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Register a new userSimulating chiral quarks in the epsilon-regime of QCD
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We present simulation results for lattice QCD with chiral fermions in small volumes, where the epsilon-expansion of chiral perturbation theory applies. Our data for the low lying Dirac eigenvalues, as well as mesonic correlation functions, are in agreement with analytical predictions. This allows us to extract values for the leading Low Energy Constants F_{pi} and Sigma.
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We investigate the effects of low-lying fermion eigenmodes on the QCD partition function in the $epsilon$-regime. The fermion determinant is approximated by a truncated product of low-lying eigenvalues of the overlap-Dirac operator. With two flavors of dynamical quarks, we observe that the lattice results for the lowest eigenvalue distribution, eigenvalue sum rules and partition function reproduce the analytic predictions made by Leutwyler and Smilga, which strongly depend on the topological charge of the background gauge configuration. The value of chiral condensate extracted from these measurements are consistent with each other. For one dynamical quark flavor, on the other hand, we find an apparent disagreement among different determinations of the chiral condensate, which may suggest the failure of the $epsilon$-expansion in the absence of massless Nambu-Goldstone boson.
We investigate the chiral properties of quenched domain-wall QCD (DWQCD) at the lattice spacings $a^{-1} simeq 1$ and 2 GeV for both plaquette and renormalization-group (RG) improved gauge actions. In the case of the plaquette action we find that the quark mass defined through the axial Ward-Takahashi identity remains non-vanishing in the DWQCD chiral limit that the bare quark mass $m_fto 0$ and the length of the fifth dimension $N_stoinfty$, indicating that chiral symmetry is not realized with quenched DWQCD up to $a^{-1} simeq 2$ GeV. The behavior is much improved for the RG-improved gauge action: while a non-vanishing quark mass remains in the chiral limit at $a^{-1}simeq 1$ GeV, the result at $a^{-1}simeq 2$ GeV is consistent with an exponentially vanishing quark mass in the DWQCD chiral limit, indicating the realization of exact chiral symmetry. An interpretation and implications are briefly discussed.
We generated configurations with the parametrized fixed-point Dirac operator D_{FP} on a (1.6 fm)^4 box at a lattice spacing a=0.13 fm. We compare the distributions of the three lowest k=1,2,3 eigenvalues in the nu= 0,1,2 topological sectors with that of the Random Matrix Theory predictions. The ratios of expectation values of the lowest eigenvalues and the cumulative eigenvalue distributions are studied for all combinations of k and nu. After including the finite size correction from one-loop chiral perturbation theory we obtained for the chiral condensate in the MSbar scheme Sigma(2GeV)^{1/3}=0.239(11) GeV, where the error is statistical only.
We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm$)^3$ and (11 fm$)^3$ and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, $chi_{rm disc}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD ``phase transition is not first order but a continuous cross-over for $m_pi=135$ MeV. The peak location determines a pseudo-critical temperature $T_c = 155(1)(8)$ MeV. Chiral $SU(2)_Ltimes SU(2)_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1)_A$ symmetry breaking is non-zero above $T_c$ and vanishes as $T$ is increased to 196 MeV.
We consider how to extract the pion form factors in the epsilon regime. Using the correlators with non-zero momenta and taking appropriate ratios of them, we eliminate the dominant finite volume effect from the zero-momentum pion mode. Our preliminary lattice result for the pion charge radius is consistent with the experiment.
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