Insights from the Interplay of K → πνν̄ and εK on the New Physics Flavour Structure

In certain new physics (NP) models, such as the Littlest Higgs model with T-parity, a strict correlation between the KL → π0νν̄ and K+ → π+νν̄ branching ratios has been observed, allowing essentially only for two branches of possible points, while in other NP frameworks, such as the general MSSM or warped extra dimensional models, no visible correlation appears. We analyse the origin of the correlation in question in a model-independent manner. We show it to be a direct consequence of the stringent experimental constraint on εK , provided that the NP enters with a universal weak phase in both ∆S = 2 and ∆S = 1 transitions. This happens in many NP scenarios with either only SM operators, or where the NP induces exclusively right-handed currents while the left-right ∆S = 2 operators are absent. On the other hand, if the NP phases in ∆S = 2 and ∆S = 1 processes are uncorrelated, εK has no power to put constraints on the K → πνν̄ system. The latter appears in particular in those NP models where K0− K̄0 mixing receives contributions from the chirally enhanced left-right operators. We discuss the stability of the correlation in question against small deviations from the assumption of universal ∆S = 2 and ∆S = 1 weak phases, and in the presence of non-negligible NP contributions to εK . ar X iv :0 90 4. 25 28 v1 [ he pph ] 1 6 A pr 2 00 9