Waiting for Precise Measurements of K^+->pi^+ nu nu and K_L->pi^0 nu nu

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  • 6 August 2004
Abstract
In view of future plans for accurate measurements of the theoretically clean branching ratios Br(K^+->pi^+ nunu) and Br(K_L->pi^0 nunu), that should take place in this decade, we collect the relevant formulae for quantities of interest and analyze their theoretical and parametric uncertainties. We point out that in addition to the angle beta in the unitarity triangle (UT) also the angle gamma can in principle be determined from these decays with respectable precision and emphasize in this context the necessity of a calculation of the charm contribution to K^+->pi^+ nunu at the NNLO level. In addition to known expressions we present several new ones that should allow transparent tests of the Standard Model (SM) and of its extensions. While our presentation is centered around the SM, we also discuss models with minimal flavour violation and scenarios with new complex phases in enhanced Z^0 penguins and/or B^0_d-bar B^0_d mixing. We give a brief review of existing results within specific extensions of the SM and investigate the interplay between the K->pi nunu complex, the B^0_{d,s}-bar B^0_{d,s} mass differences Delta M_{d,s} and the angles beta and gamma that can be measured precisely in two body B decays one day. We derive a new "golden" relation between B and K systems that involves (beta,gamma) and Br(K_L-> pi^0 nunu) and investigate the virtues of (R_t,beta), (R_b,gamma), (beta,gamma) and (etabar,gamma) strategies for the UT in the context of K->pi nunu decays with the goal of testing the SM and its extensions.

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