2007/08/09 by Mandar S. Bhagwat, Lei Chang, Yu‐xin Liu +4 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Chiral symmetry breaking #Mass matrix #Meson #Neutrino #Particle physics #Particle physics theoretical and experimental studies #Physics #Pseudoscalar #Pseudovector #Quantum Chromodynamics and Particle Interactions #Quark #Symmetry breaking #hep-ex #hep-lat #hep-ph #nucl-ex #nucl-th
paper · pdf · doi:10.1103/physrevc.76.045203
published as Phys.Rev.C76:045203,2007 · 11 pages, 2 figures
arxiv created 2007/08/09 · openalex publication_date 2007/10/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The axial-vector Ward-Takahashi identity is used to derive mass formulas for neutral pseudoscalar mesons. Flavor symmetry breaking entails nonideal flavor content for these states. Adding that the \ensuremathη' is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the \ensuremathη' mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulas are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of SU(Nf=2) and SU(Nf=3) flavor symmetry breaking are emphasized, the five-flavor spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts \ensuremathη\text\ensuremath-\ensuremathη' mixing angles of ~\ensuremath-15^\ifmmode^∘\else\textdegree\fi and \ensuremathπ0\text\ensuremath-\ensuremathη angles of ~1^\ifmmode^∘\else\textdegree\fi.