Mesoscopic QCD and the theta vacua
Aug, 2001Citations per year
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, \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.Note:
- 31 pages, revtex, 10 figures, final version to appear in Nucl. Phys. B
- 12.38.Lg
- quantum chromodynamics
- partition function
- vacuum state: Theta parameter
- fermion: flavor
- condensation: chiral
- energy: density
- critical phenomena
- susceptibility: topological
- scaling
References(48)
Figures(10)