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

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We study the penguin-mediated B¯ds→K¯∗0K∗0ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{B}}_{d(s)}\ o {\\overline{K}}^{\\ast 0}\\left({K}^{\\ast 0}\\right)\\phi $$\\end{document} transitions, proposing a new optimised observable LK*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¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}^{\\left(\\ast \\right)}{\\overline{K}}^{\\left(\\ast \\right)} $$\\end{document} modes in our earlier works if New Physics affects either the QCD penguin operator Q4 or the chromomagnetic dipole operator Q8g for both b → d and b → s transitions. The allowed range for the Wilson coefficients C4s,8gs is narrower compared to C4d,8gd since the b → s transition channel B¯d→K¯∗0ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{B}}_d\ o {\\overline{K}}^{\\ast 0}\\phi $$\\end{document} is in better agreement with the SM. However, if we add the measured branching ratio for the B¯d→K¯0ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{B}}_d\ o {\\overline{K}}^0\\phi $$\\end{document} to our analysis, the simultaneous explanation of all the experimental data for the K∗K¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}^{\\left(\\ast \\right)}{\\overline{K}}^{\\left(\\ast \\right)} $$\\end{document} and the K∗K¯∗ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}^{\\ast}\\left({\\overline{K}}^{\\left(\\ast \\right)}\\right)\\phi $$\\end{document} channels in terms of New Physics in the Wilson coefficients C4d,s or C8gd,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 (C4f , C6f ) or (C6f , C8gf ). 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 (C4f , C6f ) scenario, while discarding the (C6f , C8gf ) 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¯dB−→K¯0K−ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{B}}_d\\left({B}^{-}\\right)\ o {\\overline{K}}^0\\left({K}^{-}\\right)\\phi $$\\end{document} transitions. This should provide a strong incentive for the LHCb/Belle II experiments to measure the branching ratios of B¯d→K¯∗0ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{B}}_d\ o {\\overline{K}}^{\\left(\\ast \\right)0}\\phi $$\\end{document}, B¯s→K∗0ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{B}}_s\ o {K}^{\\ast 0}\\phi $$\\end{document} and particularly B− → K−ϕ to confirm or dismiss the conclusions hinted at by present data.