$B \to D^{**}$ -- puzzle 1/2 vs 3/2

Understanding the composition of final states in $B \to X_c l ν$ could help to get a feedback on the persisting disagreement between exclusive and inclusive determinations of $V_{cb}$. In particular the series of orbital excitations $D^{**}$ and radial excitations ($D'$, $D^*\,'$) has received a lot of attention; a misinterpretation as a scalar state of the ($D' \to D π$) spectrum tail could have induced an experimental overestimate of the broad states contribution to the total $B \to X_c l ν$ width with respect to theoretical expectations, all of them made however in the infinite mass limit: it is the so-called 1/2 vs 3/2 puzzle. We describe first attempts to measure on the lattice form factors of $B \to D^{**} l ν$ at realistic quark masses. Cleaner processes, like hadronic decays $B \to D^{**} π$ and semileptonic decays $B_s \to D_s^{**} l ν$ in the strange sector have recently been examined by phenomenologists, putting new interesting ideas on those issues with, again, the need of lattice inputs.

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