Average Kinetic Energy of Heavy Quark (${\mu }_{\pi }^2$) inside Heavy Meson of $0^{-}$ State by Bethe-Salpeter Method

Abstract

The average kinetic energy of the heavy quark inside $B$ or $D$ meson is computed by means of the instantaneous Bethe-Salpeter method. We first solve the relativistic Salpeter equation and obtain the relativistic wave function and mass of $0^{-}$ state, then we use the relativistic wave function to calculate the average kinetic energy of the heavy quark inside heavy meson of $0^{-}$ state. We find that the relativistic corrections to the average kinetic energy of the heavy quark inside $B$ or $D$ meson are quite large and cannot be ignored. We estimate ${\mu }_{\pi }^2(=-{\lambda }_1)\approx 0.35(B^0,B^{\pm })$, $0.28(D^0,D^{\pm })$, $0.43(B_s)$, $0.34(D_s)$, $0.96(B_c)$ and $0.62({\eta }_c)$ GeV${}^2$.

New version with Erratum

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