Aspects of the QCD \u03b8-vacuum

Abstract

This paper addresses two aspects concerning the θ-vacuum of Quantum Chro-modynamics. First, large-Nc chiral perturbation theory is used to calculate the first two non-trivial cumulants of the distribution of the winding number, i.e. the topological susceptibility, χtop, and the fourth cumulant, c4, up to next-to-leading order. Their large-Nc scaling is discussed, and compared to lattice results. It is found that {chi}_{mathrm{top}} = mathcal{O}left({N}_c^0right) , as known before, and {c}_4 = mathcal{O}left({N}_c^{-3}right) , correcting the assumption of mathcal{O}left({N}_c^{-2}right) in the literature. Second, we discuss the properties of QCD at θ ∼ π using chiral perturbation theory for the case of 2 + 1 light flavors, i.e. by taking the strange quark mass heavier than the degenerate up and down quark masses. It is shown that — in accordance with previous findings for Nf = 2 and Nf = 3 mass-degenerate flavors — in the region θ ∼ π two vacuum states coexist, which become degenerate at θ = π. The wall tension of the energy barrier between these degenerate vacua is determined as well as the decay rate of a false vacuum.