Radiative Corrections to the Decay B → πeν and the Heavy Quark Limit

We calculate radiative corrections to the light-cone sum rule for the semileptonic form factor in B → πeν decays and thus remove the major uncertainty in determining the CKM mixing angle |Vub| by this method. We discuss the remaining uncertainties and perspectives for further studies. The structure of the radiative corrections suggests factorization of soft (end-point) and hard rescattering contributions in heavy-to-light decays in the heavy quark limit. Submitted to Physics Letters B ∗On leave of absence from St. Petersburg Nuclear Physics Institute, 188350 Gatchina, Russia. 1. Precise determination of the CKMmixing angle |Vub| will most likely come from semileptonic B decays. Two competing strategies exist, the study of the end-point region in inclusive decays and the analysis of various exclusive decay channels, most notably B → πeν which is the easiest one to access experimentally. The theoretical challenge in the latter case is to calculate the B → π transition form factor f+(q) induced by the weak vector current: 〈π(pπ)|ūγμb|B(pB)〉 = (pB + pπ)μ f+(q) + (pB − pπ)μf−(q) . (1) Here q = (pB − pπ) is the square of the momentum transferred to the lepton pair; the second form factor f− does not contribute to the decay rate for zero mass leptons and will not be considered in this letter. The decay rate is dominated by contributions from small values of q, for which the u quark produced in the weak decay has large energy of order mb/2 in the B meson rest frame (mb is the b quark pole mass). A consistent QCD description of such processes exists up to now only in the Sudakov limit [1], in which case contributions from large transverse quark-antiquark separations are suppressed and the form factor is dominated by hard gluon exchange [2]. This limit is theoretically interesting, but not relevant for realistic b quark masses. In fact, we will argue that “soft” contributions related to large transverse distances exceed the “hard” contributions by an order of magnitude (and have opposite sign). Any theoretical approach to heavy-to-light decay form factors aiming at quantitative predictions has to deal with these “soft” terms explicitly, as do e.g. light-cone sum rules and various models [3]. The consistent separation of “hard” and “soft” contributions in heavy-to-light decays presents an unsolved problem which, to our knowledge, has never been tackled in a systematic way. In this letter we examine a possibility for such a separation, based on our calculation of the radiative corrections to the corresponding light-cone sum rules. The basic idea of the light-cone sum rule approach is to consider a two-point correlation function replacing the B meson state by a suitable interpolating current: