Implication of the B→(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 fractionB exp [B → (ρ, ω) γ] = (1.8 +0.6 −0.5 ± 0.1) × 10 −6 for the CKM phenomenology. Combined with the averaged branching fractionB exp (B → K * γ) = (4.06 ± 0.26) × 10 −5 measured earlier, this yieldsR exp [(ρ, ω) γ/K * γ] = (4.2 ± 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 yieldB th [B → (ρ, ω) γ] = (1.38 ± 0.42) × 10 −6 andR th [(ρ, ω) γ/K * γ] = (3.3 ± 1.0)%, in agreement with the BELLE data. Leaving instead the CKM-Wolfenstein parameters free, our analysis gives (at 68% C.L.) 0.16 ≤ |V td /V ts | ≤ 0.29, which is in agreement with but less precise than the indirect CKM-unitarity fit of the same, 0.18 ≤ |V td /V ts | ≤ 0.22. The isospin-violating ratio in the B → ργ decays and the SU(3)-violating ratio in the B 0 d → (ρ 0 , ω) γ decays are presented together with estimates of the direct and mixing-induced CP-asymmetries in the B → (ρ, ω) γ decays within the SM. Their measurements will overconstrain the angle α of the CKM-unitarity triangle.

Branching ratio andCPasymmetry forB→1P11γdecays

“…For this study, we consider ξ (b 1 , h 1 ) ⊥ as a free parameter and we will extract its value from the current experimental data on B → K 1 γ decays because K 1 is also an axial vector meson. This is in anology with the calculation done for the branching ratio of B → (ρ, ω) γ in terms of the branching ratio of B → K * γ by Ali et al [14].…”

“…Neglecting the W -exchange contributions in the decays, the radiative decay widths are determined by the penguin amplitudes which involve only the |dd components of these mesons, leading to identical branching ratios (modulo a tiny phase space difference). The W -exchange diagrams from the O (u) 1 and O (u) 2 operators (in our approach, we are systematically neglecting the contributions from the penguin operators O 3 , ..., O 6 ) yield contributions equal in magnitude but opposite in signs[for detailed calculation please see [14,17]]. If we use the notations and expressions given in Ref.…”

“…We follow the same frame work as done by Ali et al [14] for B → (ρ,ω) γ, because B 0 d → (b 1 ,h 1 ) γ shares many things with it. The only difference is the DA for the daughter meson.…”

“…The value of these constants is used from [14,10] and are collected in Table 1, for the numerical analysis. For this study, we consider ξ (b 1 , h 1 ) ⊥ as a free parameter and we will extract its value from the current experimental data on B → K 1 γ decays because K 1 is also an axial vector meson.…”

CPasymmetry, branching ratios, and isospin breaking effects ofB→K*γwith the perturbative QCD approach

“…The result can be compared with the ones extracted by another estimation. In the QCD Factorization, T K * 1 (0) = 0.27 ± 0.04 [25] and an updated phenomenological estimate of this quantity with the light-cone distribution amplitudes for the K * meson is T K * 1 (0) = 0.27 ± 0.02 [26]. While the central value in the updated result is the same as before, the error is reduced by a factor of 2.…”