Ward identities and the analogous Goldberger-Treiman relation in a three-flavor Spectral Quark Model

8th International Workshop on Hadron Physics

Reis, E.A.^1 ; Mota, A.L.^1 ; Dias, E.W.^1

Departamento de Ciências Naturais, Universidade Federal de São João Del Rei, C.P.110, São João del Rei

CEP 36301-160, Brazil^1

关键词: Log-moments;    Negative moments;    Particular solution;    Quark mass;    Quark model;    Quark spectral function;    Spectral function;    Ward identities;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/706/5/052012/pdf
DOI  :  10.1088/1742-6596/706/5/052012

来源: IOP

【 摘 要 】

This work presents the first results of an extension of the spectral quark model which includes different flavors. The spectral quark model is an approach based on a generalization of the Lehmann representation for the quark propagator. Gauge and chiral invariance are ensured with the help of gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its positive momenta must vanish, while the physical observables depend on negative moments and the so-called log moments. As a consequence, the model is made finite. To allow the description of mesons constituted by different flavors of quarks we introduce different spectral functions and obtain vertex functions constructed from Ward-Takahashi identities that includes two different spectral (constituent) quark masses, allowing the physical description of strange mesons, for example. We obtain some observables based on the current approach and, in particular, the spectral version of the Kaon analogous Goldberger-Treiman relation.