$\epsilon_K^\prime/\epsilon_K$: Standard Model and Supersymmetry

TL;DR

This paper explores how supersymmetric models with specific squark mass splittings can explain the observed deviation in direct CP violation in kaon decays, while remaining consistent with other rare decay measurements.

Contribution

It introduces a supersymmetric scenario with flavor mixing among left-handed squarks that can account for the measured $ ext{ extepsilon}_K^ ext{'}$ deviation, even with heavy sparticles beyond LHC reach.

Findings

Supersymmetric scenario can explain $ ext{ extepsilon}_K^ ext{'}$ deviation.

Rare decay branching ratios are only moderately affected.

Future measurements can test or constrain the model.

Abstract

I give a pedagogical introduction into flavour-changing neutral current interactions of kaons and their role to reveal or constrain physics beyond the Standard Model (SM). Then I discuss the measure $\epsilon_K^\prime$ of direct CP violation in $K\to \pi\pi$ decays, which deviates from the SM prediction by $2.8\sigma$. A supersymmetric scenario with flavour mixing among left-handed squarks can accomodate the measured value of $\epsilon_K^\prime$ even for very heavy sparticles, outside the reach of the LHC. The considered scenario employs mass splittings among the right-handed up and down squarks (to enhance $\epsilon_K^\prime$) and a gluino which is heavier than the left-handed strange-down mixed squarks by at least a factor of 1.5 (to suppress excessive contribution to $\epsilon_K$, the measure of indirect CP violation). The branching ratios of the rare decays $K^+ \to \pi^+ \nu \bar\nu$ and $K_L \to \pi^0 \nu \bar\nu$, to be measured by the NA62 and KOTO-step2 experiments, respectively, are only moderately affected. These measurements have the capability to either falsify the model or to constrain the CP phase associated with strange-down squark mixing accurately.