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In certain new physics (NP) models, such as the Littlest Higgs model withT-parity, a strict correlation between the K_L -> pi0 nu anti-nu and K+ -> pi+nu anti-nu branching ratios has been observed, allowing essentially only fortwo branches of possible points, while in other NP frameworks, such as thegeneral MSSM or warped extra dimensional models, no visible correlationappears. We analyse the origin of the correlation in question and show it to bea direct consequence of the stringent experimental constraint on epsilon_K,provided that the NP enters with comparable strength and a universal weak phasein both Delta S = 2 and Delta S = 1 transitions. This happens in many NPscenarios with either only SM operators, or where the NP induces exclusivelyright-handed currents while the left-right Delta S = 2 operators are absent. Onthe other hand, if the NP phases in Delta S = 2 and Delta S = 1 processes areuncorrelated, epsilon_K has no power to put constraints on the K -> pi nuanti-nu system. The latter appears in particular in those NP models where K^0 -anti-K^0 mixing receives contributions from the chirally enhanced left-rightoperators. We discuss the stability of the correlation in question againstsmall deviations from the assumption of universal Delta S = 2 and Delta S = 1weak phases, and in the presence of non-negligible NP contributions toepsilon_K.

Insights from the Interplay of K -> pi nu anti-nu and epsilon_K on the New Physics Flavour Structure