Speaker
Description
We discuss the Lorentz decomposition of $B \to \gamma^*$ matrix elements in terms of hadronic form factors, which are needed for a theory description of $B^- \to \ell^- \bar{\nu}_\ell \ell' \bar{\ell'}$ decays.
Our approach closely follows the Bardeen–Tung–Tarach procedure and ensures freedom from kinematic singularities, which is needed to apply dispersion relations in the photon momentum. We compare our approach to others in the literature and point out that a complete basis of structures is important for phenomenological applications, even for the case of massless leptons. In particular, we explicitly show that the supposed “collinear enhancement” for small photon momentum transfer is due to an inconsistent treatment of finite lepton masses. For a prediction of the decay rate, we link the $B \to \gamma^*$ form factors to the well-established $B \to V$ form factors.