Exclusive Semi-leptonic Decays of B-baryons into Protons

Abstract

We present a QCD-based calculation of the exclusive semileptonic decay Λb → p l ν̄l. Using the ideas of Heavy Quark Effective Theory, we discuss the factorization of the amplitude. Further, resummed Sudakov effects are put in to ensure a consistent perturbative expansion. E-mail: loinaz@walden.physics.lsa.umich.edu On sabbatical leave from the University of Michigan, Ann Arbor The study of b-hadron decays has been the subject of considerable interest in recent years, as a source of information about CKM matrix elements, [1] as a laboratory for the application of QCD [2, 3, 4, 6] and the development of theoretical tools such as Heavy Quark Effective Theory (HQET)[5]. In particular, heavy-to-light decays are interesting because they give information on Vub, but they are especially difficult to calculate because of the essential presence of strong interactions in the hadronic bound state. Recently, however, in [4] a method has been formulated for analyzing the exclusive decay B0 → π l+ νl in the region of large hadronic recoil and in the limit of a very heavy b-quark. The approach combines HQET, perturbative factorization theorems for exclusive processes [8], and exponentiation of Sudakov double-logarithms [7]. In this paper we extend this technology to study the exclusive decay Λb → p l ν̄l, also in the limit of large hadronic recoil and large b quark mass. In this limit, the method provides an asymptotic regime in which a systematic expansion exists with corrections O(αs(cΛQCDmb)), where c is a calculable constant. For some recent model-dependent calculations of Λb decays, see [9]. From the phenomenological side,to the extent that the very large mb limit is realistic our calculation is motivated by the possibility that it could provide another method for extracting Vub from data, complementary to the Bmeson studies. In addition, comparison of experiment with the predictions of our calculation will afford added insight into the applicability of perturbative QCD (PQCD) in processes with momentum transfers in the few-GeV range. Further, the analysis of this paper is useful for contrasting the decays Λb → p l ν̄l and B0 → π l+ νl, which may be helpful in elucidating the surprisingly large difference in the Λb and B 0 lifetimes recently seen in experimental data [10]. We stress that in this paper we are calculating the purely perturbative contribution to the above-mentioned exclusive decay. This would be the dominant one in the limit of a very heavy b-quark. However, for realistic values ofmb there are could be sizable nonperturbative contributions in the form of higher-twist effects . These will be discussed in a future work [15]. However, as we shall see below, numerical indications are that a nodified perturbation expansion is self-consistent even for realistic values of mb. The physical picture of this decay is similar to that for the meson, described in [4]. Sitting inside the Λb, the b-quark decays into a W − and a fast-moving, nearly on-shell u-quark. The u-quark propagates through the remaining hadronic medium, picking up a light ud pair over a distance y. Since we are considering an exclusive decay, no gluon radiation escapes. If y were large enough (O( 1 ΛQCD )) we would expect considerable gluon radiation. Thus, for exclusive processes we expect the outgoing u-quark to propagate only small distances (<< O( 1 ΛQCD ) ) before acquiring a ud pair to form the color singlet which will hadronize to form the proton. Then the hard gluons which kick these spectator quarks will typically be off-shell by O(ΛQCDmb), large enough that we might expect perturbative factorization theorems to apply. We will state the arguments and results of our approach and sketch the calculations. The calculational details will be published elsewhere [15]. Our procedure is to judiciously combine elements of [4] and [11, 12]. We first identify the sources of long-distance behaviour which must be dealt with in order to successfully apply perturbation theory. Soft divergences will arise from interactions of soft gluons with the heavy quark, and soft and collinear divergences will arise from the interactions of virtual partons travelling in the direction of the outgoing proton. As in [4], we separate out the soft divergences due to the heavy quark

Cite this paper

@inproceedings{Loinaz2008ExclusiveSD, title={Exclusive Semi-leptonic Decays of B-baryons into Protons}, author={W . A . Loinaz and R. Akhoury}, year={2008} }