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arXiv · 2202.10959

Pion model with the Nakanishi Integral Representations

R. M. Moita·J. P. B. C. de Melo·T. Frederico·W. de Paula
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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.

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R. M. Moita, J. P. B. C. de Melo, T. Frederico, W. de Paula. 2022-02-22. Pion model with the Nakanishi Integral Representations. https://arxiv.org/abs/2202.10959

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