Standard model correlations between K→πνbar 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:ρ, η, sin 2β, sin 2α, sin 2 γ. We also update the SM prediction for the rates of the K L → π 0 νν and K + → π + νν decays, their ratio a πνν , as well as for certain observables related to B Physics like the CP asymmetries a ψK S in B 0 d → J/ψ K S and a ψφ in B 0 s → J/ψ φ or the mass differences ∆m q (q = d, s) in the B 0 q −B 0 q systems. We investigate the correlations between them. The strongest correlations are between i) a πνν and a ψK S , ii) BR(K + → π + νν) and ∆m d /∆m s and iii) BR(K L → π 0 νν) 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.

CP violation in the B system and relations to K→πνν̄ decays

“…BR(B → X s νν) = 1.57 × 10 −5 BR(B → X c eν e ) 0.104 (11.31) This expression holds for all MFV models and represents another connection between Kand B-meson decays, in addition to those discussed above and in [120,122,123,145,297].…”

Rare kaon decays

“…Obviously |V td | derived from B(K + → π + νν) can be checked against |V td | extracted from the ratio ofB s − B s andB d − B d mixing. It has also been emphasized that results from K + → π + νν and K L → π 0 νν can be combined to yield sin2β 28,29 or a quantity closely related to it 23,30,31 . A number of other useful relations have also been pointed out 16,29 .…”

Theory of Cp Violation in the B-Meson System

“…In many extensions of the SM it would have been quite possible (sometimes even required) for the B-B mixing phase to differ from its SM value. 6,7,8,9,10 For instance, potentially large effects could arise in models with iso-singlet down-type quarks and tree-level flavor-changing neutral currents, 11 left-right symmetric models with spontaneous CP violation 12,13,14 (which are now excluded by the data), and SUSY models with extended minimal flavor violation.…”

“…On the contrary, only small modifications of sin 2β ψK are allowed in a class of models with so-called minimal flavor violation, 14,16,17 for which one can derive the bounds 0.52 < sin 2β ψK < 0.78.…”