Spectator interactions in B -> V gamma decays and QCD factorisation
Abstract
We study the radiative decays B -> V gamma (where V=rho, K^*) in the framework of QCD factorisation, and in particular the hard-spectator contributions to the decay amplitudes. For the phenomenologically significant chromomagnetic operator, we show by an explicit next-to-leading-order computation that the spectator interactions factorise in the heavy-quark limit, i.e. that they can be written as the convolution of a hard-scattering kernel, computable in perturbation theory, and of the light-cone distribution amplitudes for the B and V mesons which contain the soft physics. The presence of an intermediate scale of order sqrt{Lambda_QCD M_B} leads to the presence of Sudakov logarithms at all orders of perturbation theory, which we resum using the renormalization-group within the Soft-Collinear Effective Theory. We indicate how the proof of factorisation can be extended to higher orders in perturbation theory and to other (four-quark) operators, and how the resummation of large logarithms can be performed for these operators.Keywords
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