Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-08-22
Nucl.Phys. B624 (2002) 253-282
Physics
High Energy Physics
High Energy Physics - Theory
31 pages, revtex, 10 figures, final version to appear in Nucl. Phys. B
Scientific paper
10.1016/S0550-3213(01)00635-6
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, \theta, the partition function can be reduced to N_f-2 angular integrations of single Bessel functions. For two and three flavors, the \theta dependence of the QCD vacuum is studied in detail. For N_f= 2 and 3, the chiral condensate decreases monotonically as \theta increases from zero to \pi and the chiral condensate develops a cusp at \theta=\pi for degenerate quark masses in the macroscopic limit. We find a discontinuity at \theta=\pi in the first derivative of the energy density with respect to \theta for degenerate quark masses. This corresponds to the first--order phase transition in which CP is spontaneously broken, known as Dashen's phenomena.
Lenaghan Jonathan
Wilke Thomas
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