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

Abstract

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 $|E_{\pi }|\gg |E_{\rho }|$.

Comments: 7 pages, 1 figure, revised version