Optimised observables and new physics prospects in the penguin-mediated decays $B_{d(s)}\to K^{(*)0}\phi$

We study penguin-mediated $\bar{B}_{d(s)}\to\bar{K}^{*0}(K^{*0})\phi$ transitions, proposing a new optimised observable $L_{K^*\phi}$ from the ratio of the corresponding branching ratios of these decays, with limited hadronic uncertainties and enhanced New Physics sensitivity. It deviates by $1.48\sigma$ between its experimental value and SM determination within QCD factorisation. This can be accommodated together with significant deviations found in the $K^{(*)}\bar{K}^{(*)}$ 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 $b\to d$ and $b\to s$ transitions. The allowed range for the Wilson coefficients $C_{4s,8gs}$ is narrower than $C_{4d,8gd}$ since the $b\to s$ transition channel $\bar{B}_d\to\bar{K}^{*0}\phi$ is in better agreement with the SM. However, if we add the measured $\bar{B}_{d}\to \bar{K}^{0}\phi$ branching ratio, simultaneous explanation of all experimental data for $K^{(*)}\bar{K}^{(*)}$ and $K^*(\bar{K}^{(*)})\phi$ channels in terms of New Physics in $C_{4d,s}$ or $C_{8gd,s}$ only, is not possible. They can be explained more easily if we assume New Physics in both $f=d,s$ sectors. The addition of the branching ratios of the charged modes $B^-\to K^{(*)-}\phi$ to the above mix of observables results in a reduction of the parameter space for the $(C_{4f},C_{6f})$ scenario, while discarding the $(C_{6f},C_{8gf})$ scenario completely. This is because of the discrepancy of more than 1 $\sigma$ between the experimental measurements of the branching ratios of the $\bar{B}_{d}(B^-)\to\bar{K}^0(K^-)\phi$ transitions. This provides a strong incentive for the LHCb/Belle II experiments to measure the branching ratios of $\bar{B}_{d}\to\bar{K}^{(*)0}\phi$, $\bar{B}_s\to K^{*0}\phi$ and particularly $B^-\to K^-\phi$ to confirm or dismiss the conclusions hinted at by present data.