Constraints on an enhanced sbar d Z vertex from epsilon'/epsilon

TL;DR

This paper investigates how constraints on an enhanced sbar d Z vertex from epsilon'/epsilon limit rare kaon decay rates, providing bounds on various decay branching ratios and discussing implications for new physics scenarios.

Contribution

It offers the first comprehensive analysis of constraints on the sbar d Z vertex from epsilon'/epsilon and their impact on rare kaon decay predictions, including new physics considerations.

Findings

Epsilon'/epsilon strongly constrains Im Z_{ds} despite theoretical uncertainties.

Derived upper bounds on branching ratios for K_L and K^+ decays involving neutrinos and electrons.

Discussed how additional new physics contributions affect these bounds and their dependence on CKM parameters.

Abstract

We analyze rare kaon decays in models in which the dominant new effect is an enhanced sbar d Z vertex Z_{ds}. We point out that in spite of large theoretical uncertainties the CP-violating ratio epsilon'/epsilon provides at present the strongest constraint on Im Z_{ds}. Assuming 1.5 10^{-3} < epsilon'/epsilon < 3 10^{-3} and Standard Model values for the CKM parameters we obtain the bounds BR(K_L -> pi^0 nu nubar) < 3.9 10^{-10} and BR(K_L -> pi^0 e^+ e^-)_{dir} < 7.9 10^{-11}. Using the bound on Re Z_{ds} from K_L -> mu^+ mu^- we find BR(K^+ -> pi^+ nu nubar) < 2.6 10^{-10}. We also discuss new physics scenarios in which in addition to an enhanced sbar d Z vertex also neutral meson mixing receives important new contributions. In this case our most conservative bounds are BR(K_L -> pi^0 nu nubar) < 1.8 10^{-9}, BR(K_L -> pi^0 e^+ e^-)_{dir} < 2.8 10^{-10} and BR(K^+ -> pi^+ nu nubar) < 6.1 10^{-10}. The dependence of the upper bound for BR(K_L -> pi^0 nu nubar) on the CKM parameters is also analyzed.