Memorino on the ‘ 1 / 2 vs . 3 / 2 Puzzle ’ in B̄ → lν̄X c

After the successes the OPE description has scored in describing B̄ → lν̄Xc decays, we need to study what can be said about the composition of the hadronic final state Xc. The same OPE treatment yields sum rules implying the dominance of jq = 3/2 charm states in Xc over their jq = 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+2π, ... – make up Γ(B̄ → lν̄Xc) beyond B̄ → lν̄D/D, what their quantum numbers are and their mass distributions. The latter is most relevant for the determination of hadronic mass moments in B̄ → lν̄Xc. 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.