Mesoscopic QCD and the Theta Vacua
Jonathan Lenaghan, Thomas Wilke
Abstract
The partition function of QCD is analyzed for an arbitrary number of flavors, Nf, and arbitrary quark masses including the contributions from all topological sectors in the Leutwyler--Smilga regime. For given Nf and arbitrary vacuum angle, θ, the partition function can be reduced to Nf-2 angular integrations of single Bessel functions. For two and three flavors, the θdependence of the QCD vacuum is studied in detail. For Nf= 2 and 3, the chiral condensate decreases monotonically as θincreases from zero to πand the chiral condensate develops a cusp at θ=πfor degenerate quark masses in the macroscopic limit. We find a discontinuity at θ=πin the first derivative of the energy density with respect to θfor degenerate quark masses. This corresponds to the first--order phase transition in which CP is spontaneously broken, known as Dashen's phenomena.
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