Sudakov effects in B→ πℓ νℓ form factors

Abstract

In order to obtain fundamental information about the Standard Model of particle physics from experimental measurements of exclusive hadronic two-body B-decays we have to be able to quantify the non-perturbative QCD effects. Although 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, it is not possible to calculate the O( Λ QCD/ m b ) corrections in a model-independent way, because of the presence of non-factorizing long-distance contributions. It has been argued that Sudakov effects suppress these contributions and render the corresponding corrections perturbatively calculable in terms of the distribution amplitudes. In this paper we examine this claim for the simple and related example of semileptonic B→ π decays (which have similar long-distance contributions) 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, it appears that a significant fraction of the contribution comes from the non-perturbative region of large impact parameters, and is therefore incalculable. We also raise a number of theoretical issues in the derivation of the underlying formalism. Our conclusion is therefore a disappointing one. For B-decays it is 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.