Isotopic splittings and OPE in B -> D semileptonic decays

Abstract

It is shown that the kinematical difference in the decays B^- -> D^0 \ell \tilde νand B^0 -> D^+ \ell \tilde νdue to the isotopic mass splittings of the B and D mesons is compensated in the total decay rate by an appropriate difference in the lepton spectra. Thus there is no effect on the total decay rates in the linear order in the isotopic mass splittings, as required by the general consideration based on the operator product expansion. Although phenomenologically the isotopic difference in the spectra amounts to at most about 1%, in the theoretical aspect this effect can be viewed as an additional illustration of how the general OPE results emerge from the properties of exclusive channels.