Pion in the Bethe-Salpeter approach with separable kernel

TL;DR

This paper analyzes the static and dynamic properties of the pion using the Bethe-Salpeter approach with a separable kernel, correcting previous calculation errors and comparing results with experimental data.

Contribution

It introduces an analytical solution for the Bethe-Salpeter equation with a rank-one separable kernel and refits kernel parameters based on corrected calculations.

Findings

Corrected calculation of the elastic pion form factor.

Refitted kernel parameters with improved accuracy.

Results agree well with recent experimental data.

Abstract

In the paper, the static and dynamic properties of the pion in the Bethe-Salpeter approach are considered. The rank-one separable kernel of the quark-antiquark interaction is used to solve the equation analytically. Multidimensional integrals describing pion properties are calculated by several numerical methods and compared with previous papers. An error in the calculation of the interaction part of the elastic pion form factor is found. Using the corrected results, the kernel parameters are refitted. The calculated static properties as well as transition and elastic form factors are presented in comparison with the recent experimental data.