Optimised observables and new physics prospects in the penguin-mediated decays B_d(s)→ K^(*)0ϕ

We study the penguin-mediated decays B̅_d(s)→K̅^*0(K^*0)ϕ transitions. We propose 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. It 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^(*)K̅^(*) modes in our earlier works, if New Physics affects either the QCD penguin operator Q_4 or the chromomagnetic dipole operator Q_8g for both b→ d and b→ s transitions. The allowed range for the Wilson coefficients C_4s,8gs is narrower compared to C_4d,8gd since the b→ s transition B̅_d→K̅^*0ϕ) is in better agreement with the SM. If we add the measured longitudinal branching ratio for the B̅_d→K̅^0ϕ to our analysis, the simultaneous explanation of all the experimental data for the K^(*)K̅^(*) and the K^*(K̅^(*))ϕ channels in terms of New Physics in C_4d,s or C_8gd,s operators only becomes very constrained. This set of observables can be explained more easily if we assume New Physics either in (C_4f,C_6f) or C_6f,C_8gf in both f=d,s. This should provide a strong incentive for the LHCb experiment to perform a new measurement of the longitudinal branching ratio for B̅_d→K̅^*0ϕ, measured only by BaBar and Belle.