Radiative Decay $ B \to l \nu \gamma $ in the Light Cone QCD Approach

Abstract

We calculate to the leading twist 2 accuracy the rate for the decay $ B_{u} \rightarrow l \nu \gamma $ using the light cone QCD sume rules. We find $ Br( B_{u} \rightarrow l \nu \gamma) \simeq 2 \cdot 10^{-6} $. The results are used to test the applicability of the constituent quark model approximation to the same process.The latter estimate is proportional to $ 1/m_{u}^{2} $, where $ m_{u} \simeq \bar{\Lambda}_{u} $ is the "constituent quark mass", indicating that the process is of long distance type. We find that the two approaches yield similar results for the rate with the choice $ m_{u} \simeq 430-480 \;MeV $. This indicates that the constituent quark model may be used for estimates of the radiative "annihilation" contribution to this and other radiative decays. We point out that this decay may be useful for the measurement of $ |V_{ub}|$.