Analysis of mass difference of the $\pi$ and $\rho$ with Bethe-Salpeter equation

In this article, we take into account the one-pion exchange force besides the one-gluon exchange force to study the mass difference of the $\pi$ and $\rho$ mesons with the Bethe-Salpeter equation. After projecting the Bethe-Salpeter equation into an simple form, we can see explicitly that the bound energy $\mathrm{\mid }{E}_{\pi }\mathrm{\mid }\gg \mathrm{\mid }{E}_{\rho }\mathrm{\mid }$.