Probing scalar and pseudoscalar new physics using rare kaon decays

Rare kaon decays provide sensitive tests of new physics. In this work, we focus on scalar and pseudoscalar operators, analysing the $K\to \pi \ell^+\ell^-$ and $K\to \ell^+\ell^-$ decays. We highlight the complementary role of different modes: $K^+\to\pi^+\ell^+\ell^-$, in particular the forward-backward asymmetry in the muon channel as a clean probe of scalar effects, the stringent constraints from $K_L\to \mu^+\mu^-$, and the discovery potential of future measurements of $K_S\to \mu^+\mu^-$ and $K_L\to \pi^0 \ell^+\ell^-$. The interplay between charged and neutral modes underscores the complementarity of NA62, the LHCb upgrade, and KOTO-II.