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arXiv · hep-th/0108166

Mesoscopic QCD and the Theta Vacua

Jonathan Lenaghan·Thomas Wilke
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Abstract

The partition function of QCD is analyzed for an arbitrary number of flavors, N_f, and arbitrary quark masses including the contributions from all topological sectors in the Leutwyler--Smilga regime. For given N_f and arbitrary vacuum angle, θ, the partition function can be reduced to N_f-2 angular integrations of single Bessel functions. For two and three flavors, the θdependence of the QCD vacuum is studied in detail. For N_f= 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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Jonathan Lenaghan, Thomas Wilke. 2002-01-24. Mesoscopic QCD and the Theta Vacua. https://doi.org/10.1016/s0550-3213(01)00635-6

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