Standard Model correlations between K ->pi nu(nu)over-bar decays 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: <(<rho> )over bar>, <(<eta>)over bar>, sin2 beta, sin2 alpha gamma, sin(2)gamma. We also update the SM prediction for the rates of the K-L --> pi (0)nu<(<nu>) over bar> and K+ --> pi (+)nu<(<nu>)over bar> decays, their ratio a(pi nu<( <nu>)over bar>), as well as for certain observables related to B Physics li ke the CP asymmetries a(psi Ks) in B-d(0) --> J/psi K-S and a(psi phi) in B -s(0) --> J/psi phi or the mass differences Deltam(q) (q = d, s) in the B-q (0) --> (B) over bar (0)(q) systems. We investigate the correlations betwee n them. The strongest correlations are between (i) a pi nu<(<nu>)over bar> and a(psi Ks), (ii) BR(K+ --> pi (+)nu<(<nu>)over bar>) and Deltam(d)/Delta m(s) and (iii) BR(K-L --> pi (0)nu<(<nu>)over bar>) and a(psi phi). These c orrelations are likely to be violated in the presence of New Physics and th erefore provide stringent tests of the Standard Model.