Bound on $\cos\alpha$ from exclusive weak radiative B decays

Abstract

We present a bound on the weak phase $\alpha$ from isospin-breaking effects in weak radiative decays, which requires the CP-averaged branching ratios for the weak radiative decays $B^\pm\to \rho^\pm \gamma$, $B^0\to \rho^0/\omega \gamma$, $B\to K^* \gamma$ and the photon energy spectrum in $B\to\gamma \ell\nu_\ell$. We carefully identify all sources of isospin breaking, which could possibly mask information about the CKM parameters. They are introduced by diagrams with photon bremsstrahlung off the spectator quark and diagrams with annihilation penguin topologies. The former can be eliminated by combining $B\to\rho\gamma$ and $B\to K^{*}\gamma$ data, whereas the latter effects are OZI-suppressed and can be controlled by measuring also the modes $B_s\to \rho(\omega)\gamma$. The resulting bound excludes values of $\alpha$ around $90^\circ$, provided that the combined ratio ${\cal B}(B^\pm \to \rho^\pm\gamma)/{\cal B}(B^0 \to \rho^0/\omega\gamma) \times {\cal B}(B^0 \to K^{*0}\gamma)/{\cal B}(B^\pm \to K^{*\pm}\gamma)$ is found to be different from 1.