Analysis of mass difference of the $π$ and $ρ$ 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 $π$ and $ρ$ mesons with the Bethe-Salpeter equation. After projecting the Bethe-Salpeter equation into an simple form, we can see explicitly that the bound energy $|E_π|\gg |E_ρ|$.

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