The average kinetic energy of the heavy quark in [formula omitted] in the Bethe–Salpeter equation approach

Abstract

In the previous paper, based on the SU(2)f×SU(2)s heavy quark symmetries of the QCD Lagrangian in the heavy quark limit, the Bethe–Salpeter equation for the heavy baryon Λb was established with the picture that Λb is composed of a heavy quark and a scalar light diquark. In the present work, we apply this model to calculate μπ2 for Λb, the average kinetic energy of the heavy quark inside Λb. This quantity is particularly interesting since it can be measured in experiments and since it contributes to the inclusive semileptonic decays of Λb when contributions from higher order terms in 1/Mb expansions are taken into account and consequently influences the determination of the Cabibbo–Kobayashi–Maskawa matrix elements Vub and Vcb. We find that μπ2 for Λb is 0.25GeV2∼0.95GeV2, depending on the parameters in the model including the light diquark mass and the interaction strength between the heavy quark and the light diquark in the kernel of the BS equation. We also find that this result is consistent with the value of μπ2 for Λb which is derived from the experimental value of μπ2 for the B meson with the aid of the heavy quark effective theory.