Standard Model correlations between K -> πν\barνdecays and observables in B Physics

Including the recent preliminary results of BaBar and BELLE experiments, we update the currently allowed intervals for various CKM parameters: $\barρ$, $\barη$, $\sin2β$, $\sin2α$, $\sin^2γ$. We also update the SM prediction for the rates of the $K_L \to π^0 ν\barν$ and $K^+ \to π^+ ν\barν$ decays, their ratio $a_{πν\barν}$, as well as for certain observables related to $B$ Physics like the CP asymmetries $a_{ψK_S}$ in $B^0_d \to J/ψK_S$ and $a_{ψϕ}$ in $B^0_s \to J/ψϕ$ or the mass differences $Δm_q$ ($q=d,s$) in the $B^0_q-\bar B^0_q$ systems. We investigate the correlations between them. The strongest correlations are between i) $a_{πν\barν}$ and $a_{ψK_S}$, ii) $\BR(K^+ \to π^+ ν\barν)$ and $Δm_d/Δm_s$ and iii) $\BR(K_L \to π^0 ν\barν)$ and $a_{ψϕ}$. These correlations are likely to be violated in the presence of New Physics and therefore provide stringent tests of the Standard Model.

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