Optimised observables and new physics prospects in the penguin-mediated decays Bd(s) → K(∗)0ϕ

A bstract We study the penguin-mediated B̄d(s)→ K̄⁰(K⁰)φ B ¯ d s → K ¯ ∗ 0 K ∗ 0 ϕ transitions, proposing a new optimised observable L K*ϕ from the ratio of longitudinal branching ratios of these decays, with limited hadronic uncertainties and enhanced sensitivity to New Physics. This observable exhibits a deviation at the 1 . 48 σ level between its experimental value and its SM determination within QCD factorisation. This result can be accommodated together with the significant deviations found for the K( )K̄( ) K ∗ K ¯ ∗ modes in our earlier works if New Physics affects either the QCD penguin operator Q 4 or the chromomagnetic dipole operator Q 8 g for both b → d and b → s transitions. The allowed range for the Wilson coefficients C 4 s ,8 gs is narrower compared to C 4 d ,8 gd since the b → s transition channel B̄d→ K̄⁰φ B ¯ d → K ¯ ∗ 0 ϕ is in better agreement with the SM. However, if we add the measured branching ratio for the B̄d→ K̄⁰φ B ¯ d → K ¯ 0 ϕ to our analysis, the simultaneous explanation of all the experimental data for the K( )K̄( ) K ∗ K ¯ ∗ and the K^(K̄( ))φ K ∗ K ¯ ∗ ϕ channels in terms of New Physics in the Wilson coefficients C 4 d , s or C 8 gd , s only, is not possible. This set of observables can be explained more easily if we assume New Physics in both f = d , s sectors, either in ( C 4 f , C 6 f ) or ( C 6 f , C 8 gf ). The addition of the branching ratios of the charged modes B − → K (∗)− ϕ to the above mix of observables results in a reduction of the parameter space for the ( C 4 f , C 6 f ) scenario, while discarding the ( C 6 f , C 8 gf ) scenario completely. This can be traced to the discrepancy of more than 1 σ between the experimental measurements of the branching ratios of the B̄d(B⁻)→ K̄⁰(K⁻)φ B ¯ d B − → K ¯ 0 K − ϕ transitions. This should provide a strong incentive for the LHCb/Belle II experiments to measure the branching ratios of B̄d→ K̄( )0φ B ¯ d → K ¯ ∗ 0 ϕ , B̄ₛ→ K⁰φ B ¯ s → K ∗ 0 ϕ and particularly B − → K − ϕ to confirm or dismiss the conclusions hinted at by present data.