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Aspects of the QCD θ-vacuum

  • Thomas VonkEmail author
  • Feng-Kun Guo
  • Ulf-G. Meißner
Open Access
Regular Article - Theoretical Physics

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 θπ 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 θπ 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 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  2. 2.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  3. 3.School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  4. 4.Institute for Advanced SimulationInstitut für Kernphysik and Jülich Center for Hadron PhysicsJülichGermany
  5. 5.Tbilisi State UniversityTbilisiGeorgia

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