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 (hermitian) 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 100200 MeV.At the critical point, the quark density of states is given by ν _{Q} (λ) ∼ λ ^{{1}/{3}}. Using Grassmaniian 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 nonzero quark mass. The generalization of our construction to arbitrary flavors is also discussed. Some recommendations for lattice simulations are suggested.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1996
 DOI:
 10.1016/05503213(96)004130
 arXiv:
 arXiv:hepph/9603308
 Bibcode:
 1996NuPhB.478..605J
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 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.)