Constraining the Unitarity Triangle with B→Vγ

Abstract

We discuss the exclusive radiative decays $B\to K^{*}\gamma$, $B \to\rho\gamma$, and $B\to\omega\gamma$ in QCD factorization within the Standard Model. The analysis is based on the heavy-quark limit of QCD. Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit. Special emphasis is placed on constraining the CKM-unitarity triangle from these observables. We propose a theoretically clean method to determine CKM parameters from the ratio of the $B\to\rho l\nu$ decay spectrum to the branching fraction of $B\to\rho\gamma$. The method is based on the cancellation of soft hadronic form factors in the large energy limit, which occurs in a suitable region of phase space. The ratio of the $B\to\rho\gamma$ and $B\to K^{*}\gamma$ branching fractions determines the side $R_{t}$ of the standard unitarity triangle with reduced hadronic uncertainties. The recent Babar bound on $B(B^0\to\rho^0\gamma)$ implies $R_t < 0.81 (\xi/1.3)$, with the limiting uncertainty coming only from the SU(3) breaking form factor ratio $\xi$. This constraint is already getting competitive with the constraint from $B_{s}$-$\bar B_{s}$ mixing. Phenomenological implications from isospin-breaking effects are briefly discussed.