Factorization and the Soft Overlap Contribution to Heavy-to-Light Form Factors

Using the formalism of soft-collinear effective theory, a complete separation of short- and long-distance contributions to heavy-to-light transition form factors at large recoil is performed. The universal functions $ζ_M(E)$ parameterizing the ``soft overlap'' contribution to the form factors are defined in terms of matrix elements in the effective theory. Endpoint configurations corresponding to kinematic situations where one of the valence partons in the external mesons carries very small momentum are accounted for in terms of operators involving soft-collinear messenger fields. They contribute at leading order in $Λ_{\rm QCD}/E$ and spoil factorization. An analysis of operator mixing and renormalization-group evolution in the effective theory reveals that the intermediate scale $\sqrt{EΛ}$ is without significance to the soft functions $ζ_M(E)$, and that the soft overlap contribution does not receive a significant perturbative (Sudakov) suppression.

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