Standard Model correlations between K -> \pi \nu \bar\nu decays and observables in B Physics

Abstract

Including the recent preliminary results of BaBar and BELLE experiments, we update the currently allowed intervals for various CKM parameters: $\bar{\rho }$, $\bar{\eta }$, $\sin 2\beta$, $\sin 2\alpha$, ${\sin }^2\gamma$. We also update the SM prediction for the rates of the $K_L\to {\pi }^0\nu \bar{\nu }$ and $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ decays, their ratio $a_{\pi \nu \bar{\nu }}$, as well as for certain observables related to $B$ Physics like the CP asymmetries $a_{\psi K_S}$ in $B_d^0\to J/\psi K_S$ and $a_{\psi \varphi }$ in $B_s^0\to J/\psi \varphi$ or the mass differences $\Delta m_q$ ($q=d,s$) in the $B_q^0-{\bar{B}}_q^0$ systems. We investigate the correlations between them. The strongest correlations are between i) $a_{\pi \nu \bar{\nu }}$ and $a_{\psi K_S}$, ii) $\text{BR}(K^{+}\to {\pi }^{+}\nu \bar{\nu })$ and $\Delta m_d/\Delta m_s$ and iii) $\text{BR}(K_L\to {\pi }^0\nu \bar{\nu })$ and $a_{\psi \varphi }$. These correlations are likely to be violated in the presence of New Physics and therefore provide stringent tests of the Standard Model.

Comments: 24 pages, LaTeX2e, typos in eq. (36) and eq. (55) corrected, published version