Pion electromagnetic form factor with Minkowskian dynamics

TL;DR

This paper presents a novel calculation of the pion electromagnetic form factor directly in Minkowski space using the Bethe-Salpeter equation and Nakanishi representation, achieving excellent agreement with experimental data.

Contribution

It introduces the first Minkowski space solution of the Bethe-Salpeter equation for the pion form factor using Nakanishi representation, incorporating lattice-inspired parameters and light-front formalism.

Findings

Successful comparison with experimental data across all momentum transfers

First Minkowski space calculation of the pion form factor from Bethe-Salpeter solutions

Evaluation of light-front valence form factor and end-point effects

Abstract

The pion electromagnetic form factor has been calculated for the first time from the solutions of the Bethe-Salpeter equation, obtained directly in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The one-gluon exchange kernel contains as inputs the quark and gluon masses, as well as a scale parameter featuring the extended quark-gluon vertex. The range of variability of these parameters is suggested by lattice calculations. After presenting a very successful comparison with the existing data in the whole range of the momentum transfer, we show how inserting the light-front (LF) formalism in our approach allows to achieve further interesting results, like the evaluation of the LF valence form factor and a first investigation of the end-points effects.