We build a set of new observables using closely related non-leptonic penguin-mediated $B_d$ and $B_s$ decays: ${\bar B}_{d,s} \to K^{*0} \bar{K}^{*0}$, ${\bar B}_{d,s} \to K^{0} \bar{K}^{0}$, ${\bar B}_{d,s} \to K^{0} \bar{K}^{*0}$ and ${\bar B}_{d,s} \to \bar{K}^{0} {K^{*0}}$ together with their CP conjugate partners. These optimised observables are designed to reduce hadronic uncertainties, mainly coming from form factors and power-suppressed infrared divergences, and thus maximize their sensitivity to New Physics (NP). The deviations observed with respect to the Standard Model (SM) in the ratios of branching ratios of ${\bar B}_{d,s} \to K^{*0} \bar{K}^{*0}$ ($2.6\sigma$) and ${\bar B}_{d,s} \to K^{0} \bar{K}^{0}$ ($2.4\sigma$) can be explained by simple NP scenarios involving the Wilson coefficients ${\cal C}_4$ and ${\cal C}_6$ associated with QCD penguin operators and the coefficient ${\cal C}_{8g}$ of the chromomagnetic operator. The optimised observables for ${\bar B}_{d,s} \to K^{0} \bar{K}^{*0}$ and ${\bar B}_{d,s} \to \bar{K}^{0} {K^{*0}}$ show distinctive patterns of deviations with respect to their SM predictions under these NP scenarios. The pattern of deviations of individual branching ratios, though affected by significant hadronic uncertainties, suggests that NP is needed both in $b\to d$ and $b\to s$ transitions. We provide the regions for the Wilson coefficients consistent with both optimised observables and individual branching ratios. The NP scenarios considered to explain the deviations of ${\bar B}_{d,s} \to K^{*0} \bar{K}^{*0}$ and ${\bar B}_{d,s} \to K^{0} \bar{K}^{0}$ can yield deviations up to an order of magnitude among the observables that we introduced for ${\bar B}_{d,s} \to K^{0} \bar{K}^{*0}$ and ${\bar B}_{d,s} \to \bar{K}^{0} {K^{*0}}$. Probing these new observables experimentally by improving the measurements of individual branching ratios of penguin-mediated decays would confirm the consistency of the deviations already observed and provide a highly valuable hint of NP in the non-leptonic sector.
Elia Bertoldo, Clara Fernández, Giada Caneva