Eur. Phys. J. C (2007) 52: 975-985
https://doi.org/10.1140/epjc/s10052-007-0425-1

Regular Article - Theoretical Physics

Memorino on the ‘1/2 versus 3/2 puzzle’ in B̄→lν̄X_c – a year later and a bit wiser

¹ Department of Physics, University of Notre Dame du Lac, Notre Dame, IN, 46556, USA
² DESY, Platanenallee 6, 15738, Zeuthen, Germany
³ LPTh, Univ. de Paris Sud, 91405, Orsay CEDEX, France
⁴ LAL, 91898, Orsay CEDEX, France

^* e-mail: ibigi@nd.edu

Received: 30 August 2007
Published online: 16 October 2007

Abstract

The OPE treatment that has been so successful in describing inclusive B̄→lν̄X_c decays yields sum rules (in particular the Uraltsev sum rule and its higher moments) implying the dominance of the P wave 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, which illustrate the OPE results, and by preliminary lattice findings. Its failure would indicate a significant limitation in our theoretical understanding of B̄→lν̄X_c. 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 j_q=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.