B decays to radially excited D mesons in heavy quark effective theory

摘要

Semileptonic transitions B → D~((n))ℓν, where D~((n))(n ≠ 0) is a radially excited meson, have recently attracted much attention as a way to understand some puzzles between theory and data. In the heavy quark limit the inelastic Isgur-Wise function vanishes at zero recoil, ξ~((n))(1) = 0(n ≠ 0). We consider here the 1/m_Q corrections within heavy quark effective theory. We find simple formulas that involve the derivative of the inelastic IW function at w = 1, ξ~((n)′)(l)(w ≠ 0). We propose a number of ways of isolating this important quantity in practice, with emphasis on lattice QCD. We formulate also a generalization to the inelastic case of Luke's theorem.