$B$ decays to radially excited $D$ mesons in Heavy Quark Effective Theory

Abstract

Semileptonic transitions $\overline{B}\to D^{(n)}\ell \overline{\nu }$, where $D^{(n)}(n\ne 0)$ is a radially excited meson, have recently attracted much attention as a way to understand some puzzles between theory and data. Following closely the formalism of Falk and Neubert for the elastic case, we study the $1/m_Q$ corrections to the heavy quark limit, in which the inelastic Isgur-Wise function vanishes at zero recoil, ${\xi }^{(n)}(1)=0(n\ne 0)$. We find simple formulas that involve the derivative ${\xi }^{(n{)}^{\prime }}(1)$, and we propose a number of ways of isolating this quantity in practice. We formulate also a generalization to the inelastic case of Luke's theorem. On the other hand, although some $1/m_Q$ HQET results are satisfied in the Bakamjian-Thomas relativistic quark model, we emphasize the problems concerning these corrections in this scheme.

arXiv comment13 pages

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