Pion wave-function as a bound system in 3 + 1 dimensional QCD

Abstract

We investigate the Bethe-Salpeter-like amplitude in 3 + 1 dimensions. This involves a system comprising a quark and an antiquark combined by gauge fields to satisfy gauge invariance. We derive the equation of motion for this system and construct a series of convolution integro-differential equations. By solving these equations and using the Ward Identity, we obtain the pion wave function and then the pion form factor. Our form of the pion form factor explains well the inclination of the large q2 region of experimental data. Thus, our pion wave function shows the real trailing-off property, which reflects the confinement property. Keywords: Bethe-Salpeter-like amplitude, Bound system, Pion wave function, Pion form factor