Probing new physics with the kaon decays $K\to\pi\pi\!\not\!\!E$

TL;DR

This paper discusses how recent measurements of rare kaon decays constrain new physics models, highlighting potential signals in specific decay modes that could be explored with current or future experiments.

Contribution

It identifies that while standard model-compatible results limit some new physics contributions, parity-odd operators could still produce detectable effects in certain kaon decay channels.

Findings

Standard model predictions constrain $s o d ot ext{E}$ operators.

Parity-odd operators may enhance $K o ext{pipi} ot ext{E}$ decay rates.

Potential for future experiments to detect new physics signals.

Abstract

The latest search for the rare kaon decay $K^+\to\pi^+\nu\bar\nu$ by the NA62 experiment has produced evidence for it with a branching fraction consistent with the prediction of the standard model. The new result implies that in this decay, with the $\nu\bar\nu$ pair appearing as missing energy ($\not\!\!E$), the room for possible new physics is no longer sizable and that therefore its contributions to underlying four-particle $s\to d\!\not\!\!E$ operators with parity-even $ds$ quark bilinears have become significantly constrained. Nevertheless, we point out that appreciable manifestations from beyond the standard model induced by the corresponding operators with mainly parity-odd $ds$ quark bilinears could still occur in $K\to\pi\pi\!\not\!\!E$ modes, on which there are only minimal empirical details at present. We find in particular that new physics of this kind may enhance the branching fraction of $K_L\to\pi^0\pi^0\!\not\!\!E$ to values reaching its current experimental upper limit and the branching fractions of $K^+\to\pi^+\pi^0\!\not\!\!E$ and $K_L\to\pi^+\pi^-\!\not\!\!E$ to the levels of $10^{-7}$ and $10^{-6}$, respectively. Thus, quests for these decays in existing kaon facilities such as KOTO and NA62 or future ones could provide valuable information complementary to that gained from $K\to\pi\!\not\!\!E$.