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 \( {\chi}_{\mathrm{top}} = \mathcal{O}\left({N}_c^0\right) \), 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.
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Vonk, T., Guo, FK. & Meißner, UG. Aspects of the QCD θ-vacuum. J. High Energ. Phys. 2019, 106 (2019). https://doi.org/10.1007/JHEP06(2019)106
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DOI: https://doi.org/10.1007/JHEP06(2019)106