Application of Mössbauer-Type Sum Rules for $B$ Meson Decays

Abstract

Sum rules originally derived for the Mössbauer Effect are applied to weak semileptonic B decays. The sum rules follow from assuming that the decay by electroweak boson emission of an unstable nucleus or heavy quark in a bound system is described by a pointlike coupling to a current which acts only on the decaying object, that the Hamiltonian of the bound state depends on the momentum of the decaying object only in the kinetic energy and that the boson has no final state interactions. The decay rate and the first and second moments of the boson energy spectrum for fixed momentum transfer are shown to be the same as for a noninteracting gas of such unstable objects with a momentum distribution the same as that of the bound state. B meson semileptonic decays are shown to be dominated by the lowest-lying states in the charmed meson spectrum.