Pion model with the Nakanishi Integral Representations

2022/02/22 by Moita, R. M., de Melo, J. P. B. C., Frederico, T. +1
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Nuclear Theory (nucl-th)

paper · doi:10.48550/arxiv.2202.10959

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 (p²), 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(γ,z), for the Nakanishi integral representation of each scalar function, χ_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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