Minimal Ward-Takahashi Vertices and Pion Light Cone Distribution Amplitudes from Gauge Invariant, Nonlocal, Dynamical Quark Model

TL;DR

This paper demonstrates that a gauge-invariant, nonlocal quark model produces minimal Ward-Takahashi vertices and analyzes the resulting pion light-cone distribution amplitudes, revealing flat-like and asymptotic modifications influenced by quark masses.

Contribution

It introduces a gauge-invariant, nonlocal quark model that generates minimal vertices satisfying Ward-Takahashi identities and explores their impact on pion distribution amplitudes.

Findings

The model yields flat-like pion distribution amplitudes in the chiral limit.

Mass corrections induce asymptotic-like modifications to the distribution amplitudes.

The variable u in distribution amplitudes corresponds to the Feynman parameter.

Abstract

The gauge-invariant, nonlocal, dynamical quark model is proved to generate the minimal vertices which satisfy the Ward-Takahashi identities. In the chiral limit, the momentum-dependent quark self-energy results in a flat-like form with some end point delta-funtions for the light-cone pion distribution amplitudes, similarly found in the Nambu Jona-Lasino model with constant constituent mass. The leading order nonzero pion and current quark masses corrections lead concave type asymptotic-like form modifications to twist-2 pion distribution amplitude with end point pillars and twist-3 tensor pion distribution amplitude above the flat-like form backgrounds. A by-product of our investigation shows that the variable u appearing in pion light-cone distribution amplitudes is just the standard Feynman parameter in the Feynman parameter integrals; also chiral perturbation works well for these amplitudes.