Pion model with the Nakanishi Integral Representations

TL;DR

This paper develops a pion model using an analytic Bethe-Salpeter amplitude combined with lattice QCD-inspired quark mass functions, enabling the construction of Nakanishi integral representations and light-front wave functions.

Contribution

It introduces a novel approach to modeling the pion with an analytic BSA and Nakanishi representation based on lattice QCD data, including a specific quark mass function form.

Findings

Reproduces lattice QCD results for the quark mass function

Constructs Nakanishi weight functions for the BSA

Derives pion light-front wave functions from the model

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.