Aspects of the QCD θ-vacuum

Abstract

Abstract This paper addresses two aspects concerning the θ-vacuum of Quantum Chro-modynamics. First, large-N c 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, χ top, and the fourth cumulant, c 4, up to next-to-leading order. Their large-N c scaling is discussed, and compared to lattice results. It is found that χ top = O N c 0 $$ {\chi}_{\mathrm{top}} = \mathcal{O}\left({N}_c^0\right) $$ , as known before, and c 4 = O N c − 3 $$ {c}_4 = \mathcal{O}\left({N}_c^{-3}\right) $$ , correcting the assumption of O N c − 2 $$ \mathcal{O}\left({N}_c^{-2}\right) $$ 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 N f = 2 and N f = 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.

Keywords

• Chiral Lagrangians
• Effective Field Theories
• 1/N Expansion