Dirac spectrum in QCD and Quark Masses

Abstract

We use a chiral random matrix model to investigate the effects of massive quarks on the distribution of eigenvalues of QCD inspired Dirac operators. Kalkreuter's lattice analysis of the spectrum of the massive (hermitean) Dirac operator for two colors and Wilson fermions is shown to follow from a cubic equation in the quenched approximation. The quenched 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 phases are distinguishable by the quark density of states at zero virtuality, with a critical quark mass of the order of 100-200 MeV. At the critical point, the quark density of states is given by ${\nu }_Q(\lambda )\sim |\lambda {|}^{1/3}$. Using Grassmannian techniques, we derive an integral representation for the resolvent of the massive Dirac operator with one-flavor in the unquenched approximation, and show that near zero virtuality, the distribution of eigenvalues is quantitatively changed by a non-zero quark mass. The generalization of our construction to arbitrary flavors is also discussed. Some recommendations for lattice simulations are suggested.

11 pages, LaTEX using RevTEX, 4 eps figures included. (Comparison between the Wilson and staggered fermions added in section 4, one combined plot replaced by three separate plots for better presentation, one reference added.)

References in corpus (6)

• A random matrix model for chiral symmetry breaking
• Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem
• Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator
• Finite-Temperature QCD on the Lattice
• Finite Temperature QCD on the Lattice
• Numerical analysis of the spectrum of the Dirac operator in four-dimensional SU(2) gauge fields

Cited by in corpus (31)

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