Predicting $B -> \rho \gamma$ and $B_s -> \rho \gamma$ using holographic AdS/QCD Distribution Amplitudes for the $\rho$ meson

Abstract

We derive holographic AdS/QCD Distribution Amplitudes for the transversely polarised $\rho$ meson and we use them to predict the branching ratio for the decays $\bar B^\circ\rightarrow \rho^\circ \gamma$ and $\bar B^\circ_s\rightarrow \rho^\circ \gamma$ beyond leading power accuracy in the heavy quark limit. For $\bar B^\circ\rightarrow \rho^\circ \gamma$, our predictions agree with those generated using Sum Rules (SR) Distribution Amplitudes and with the data from the BaBar and Belle collaborations. In computing the weak annihilation amplitude which is power-supressed in $\bar B^\circ\rightarrow \rho^\circ \gamma$ but is the leading contribution in $\bar{B}^{\circ}_s\rightarrow \rho^\circ \gamma$, we find that, in its present form, the AdS/QCD DA avoids the end-point divergences encountered with the SR DA .Comment: 21 pages, 4 figures. A discussion of the influence of scale evolution of the DA on the infrared divergence problem is now included. Accepted by Physical Review