Implication of the $B\to (\rho ,\omega )\gamma$ Branching Ratios for the CKM Phenomenology

Abstract

We study the implication of the recent measurement by the BELLE collaboration of the averaged branching fraction ${\bar{B}}_{exp}[B\to (\rho ,\omega )\gamma ]=(1.8_{-0.5}^{+0.6}\pm 0.1)\times 10^{-6}$ for the CKM phenomenology. Combined with the averaged branching fraction ${\bar{B}}_{exp}(B\to K^{\ast }\gamma )=(4.06\pm 0.26)\times 10^{-5}$ measured earlier, this yields ${\bar{R}}_{exp}[(\rho ,\omega )\gamma /K^{\ast }\gamma ]=(4.2\pm 1.3)$ for the ratio of the two branching fractions. Updating earlier theoretical analysis of these decays based on the QCD factorization framework, and constraining the CKM-Wolfenstein parameters from the unitarity fits, our results yield ${\bar{B}}_{th}[B\to (\rho ,\omega )\gamma ]=(1.38\pm 0.42)\times 10^{-6}$ and ${\bar{R}}_{th}[(\rho ,\omega )\gamma /K^{\ast }\gamma ]=(3.3\pm 1.0)$, in agreement with the BELLE data. Leaving instead the CKM-Wolfenstein parameters free, our analysis gives (at 68% C.L.) $0.16\le |V_{td}/V_{ts}|\le 0.29$, which is in agreement with but less precise than the indirect CKM-unitarity fit of the same, $0.18\le |V_{td}/V_{ts}|\le 0.22$. The isospin-violating ratio in the $B\to \rho \gamma$ decays and the SU(3)-violating ratio in the $B_d^0\to ({\rho }^0,\omega )\gamma$ decays are presented together with estimates of the direct and mixing-induced CP-asymmetries in the $B\to (\rho ,\omega )\gamma$ decays within the SM. Their measurements will overconstrain the angle $\alpha$ of the CKM-unitarity triangle.

Comments: 21 pages, 3 figures. Included a discussion of model-dependent estimates of the long-distance/rescattering contributions in radiative B-decays; added a reference. Version accepted for publication in Physics Letters B