Theory of the Endpoint Region of Exclusive Rare B Decays

The third row of the CKM matrix is poorly determined because it involves the top quark. Of the first two rows, the Vub element is the least well known, with a precision of about 20% in its magnitude, |Vub|. The measurement of |Vub| through inclusive charmless semileptonic B decays is complicated by the large background from charmfull semileptonic B decays. Experimentally, cuts may be imposed to suppress or eliminate the background, but this introduces theoretical uncertainties. Some years ago it was guessed1 that this method would eventually reach a precision of 5%, but by now new complications from theory have been discovered2, so the eventual precision of the method is expected to be significantly worse. Alternatively one may look to determine |Vub| from exclusive semileptonic B decays, such as B → πlν or B → ρlν. The difficulty here is from theory: the form factors are not well known. Eventually, unquenched lattice QCD calculations may produce accurate form factors (at least in a restricted region of phase space, but that’s all that is needed to extract |Vub|). However, the precision at the moment is no better than3 20%. In this talk I describe a method that relies on exclusive decays which can be used to determine |Vub| to high precision, possibly a couple of percent. The trick is to let experiment, rather than theorists, determine the form factors. Hence, the main result of our work4,5,6can be framed as a recipe for experiment. Measure the ratio of B decay rates,