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Dynamical Chiral Symmetry Breaking in Effective Models of QCD in the Bethe-Salpeter Approach

K. Naito·K. Yoshida·Y. Nemoto·M. Oka·M. Takizawa
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Abstract

Dynamical breaking of chiral symmetry in effective models of QCD is studied. Introducing a cut-off function or a non-local 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.

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K. Naito, K. Yoshida, Y. Nemoto, M. Oka, M. Takizawa. 1998-12-25. Dynamical Chiral Symmetry Breaking in Effective Models of QCD in the Bethe-Salpeter Approach. https://doi.org/10.1103/physrevc.59.1095

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