Memorino on the `1/2 vs. 3/2 Puzzle' in $\bar B \to l \bar νX_c$

Abstract

After the successes the OPE description has scored in describing $\bar B \to l \bar νX_c$ decays, we need to study what can be said about the composition of the hadronic final state $X_c$. The same OPE treatment yields sum rules implying the dominance of $j_q = 3/2$ charm states in $X_c$ over their $j_q=1/2$ counterparts. This prediction is supported by other general arguments as well as quark model calculations. At present it is unclear to which degree data conform to these predictions. More experimental information is essential. We want to ask our experimental colleagues for a redoubled effort to establish, which hadronic configurations -- $D/D^* + π, D/D^* + 2 π, ...$ -- make up $Γ(\bar B \to l \bar νX_c)$ beyond $\bar B \to l \bar νD/D^*$, what their quantum numbers are and their mass distributions. The latter is most relevant for the determination of hadronic mass moments in $\bar B \to l \bar νX_c$. Since all this will require considerable effort on their part, we want to explain the theoretical issues involved, why they carry `gravitas' -- i.e. are weighty -- and why a better understanding of them will be of significant value. In this brief memo we sketch the underlying arguments based on heavy quark theory, the OPE, a special class of quark models and lattice QCD in a nutshell. After summarizing the experimental situation we conclude with two lists, namely one with measurements that need to be done and one with items of theoretical homework. Some of the latter can be done by employing existing theoretical tools, whereas others need new ideas.