Isospin corrections to charmless semileptonic B-->V transitions.

We compute isospin corrections to the charmless semileptonic B → V transitions arising from ρ− ω mixing and discuss its relevance in the determination of Vub. PACS numbers: 13.20.He, 12.15.Hh, 12.40.Vv. 11.30.Hv The first measurement of an exclusive charmless semileptonic B decay has been reported recently by the CLEO Collaboration [1,4]. The yields for B → πlνl reported in Refs. [1,4] turn out to be strongly dependent on the theoretical models [2,3] used for the detection efficiencies, as it does the extraction of the CKM parameter |Vub| from these results. The |Vub| parameter can be determined from exclusive charmless semileptonic B decays and also from the end-point region of the lepton spectrum in inclusive semileptonic B decays. Althought one does not expect that exclusive measurements will provide a better determination of |Vub| than the inclusive measurements does [4], the former are important for several reasons. Besides the complementary determination of |Vub| provided by exclusive B decays, these measurements will allow to test available theoretical models for form factors (relativistic [2] and non-relativistic [3] quark models, QCD sum rules [5]). In this paper we are concerned with important isospin breaking corrections to B → V lν (V = ρ, ρ and ω) decays which have not been considered in previous analysis. There are several motivations to consider all sources of theoretical corrections in the calculation of charmless B → V semileptonic decays. From the experimental point of view, the study of these decays can be sensible improved at the B factory. In fact, actual measurements by the CLEO collaboration [6] provide the upper limit B(B → ρ0l−ν̄l) < (1.6− 2.7)× 10, which lies at the verge of theoretical predictions. Among the theoretical motivations we can mention the following: (a) the decay rate of B → ρlν provides 3 – 14 % [2,3,5] of the inclusive B → Xulνl decays, (b) the ratio of decay widths for (B → V lν)/(B → πlν) and the polarization of the daugther vector mesons can be used to discriminate