Weak form factors for heavy meson decays: an update

The knowledge of the weak transition form factors of heavy mesons is crucial for a proper extraction of the quark mixing parameters, for the analysis of non-leptonic decays and CP violating effects and, related to it, for a search of New Physics. Theoretical approaches for calculating these form factors are quark models [1–8], QCD sum rules [9–12], and lattice QCD [13]. Although in recent years considerable progress has been made, the theoretical uncertainties are still uncomfortably large. An accuracy better than 15% has not been attained. Moreover each of the above methods has only a limited range of applicability, namely: QCD sum rules are suitable for describing the low q region of the form factors. The higher q region is hard to get and higher order calculations are not likely to give real progress because of the appearance of many new parameters. The accuracy of the method cannot be arbitrarily improved because of the necessity to isolate the contribution of the states of interest from others. Lattice QCD gives good results for the high q region. But because of the many numerical extrapolations involved this method does not provide for a full picture of the form factors and for the relations between the various decay channels. Quark models do provide such relations and give the form factors in the full q range. However, quark models are not closely related to the QCD Lagrangian (or at least this relationship is not well understood yet) and therefore have input parameters which are not directly measurable and may not be of fundamental significance. In this situation it becomes evident that a combination of various methods will be fruitful. It is the purpose of this paper to obtain this way reliable predictions for many decay form factors in their full q ranges. To achieve this goal, one needs a general frame for the description of the large variety of processes. This can be only a suitable quark model, because only a quark model can connect different processes through the soft wave functions of the mesons and describes the full q range of the form factors . The shortcomings of this model will be greatly diminished by incorporating the results from the more fundamental QCD based methods. Historically, constituent quark models have been first to analyse the meson transition form factors. Although a rigorous derivation of this approach as an effective theory of QCD in the nonperturbative regime has not been obtained, relativistic quark models work surprisingly well for the description of the meson spectra and form factors. Moreover, constituent quark models provide so far the only operative method for dealing with excited states.