Connections between epsilon'/epsilon and Rare Kaon Decays in Supersymmetry

TL;DR

This paper investigates how supersymmetric models influence rare kaon decays and CP violation, establishing bounds on decay rates and emphasizing the importance of experimental measurements to understand supersymmetry effects.

Contribution

It provides new bounds on rare kaon decay branching ratios within supersymmetry, linking CP violation constraints to decay predictions and highlighting the role of chromomagnetic penguins.

Findings

Bound on BR(K_L → π^0 ν ν̄) ≤ 1.2×10^{-10}

Bound on BR(K^+ → π^+ ν ν̄) ≤ 1.7×10^{-10}

Enhanced BR(K_L → π^0 e^+ e^-) possible with supersymmetry

Abstract

We analyze the rare kaon decays $K_L \to \pi^0 \nu \bar \nu$, $K^+ \to \pi^+ \nu \bar \nu$, $K_L \to \pi^0 e^+ e^-$ and $K_L \to \mu^+ \mu^-$ in conjunction with the CP violating ratio $\epsilon'/\epsilon$ in a general class of supersymmetric models in which $Z$- and magnetic-penguin contributions can be substantially larger than in the Standard Model. We point out that radiative effects relate the double left-right mass insertion to the single left-left one, and that the phenomenological constraints on the latter reflect into a stringent bound on the supersymmetric contribution to the $Z$ penguin. Using this bound, and those coming from recent data on $\epsilon'/\epsilon$ we find ${\rm BR}(K_L \to \pi^0 \nu \bar \nu)\lsim 1.2\cdot 10^{-10}$, ${\rm BR}(K^+ \to \pi^+ \nu \bar \nu)\lsim 1.7\cdot 10^{-10}$, ${\rm BR}(K_L \to \pi^0 e^+ e^-)_{\rm dir}\lsim 2.0\cdot 10^{-11}$, assuming the usual determination of the CKM parameters and neglecting the possibility of cancellations among different supersymmetric effects in $\epsilon'/\epsilon$. Larger values are possible, in principle, but rather unlikely. We stress the importance of a measurement of these three branching ratios, together with improved data and improved theory of $\epsilon'/\epsilon$, in order to shed light on the realization of various supersymmetric scenarios. We reemphasize that the most natural enhancement of $\epsilon'/\epsilon$, within supersymmetric models, comes from chromomagnetic penguins and show that in this case sizable enhancements of $BR(K_L \to \pi^0 e^+ e^-)_{\rm dir}$ can also be expected.