Minimal Ward–Takahashi Vertices and Light Cone Pion Distribution Amplitudes from the GND Quark Model

The gauge-invariant, nonlocal, dynamical quark model is shown to generate minimal vertices that satisfy the Ward–Takahashi identities and the flat-like form of the light-cone pion distribution amplitudes. Non-flat form amplitudes can be produced only if we take a finite momentum cutoff and include nonzero pion mass corrections or go beyond the minimal vertices. A by-product of our investigation shows that the variable u appearing in light-cone pion distribution amplitudes is just the standard Feynman parameter in the Feynman parameter integrals.