Isgur-Wise function in $B_c$ decays to charmonium with the Bethe-Salpeter method

Abstract

The Isgur-Wise function vastly reduces the weak-decay form factors of ground heavy mesons.In this paper, we extract the Isgur-Wise functions from the instantaneous Bethe-Salpeter method, and give the numerical results for the B c decays to charmonium where the final states include 1S, 1P , 2S and 2P . The overlapping integral of the wave functions for the initial and final states is the leading order Isgur-Wise function, as the heavy quark effective theory does. In the case of accurate calculation, we need to introduce more high-order Isgur-Wise functions which are the overlapping integrals with the relative momentum between the quark and antiquark. The higher order Isgur-Wise functions provide greater relativistic corrections especially involving the excited state, and therefore are necessary to be adopted.