Standard Model predictions for rare K and B decays without new physics infection

Abstract

AbstractThe Standard Model (SM) does not contain by definition any new physics (NP) contributions to any observable but contains four CKM parameters which are not predicted by this model. We point out that if these four parameters are determined in a global fit which includes processes that are infected by NP and therefore by sources outside the SM, the resulting so-called SM contributions to rare decay branching ratios cannot be considered asgenuineSM contributions to the latter. On the other handgenuineSM predictions, that arefreefrom the CKM dependence, can be obtained for suitable ratios of theKandBrare decay branching ratios to$$\Delta M_s$$ΔMs,$$\Delta M_d$$ΔMdand$$|\varepsilon _K|$$|εK|, all calculated within the SM. These three observables contain by now only small hadronic uncertainties and are already well measured so that rather precise SM predictions for the ratios in question can be obtained. In this context therapid testof NP infection in the$$\Delta F=2$$ΔF=2sector is provided by a$$|V_{cb}|-\gamma $$|Vcb|-γplot that involves$$\Delta M_s$$ΔMs,$$\Delta M_d$$ΔMd,$$|\varepsilon _K|$$|εK|, and the mixing induced CP-asymmetry$$S_{\psi K_S}$$SψKS. As with the present hadronic matrix elements this test turns out to benegative, assuming negligible NP infection in the$$\Delta F=2$$ΔF=2sector and setting the values of these four observables to the experimental ones, allows to obtain SM predictions for allKandBrare decay branching ratios that are most accurate to date and as a byproduct to obtain the full CKM matrix on the basis of$$\Delta F=2$$ΔF=2transitionsalone.Using this strategy we obtain SM predictions for 26 branching ratios for rare semileptonic and leptonicKandBdecays with the$$\mu ^+\mu ^-$$μ+μ-pair or the$$\nu {\bar{\nu }}$$νν¯pair in the final state. Most interesting turn out to be the anomalies in the low$$q^2$$q2bin in$$B^+\rightarrow K^+\mu ^+\mu ^-$$B+→K+μ+μ-($$5.1\sigma $$5.1σ) and$$B_s\rightarrow \phi \mu ^+\mu ^-$$Bs→ϕμ+μ-($$4.8\sigma $$4.8σ).