Two-Flavor Lattice-QCD Simulation in theϵRegime with Exact Chiral Symmetry

Abstract

We perform lattice simulations of two-flavor QCD using Neuberger's overlap fermion, with which the exact chiral symmetry is realized at finite lattice spacings. The regime is reached by decreasing the light quark mass down to 3 MeV on a 16 3 32 lattice with a lattice spacing 0:11 fm. We find a good agreement of the low-lying Dirac eigenvalue spectrum with the analytical predictions of the chiral random matrix theory, which reduces to the chiral perturbation theory in the regime. The chiral condensate is extracted as MS 2 GeV 251 7 11 MeV 3 , where the errors are statistical and an estimate of the higher order effects in the expansion.In quantum chromodynamics (QCD), it is widely believed that chiral symmetry is spontaneously broken, making pions nearly massless while giving masses of order QCD , the QCD scale, to the other hadrons. In fact, chiral perturbation theory (ChPT), an effective theory based on the spontaneously broken chiral symmetry, describes low energy interactions of pions very accurately. Nevertheless, theorists have not been successful in analytically solving QCD and deriving the chiral symmetry breaking, due to its highly nonperturbative dynamics.The most promising approach to establishing the link between QCD and ChPT is to utilize the numerical simulation of lattice QCD, with which the every prediction of ChPT can be tested in principle. For instance, the presence of the so-called chiral logarithms, the effect of a pion cloud, should be reproduced. Such a numerical test is, however, not an easy task, because of rapidly increasing computational cost in the small quark mass region where ChPT is reliably applied. Another serious problem is the explicit violation of the chiral symmetry at finite lattice spacings in the conventional fermion formulations, with which the conclusive test of ChPT requires wellcontrolled and thus computationally demanding continuum extrapolation.In this work we improve this situation in two ways. First, we employ Neuberger's overlap fermion [1,2] for dynamical quarks. It preserves exact chiral symmetry at finite lattice spacings, and hence ChPT can be applied before taking the continuum limit. Although the numerical cost of the overlap fermion is almost 100 times higher than that of the other fermions, new computational facilities at KEK enable us to carry out such a work.Second, we study the correspondence between QCD and ChPT in the so-called regime [3][4][5], which is characterized by the small pion mass m satisfying m L & 1 with L the box size. In this regime ChPT is safely applied as an expansion in terms of 2 m = QCD , provided that the condition 1= QCD L 2 1, the usual condition that the box size is larger than the inverse QCD scale, is satisfied. We set the sea quark mass to 3 MeV, for which m L ' 1:0. With the space-time volume L 3 T ' 1:8 fm 3 3:5 fm, the numerical cost is still not prohibitive even with such a small sea quark mass, since the finite volume provides a natural lower bound on the lowest eigenvalue of the Dirac operator.In the regime, zero-momentum...

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