Kaon physics in the SMEFT

TL;DR

Kaon physics is a highly sensitive probe of NP that benefits from a model-independent SMEFT framework to connect high-scale Wilson coefficients to low-energy observables such as $K^+\to \pi^+ \nu \bar{\nu}$, $K_L\to \pi^0 \nu \bar{\nu}$, $\epsilon'/\epsilon$, and $\Delta S=2$ mixing. The paper surveys SMEFT analyses in the Kaon sector, detailing master formulae that incorporate full renormalization-group running above and below the electroweak scale and state-of-the-art hadronic inputs from lattice QCD, as well as WET matching and higher-dimensional operators. It highlights how rare Kaon decays yield correlated constraints on SMEFT Wilson coefficients, especially in $Z'$-motivated scenarios, and how $\Delta S=2$ observables extend sensitivity to dimension-eight effects via $M_{12}$ with back-rotation ensuring consistent flavor bases. Overall, the SMEFT approach provides a coherent, high-precision framework to constrain NP scales in Kaon physics and guides future experimental and theoretical efforts to refine these constraints, including potential exploration of the $\Delta I=1/2$ rule within SMEFT.

Abstract

Kaon physics observables are highly sensitive to New Physics (NP) effects and form in combination with the Standard Model Effective Field Theory (SMEFT) a powerful tool to study physics that goes beyond the Standard Model paradigm. We review recent SMEFT analyses in the Kaon sector and point out novel directions that might be investigated in the future.