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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 thisuncertainty can be practically removed by considering within the SM suitableratios of various branching ratios. This includes the branching ratios for$K^+\to\pi^+\nu\bar\nu$, $K_{L}\to\pi^0\nu\bar\nu$, $K_S\to\mu^+\mu^-$,$B_{s,d}\to\mu^+\mu^-$ and $B\to K(K^*)\nu\bar\nu$. Also $\epsilon_K$, $\DeltaM_d$, $\Delta M_s$ and the mixing induced CP-asymmetry $S_{\psi K_S}$, allmeasured already very precisely, play an important role in this analysis. Thehighlights of our analysis are 16 $|V_{cb}|$ and $|V_{ub}|$ independent ratiosthat often are independent of the CKM arameters or depend only on the angles$\beta$ and $\gamma$ in the Unitarity Triangle with $\beta$ already preciselyknown and $\gamma$ to be measured precisely in the coming years by the LHCb andBelle II collaborations. Once $\gamma$ Once $\gamma$ is measured preciselythese 16 ratios taken together are expected to be a powerful tool in the searchfor new physics. Assuming no NP in $|\epsilon_K|$ and $S_{\psi K_S}$ wedetermine independently of $|V_{cb}|$:$\mathcal{B}(K^+\to\pi^+\nu\bar\nu)_\text{SM}= (8.60\pm0.42)\times 10^{-11}$and $\mathcal{B}(K_L\to\pi^0\nu\bar\nu)_\text{SM}=(2.94\pm 0.15)\times10^{-11}$. This are the most precise determinations to date. Assuming no NP in$\Delta M_{s,d}$ allows to obtain analogous results for all $B$ decay branchingratios considered in our paper without any CKM uncertainties.

Standard Model Predictions for Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties