Pion model with the Nakanishi integral representation

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, Gi(γ, z), for the Nakanishi integral representation of each scalar function, χi(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.