Gauge invariance and form factors for the decayB→γl+l−

Abstract

We analyze the form factors for the $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\gamma}{l}^{+}{l}^{\ensuremath{-}}$ weak transition. We show that making use of the gauge invariance of the $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\gamma}{l}^{+}{l}^{\ensuremath{-}}$ amplitude, the structure of the form factors in the resonance region, and their relations at large values of the photon energy results in efficient constraints on the behavior of the form factors. Based on these constraints, we propose a simple parametrization of the form factors and apply it to the lepton forward-backward (FB) asymmetry in the $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\gamma}{l}^{+}{l}^{\ensuremath{-}}$ decay. We find that the behavior of the FB asymmetry as a function of the photon energy, as well as the location of its zero, depend only weakly on the $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\gamma}$ form factors, and thus constitutes a powerful tool for testing the standard model.