCD
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We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical Mobius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 , mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.
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We investigate the high-temperature phase of QCD using lattice QCD simulations with $N_f = 2$ dynamical Mobius domain-wall fermions. On generated configurations, we study the axial $U(1)$ symmetry, overlap-Dirac spectra, screening masses from mesonic correlators, and topological susceptibility. We find that some of the observables are quite sensitive to lattice artifacts due to a small violation of the chiral symmetry. For those observables, we reweight the Mobius domain-wall fermion determinant by that of the overlap fermion. We also check the volume dependence of observables. Our data near the chiral limit indicates a strong suppression of the axial $U(1)$ anomaly at temperatures $geq$ 220 MeV.
Using lattice QCD simulations with $N_f = 2$ dynamical fermions, we study the axial $U(1)$ symmetry, topological charge, and Dirac eigenvalue spectra in the high-temperature phase in which the chiral symmetry is restored. Our gauge ensembles are generated with Mobius domain-wall fermions, but the measurements such as susceptibilities are reweighted to those for the overlap fermions by using overlap/domain-wall reweighting technique. We find that the $U(1)_A$ and topological susceptibilities are strongly suppressed in the small quark mass region, which is related to the reduction of chiral-zero and low-nonzero modes on the Dirac spectra. We also examine their volume dependence.
The axial $U(1)$ symmetry in the high-temperature phase is investigated with $N_f = 2$ lattice QCD simulations. The gauge ensembles are generated with Mobius domain-wall fermions, and the overlap/domain-wall reweighting is applied. We find that the $U(1)_A$ susceptibility evaluated from the spectrum of overlap-Dirac eigenvalues is strongly suppressed in the chiral limit. We also study its volume dependence.
The current status of some nucleon isovector observables, the vector charge, (g_V), axial charge, (g_A), quark momentum fraction, (langle x rangle_{u-d}), and quark helicity fraction, (langle x rangle_{Delta u - Delta d}), calculated using recent RBC/UKQCD 2+1-flavor dynamical domain-wall fermions (DWF) lattice QCD ensembles are reported: with Iwasaki gauge action at inverse lattice spacing, (a^{-1}), of about 1.7 GeV, linear lattice extent, (L), of about 2.7 fm, pion mass, (m_pi), of about 420 and 330 MeV, and with Iwasaki(times)DSDR gauge action at (a^{-1}) of about 1.4 GeV, (L) of about 4.6 fm, and (m_pi) of about 250 and 170 MeV. The calculations have been refined with enhanced statistics, in particular through successful application of the all-mode-averaging (AMA) technique for the 170- and 330-MeV ensembles. As a result, the precision agreement seen in the charge ratio, (g_A/g_V), for 420-MeV and 250-MeV ensembles that share the finite-size scaling parameter (m_pi L) of about 5.8 is more significant with new values of 1.17(2) and 1.18(4) respectively. We also studied the dependence on the source-sink separation in the lightest ensemble of 170-MeV, by comparing the cases with the separation of about 1.0 and 1.3 fm and did not see any dependence: contamination from the excited states are well under control in our choice of source and sink smearing. The axial charge, (g_A) and the ratio, (g_A/g_V), shows a long-range autocorrelation that extends the entire range of configurations that were so far analyzed, almost 700 hybrid Molecular Dynamics time, in the lightest ensemble of (m_pi=170) MeV. The other observables do not show any autocorrelation with the interval of 16 trajectories.
The chiral susceptibility, or the first derivative of the chiral condensate with respect to the quark mass, is often used as a probe for the QCD phase transition since the chiral condensate is an order parameter of $SU(2)_L times SU(2)_R$ symmetry breaking. However, the chiral condensate also breaks the axial $U(1)$ symmetry, which is usually not paid attention to as it is already broken by anomaly. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial $U(1)$ anomaly contributes to the chiral phase transition. Employing a chirally symmetric lattice Dirac operator, and its eigenmode decomposition, we separate the axial $U(1)$ breaking effects from others. Our result in two-flavor QCD indicates that the chiral susceptibility is dominated by the axial $U(1)$ anomaly at temperatures $Tgtrsim 190$ MeV after the quadratically divergent constant is subtracted.
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