Light meson mass spectra and pion electromagnetic form factor 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 antiquark combined by gauge fields to satisfy gauge invariance. We derive the equation of motion for this system and construct a series of eigenvalue differential equations including the contribution of magnetic field for meson wave-functions. By solving these equations, we obtain meson mass spectra and the corresponding meson wave-functions including pion wave function. In addition, using this pion wave function, we obtain the pion electromagnetic form factor including the contribution of a magnetic field. Keywords: Bethe-Salpeter-like amplitude, Bound system, Meson mass spectra, Pion electromagnetic form factor