B decays to radially excited D

Abstract

We discuss the possibility to measure in present experiments, especially LHCb, the non leptonic decay branching ratio $B \to D' \pi$, and emphasize phenomenological implications on $B \to D' l \nu$ semileptonic decay. We have estimated by lattice QCD the $D'$ decay constant $f_{D'}$ that parameterizes the $D'$ emission contribution to the Class-III non leptonic decay $B^- \to D^0 \pi^-$. In addition, we provide a new estimate of the decay constants $f_{D_{s,q}}$ which read $f_{D_{s}}=252(3)$ MeV and $f_{D_{s}}/f_{D}=1.23(1)(1)$.