Implication of the $B \to (ρ, ω) γ$ Branching Ratios for the CKM Phenomenology

Abstract

We study the implication of the recent measurement by the BELLE collaboration of the averaged branching fraction $\bar B_{exp} [B \to (ρ, ω) γ] = (1.8^{+0.6}_{-0.5} \pm 0.1) \times 10^{-6}$ for the CKM phenomenology. Combined with the averaged branching fraction $\bar B_{exp} (B \to K^* γ) = (4.06 \pm 0.26) \times 10^{-5}$ measured earlier, this yields $\bar R_{exp} [(ρ, ω) γ/K^* γ] = (4.2 \pm 1.3)%$ 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 $\bar B_{th} [B \to (ρ, ω) γ] = (1.38 \pm 0.42) \times 10^{-6}$ and $\bar R_{th} [(ρ, ω) γ/K^* γ] = (3.3 \pm 1.0)%$, in agreement with the BELLE data. Leaving instead the CKM-Wolfenstein parameters free, our analysis gives (at 68% C.L.) $0.16\leq |V_{td}/V_{ts}| \leq 0.29$, which is in agreement with but less precise than the indirect CKM-unitarity fit of the same, $0.18 \leq |V_{td}/V_{ts}| \leq 0.22$. The isospin-violating ratio in the $B \to ργ$ decays and the SU(3)-violating ratio in the $B_d^0 \to (ρ^0, ω) γ$ decays are presented together with estimates of the direct and mixing-induced CP-asymmetries in the $B \to (ρ,ω) γ$ decays within the SM. Their measurements will overconstrain the angle $α$ of the CKM-unitarity triangle.