SEARCHING FOR NEW PHYSICS IN RARE K AND B DECAYS WITHOUT |Vcb| AND |Vub| UNCERTAINTIES

We reemphasize the strong dependence of the branching ratios B(K+ → π+VV) and B(KL → π0VV) on |Vcb| that is stronger than in rare B decays, in particular for KL → π0VV. Thereby the persistent tension between inclusive and exclusive determinations of |Vcb| weakens the power of these theoretically clean decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of the two branching ratios between each other and with other observables like the branching ratios for KS → μ+μ-, Bs,d → μ+μ- and B → K(K*)VV. We use as basic CKM parameters Vus, |Vcb|, and the angles β and γ in the unitarity triangle (UT) with the latter two determined through the measurements of tree-level B decays. This avoids the use of the problematic |Vub|. A ratio involving B(K+ → π+VV) and B(Bs → μ+μ-) while being |Vcb|-independent exhibits sizable dependence on the angle γ. It should be of interest for several experimental groups in the coming years. We point out that the |Vcb|-independent ratio of B(B+ → K+VV) and B(Bs → μ+μ-) from Belle II and LHCb signals a 1.8σ tension with its SM value. As a complementary test of the Standard Model, we propose to extract |Vcb| from different observables as a function of β and γ. We illustrate this with ϵK, ΔMd, and ΔMs finding tensions between these three determinations of |Vcb| within the SM. We point out that from ΔMs and SψKS alone, one finds |Vcb| = 41.8(6)×10-3 and |Vub| = 3.65(12) × 10-3. We stress the importance of a precise measurement of γ. Assuming no NP in |ϵK| and SψKS , we determine independently of |Vcb| and γ: B(K+ → π+VV)SM = (8.60 ± 0.42) × 10-11 and B(KL → π0VV)SM = (2.94 ± 0.15) × 10-11 with only CKM uncertainty coming from β, that is already precisely known. These are the most precise determinations to date. Assuming no NP in ΔMs,d allows to obtain analogous results for all B decay branching ratios considered in our paper without any CKM uncertainties.