DIRAC SPECTRUM IN QCD AND QUARK MASSES

We use a chiral random matrix model to investigate the effects of mass ive quarks on the distribution of eigenvalues of QCD inspired Dirac op erators, Kalkreuter's lattice analysis of the spectrum of the massive (hermitian) Dirac operator for two colors and Wilson fermions is shown to follow from a cubic equation in the quenched approximation. The qu enched spectrum shows a Mott transition from a (delocalized) Goldstone phase softly broken by the current mass, to a (localized) heavy quark phase, with quarks localized over their Compton wavelength, Both phas es are distinguishable by the quark density of states at zero virtuali ty, with a critical quark mass of the order of 100-200 MeV. At the cri tical point, the quark density of states is given by nu(Q)(lambda) sim ilar to \lambda\(1/3). Using Grassmannian techniques, we derive an int egral representation for the resolvent of the massive Dirac operator w ith one flavor in the unquenched approximation, and show that near zer o virtuality the distribution of eigenvalues is quantitatively changed by a non-zero quark mass, The generalization of our construction to a rbitrary flavors is also discussed. Some recommendations for lattice s imulations are suggested.