Searching for New Physics in Rare \(K\) and \(B\) Decays without \(|V_{cb}|\) and \(|V_{ub}|\) Uncertainties

We reemphasize the strong dependence of branching ratios $B(K^+\to\pi^+\nu\bar\nu)$ and $B(K_L\to\pi^0\nu\bar\nu)$ on $|V_{cb}|$ that is stronger than in rare $B$ decays, particular for $K_L\to\pi^0\nu\bar\nu$. Thereby persistent tension between inclusive exclusive determinations weakens power these theoretically clean decays search new physics (NP). demonstrate how this uncertainty can be practically removed by considering within SM suitable two each other with observables like $K_S\to\mu^+\mu^-$, $B_{s,d}\to\mu^+\mu^-$ $B\to K(K^*)\nu\bar\nu$. use as basic CKM parameters $V_{us}$, angles $\beta$ $\gamma$ unitarity triangle (UT) latter determined through measurements tree-level decays. This avoids problematic $|V_{ub}|$. A ratio involving $B(B_s\to\mu^+\mu^-)$ while being $|V_{cb}|$-independent exhibits sizable angle $\gamma$. It should interest several experimental groups coming years. point out $B(B^+\to K^+\nu\bar\nu)$ from Belle II LHCb signals a $1.8\sigma$ its value. As complementary test Standard Model, we propose to extract different function illustrate $\epsilon_K$, $\Delta M_d$ M_s$ finding tensions three SM. From $S_{\psi K_S}$ alone find $|V_{cb}|=41.7(6)\times 10^{-3}$ $|V_{ub}|=3.64(12)\times 10^{-3}$. stress importance precise measurement