Implications of $B \to \rho \gamma$ measurements in the standard model and supersymmetric theories

Abstract.

We study the implications of the recently improved upper limits on the branching ratios for the decays $B \to \rho \gamma$, expressed as $R(\rho \gamma/K^* \gamma)\equiv {\cal B}(B \to \rho \gamma)/{\cal B}(B \to K^* \gamma) \le 0.047$. We work out the constraints that the current bound on $R(\rho \gamma/K^* \gamma)$ implies on the parameters of the quark mixing matrix in the standard model (SM). Using the present profile of the unitarity triangle, we predict this ratio to lie in the range $0.010 \leq R(\rho\gamma/K^*\gamma) \leq 0.046$ (at 95% C.L.), with the central value $R(\rho\gamma/K^*\gamma)=0.023$. We also work out the correlations involving $R(\rho \gamma/K^* \gamma)$, the isospin-violating ratio $\Delta (\rho \gamma)$, and the direct CP-violating asymmetry $A_{CP}(\rho \gamma)$ in $B \to \rho \gamma$ decays in the SM, in the minimal supersymmetric extension of the SM (MSSM), and in an extension of the MSSM involving an additional flavor-changing structure in $b \to d$ transitions.