Pion model with the Nakanishi Integral Representations

Abstract

In the present work, we describe a model for the pion based on an analytic expression for the Bethe-Salpeter (BSA) amplitude, combined with some ingredients from Lattice QCD calculations. The running quark mass function $M(p^2)$, used here, reproduces well the results of Lattice QCD calculations. The analytical form of the running quark mass function contains a single time-like pole, which implies in time-like poles of the dressed quark propagator. Such a form allows to build the weight functions, $G_i(\gamma ,z)$, for the Nakanishi integral representation of each scalar function, ${\chi }_i(k,p)$, appearing in the decomposition of the Bethe-Salpeter amplitude in terms of Dirac operators, Such scalar amplitudes can also be used to obtain the pion valence light-front wave function.

Comments: 6 pages, 5 figures (eps). Contribuition to the "19 th International Conference on Hadron Spectroscopy and Structure (HADRON 2021)", Mexico, 2021 To appear "Suplemento de la Revista Mexicana de Fisica"