Pion scalar, vector and tensor form factors from a contact interaction

TL;DR

This paper computes pion scalar, vector, and tensor form factors using a contact interaction model in QCD, incorporating a modified kernel that preserves symmetries and improves agreement with lattice QCD results.

Contribution

It introduces a modified Bethe-Salpeter kernel within a contact interaction model that preserves Ward-Takahashi identities and enhances the accuracy of form factor calculations.

Findings

Form factors and radii agree with lattice QCD data.

Modified kernel improves the location of mass poles.

Tensor structures in vertices are generated, affecting results.

Abstract

The pion scalar, vector and tensor form factors are calculated within a symmetry-preserving contact interaction model (CI) of quantum chromodynamics (QCD), encompassed within a Dyson-Schwinger and Bethe-Salpeter equations approach. In addition to the traditional rainbow-ladder truncation, a modified interaction kernel for the Bethe-Salpeter equation is adopted. The implemented kernel preserves the vector and axial-vector Ward-Takahashi identities, while also providing additional freedom. Consequently, new tensor structures are generated in the corresponding interaction vertices, shifting the location of the mass poles appearing in the quark-photon and quark tensor vertex and yielding a notorious improvement in the final results. Despite the simplicity of the CI, the computed form factors and radii are compatible with recent lattice QCD simulations.