$B$ decays to radially excited $D$ mesons in Heavy Quark Effective Theory
Résumé
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/mQ corrections within heavy quark effective theory. We find simple formulas that involve the derivative of the inelastic IW function at w=1, ξ(n)′(1)(n≠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.