Pion inspired by QCD: Nakanishi and Light-Front Integral Representations

TL;DR

This paper develops a framework using Nakanishi integral representation to analyze the pion structure in Minkowski space, combining analytical models with lattice QCD data to compute various pion observables.

Contribution

It introduces a novel approach to represent the pion Bethe-Salpeter amplitude in Minkowski space using Nakanishi functions, integrating lattice QCD results.

Findings

Calculated pion decay constant and momentum distributions.

Derived Nakanishi weight functions for scalar amplitudes.

Connected Minkowski space analysis with lattice QCD data.

Abstract

The pion structure in Minkowski space is explored using the Nakanishi integral representation. A general framework is developed for the pion Bethe-Salpeter amplitude based on the Kallen-Lehmann representation of the dressed quarks with an ansatz for the pseudo-scalar $\pi-q\bar q$ vertex fulfilling the axial Ward-Takahashi identity. The Nakanishi weight functions are derived for the scalar amplitudes associated with the decomposition of the pion Bethe-Salpeter amplitude in different operator bases in the Dirac spinor space in terms of the involved spectral densities. The approach is applied to an analytical model of the pion Bethe-Salpeter amplitude, which is combined with Landau gauge lattice QCD results for the quark running mass at space-like momentum. From the Nakanishi integral representation several pion observables were calculated, such as the decay constant, the spin decomposition of the valence probabilities, longitudinal and transverse momentum distributions from the valence component of the light-front wave function.