Semileptonic $B_c$ Decay and Heavy Quark Spin Symmetry

Abstract

Semileptonic decay of the $B_c$ meson is studied in the heavy quark limit. The six possible form factors for $B_c \rightarrow B_s (B^0),B_s^* (B^{*0})$ semileptonic decay are determined by two invariant functions. Only one of these functions contributes at zero recoil, where it is calculable to lowest order in an operator product expansion in terms of the meson decay constant $f_B$ and the $B_c$ wavefunction. A similar result is found for $B_c \rightarrow D^0,D^{*0}$ and for $B_c\rightarrowη_c,J/ψ$ semileptonic decay for a restricted kinematic region. Semileptonic $B_c$ decay provides a means for determining the KM mixing angle $|V_{ub}|$.