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

Abstract

Abstract We study the penguin-mediated B ¯ d s → K ¯ ∗ 0 K ∗ 0 ϕ $$ {\overline{B}}_{d(s)}\to {\overline{K}}^{\ast 0}\left({K}^{\ast 0}\right)\phi $$ 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 ∗ K ¯ ∗ $$ {K}^{\left(\ast \right)}{\overline{K}}^{\left(\ast \right)} $$ 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 channel B ¯ d → K ¯ ∗ 0 ϕ $$ {\overline{B}}_d\to {\overline{K}}^{\ast 0}\phi $$ is in better agreement with the SM. However, if we add the measured branching ratio for the B ¯ d → K ¯ 0 ϕ $$ {\overline{B}}_d\to {\overline{K}}^0\phi $$ to our analysis, the simultaneous explanation of all the experimental data for the K ∗ K ¯ ∗ $$ {K}^{\left(\ast \right)}{\overline{K}}^{\left(\ast \right)} $$ and the K ∗ K ¯ ∗ ϕ $$ {K}^{\ast}\left({\overline{K}}^{\left(\ast \right)}\right)\phi $$ channels in terms of New Physics in the Wilson coefficients C 4d,s or C 8gd,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 4f , C 6f ) or (C 6f , C 8gf ). 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 4f , C 6f ) scenario, while discarding the (C 6f , C 8gf ) scenario completely. This can be traced to the discrepancy of more than 1 σ between the experimental measurements of the branching ratios of the B ¯ d B − → K ¯ 0 K − ϕ $$ {\overline{B}}_d\left({B}^{-}\right)\to {\overline{K}}^0\left({K}^{-}\right)\phi $$ transitions. This should provide a strong incentive for the LHCb/Belle II experiments to measure the branching ratios of B ¯ d → K ¯ ∗ 0 ϕ $$ {\overline{B}}_d\to {\overline{K}}^{\left(\ast \right)0}\phi $$ , B ¯ s → K ∗ 0 ϕ $$ {\overline{B}}_s\to {K}^{\ast 0}\phi $$ and particularly B − → K − ϕ to confirm or dismiss the conclusions hinted at by present data.

Keywords

• Bottom Quarks
• Effective Field Theories
• Properties of Hadrons
• Rare Decays