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

Ali, A.; Lunghi, E.; Parkhomenko, A. Ya.

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

Authors

Ali, A.

Lunghi, E.

Parkhomenko, A. Ya.

Description

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.
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