Sudakov effects in B -> pi l nu form factors

Abstract

In order to obtain information about the Standard Model from exclusive hadronic two-body B-decays, we have to quantify non-perturbative QCD effects. Approaches based on the factorization of mass singularities into hadronic distribution amplitudes and form factors provide a rigorous theoretical framework for the evaluation of these effects in the heavy quark limit. But it is not possible to calculate power corrections in a model-independent way, because of non-factorizing long-distance contributions. It has been argued that Sudakov effects suppress these contributions and render the corresponding corrections perturbatively calculable. In this paper we examine this claim for the related example of semileptonic B -> pi decays and conclude that it is not justified. The uncertainties in our knowledge of the mesons' distribution amplitudes imply that the calculations of the form factors are not sufficiently precise to be useful phenomenologically. Moreover, a significant contribution comes from the non-perturbative region of large impact parameters, and is therefore uncalculable. We also raise a number of theoretical issues in the derivation of the underlying formalism. For B-decays it is thus not possible to invoke Sudakov effects to calculate amplitudes for decays which have long-distance divergences (end-point singularities) in the standard hard-scattering approach.

39 pages, 10 figures

References in corpus (1)

• Perturbative QCD factorization of $\pi {\gamma }^{\ast }\to \gamma (\pi )$ and $B\to \gamma (\pi )l\bar{\nu }$

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