Abstract
The OPE treatment that has been so successful in describing inclusive B̄→lν̄Xc decays yields sum rules (in particular the Uraltsev sum rule and its higher moments) implying the dominance of the P wave 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, which illustrate the OPE results, and by preliminary lattice findings. Its failure would indicate a significant limitation in our theoretical understanding of B̄→lν̄Xc. Some experimental issues have been clarified since a preliminary version of this note had appeared; yet, the verdict on the composition of the final states beyond D, D* and the two narrow jq=3/2 resonances remains unsettled. Establishing which hadronic configurations – D/D*+π,D/D*+2π,... – contribute, what their quantum numbers are, and their mass distributions will require considerable experimental effort. We explain the theoretical issues involved and why a better understanding of them will be of considerable value. Having significant contributions from a mass continuum distribution below 2.5 GeV raises serious theoretical questions for which we have no good answer. Two lists are given, 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.
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Bigi, I., Blossier, B., Le Yaouanc, A. et al. Memorino on the ‘1/2 versus 3/2 puzzle’ in B̄→lν̄Xc – a year later and a bit wiser. Eur. Phys. J. C 52, 975–985 (2007). https://doi.org/10.1140/epjc/s10052-007-0425-1
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DOI: https://doi.org/10.1140/epjc/s10052-007-0425-1