1998/05/31 by K. Naito, K. Yoshida, Y. Nemoto +3
Physics and Astronomy · #Bethe–Salpeter equation #Black Holes and Theoretical Physics #Chiral symmetry breaking #Effective action #Feynman diagram #Lagrangian #Mathematical physics #Meson #Noether's theorem #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Symmetry breaking #hep-ph
paper · pdf · doi:10.1103/physrevc.59.1095
published as Phys. Rev. C 59, 1095 (1999) · 25 pages, LaTeX
arxiv created 1998/12/25 · openalex publication_date 1999/02/01 · arxiv updated 2016/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Dynamical breaking of chiral symmetry in effective models of QCD is studied. Introducing a cutoff function or a nonlocal interaction, the Noether current must be modified and thus the Ward-Takahashi identity and the PCAC relation are modified accordingly. We point out that the pion decay constant must be defined consistently with the Noether current so that the low-energy relations are satisfied. We define the proxy of the Noether current for general effective models, which is consistent with loop expansion of the Cornwall-Jackiw-Tomboulis effective action. A general formula for the pion decay constant in terms of the Bethe-Salpeter amplitude is derived. The effective Pagels-Stokar formula is proposed, which is useful to estimate the decay constant without solving the Bethe-Salpeter equation.