Long distance contributions to the rare kaon decay $K\to\pi\ell^{+}\ell^{-}$

Understand

The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model.

• This natural suppression makes these decays sensitive to the effects of potential New Physics.
• To discern such New Physics one must be able to control the errors on the Standard Model prediction of the decay amplitude.
• These particular decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty.