Standard Model Predictions for Rare K and B Decays without |V_cb| and |V_ub| Uncertainties

The persistent tensions between inclusive and exclusive determinations of |V_cb| and |V_ub| weaken the power of theoretically clean rare K and B 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 various branching ratios. This includes the branching ratios for K⁺→ p⁺νν, K_L→ π⁰νν, K_S→m⁺m^-, B_s,d→m⁺m^-and B→K(K^∗)νν. Also ϵ_K, ΔM_d, ΔM_sand the mixing induced CP-asymmetry S_φK_S, all measured already very precisely, play an important role in this analysis. The highlights of our analysis are 16 |V_cb| and |V_ub| independent ratios that often are independent of the CKM parameters or depend only on the angles b and g in the Unitarity Triangle with b already precisely known and g to be measured precisely in the coming years by the LHCb and Belle II colaborations. Once g is measured precisely these 16 ratios taken together are expected to be a powerful tool in the search for new physics. On the other hand within the SM they imply that to obtain the SM predictions for rare Kaon decays only the experimental values of jeKj and SyKS are needed. In particular we find: B(K⁺→p⁺νν)SM = (8:60±0:42)×10^-11and B(K_L→ π⁰νν)SM = (2:94±0:15)×10^-11. This are the most precise determinations to date. Similarly, to obtain the SM predictions for all rare B decay branching ratios only the knowledge of the experimental values of ΔM_s,dis required.