Structure-Dependent QED Effects in Exclusive B Decays at Subleading Power

Abstract

We derive a factorization theorem for the structure-dependent QED effects in the weak exclusive process $B^{-}\to {\ell }^{-}{\bar{\nu }}_{\ell }$, i.e., effects probing the internal structure of the $B$ meson. The derivation requires a careful treatment of endpoint-divergent convolutions common to subleading-power factorization formulas. We find that the decay amplitude is sensitive to two- and three-particle light-cone distribution amplitudes of the $B$ meson as well as to a new hadronic parameter $F(\mu ,\Lambda )$, which generalizes the notion of the $B$-meson decay constant in the presence of QED effects. This is the first derivation of a subleading-power factorization theorem in which the soft functions are non-perturbative hadronic matrix elements.

5 pages, 2 figures, v2: inclusion of soft-collinear modes in the factorization theorem, explicit expression for IR poles in the virtual amplitude given, references added, main conclusions unchanged, v3: clarifications added, definition of hadronic parameter F adjusted, matches journal version, v4: corrected operator definition, scheme-dep. terms and sign in three-particle contribution corrected

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• Threshold factorization of the Drell-Yan quark-gluon channel and two-loop soft function at next-to-leading power
• On sum rules for semi-leptonic $b\to c$ and $b\to u$ decays
• Structure-dependent QED effects in exclusive $B$-meson decays
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• $B_c\to {\eta }_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics
• The Simplest B Decay, Precisely