Constraints on new physics from $K \to \pi \nu \bar\nu$

TL;DR

This paper investigates how various new physics scenarios could affect the rare kaon decay processes, providing constraints on new physics models based on these decay rates.

Contribution

It systematically analyzes different types of new physics effects on $K o \pi u ar u$ decays, including neutrino couplings and isospin interactions, extending previous studies.

Findings

Right-handed neutrino contributions are additive to the Standard Model.

Neutrino lepton flavor violation introduces CP-conserving effects.

Sensitivity to new physics scales is limited to a few GeV for certain interactions.

Abstract

We study generic effects of new physics on the rare decay modes $K_L \to \pi^0 \nu \bar\nu$ and $K^+ \to \pi^+ \nu \bar\nu$. We discuss several cases: left-handed neutrino couplings; right handed neutrino couplings; neutrino lepton flavour violating (LFV) interactions; and $\Delta I =3/2$ interactions. The first of these cases has been studied before as it covers many new physics extensions of the standard model; the second one requires the existence of a new light (sterile) right-handed neutrino and its contribution to both branching ratios is always additive to the SM. The case of neutrino LFV couplings introduces a CP conserving contribution to $K_L \to \pi^0 \nu \bar\nu$ which affects the rates in a similar manner as a right handed neutrino as neither one of these interferes with the standard model amplitudes. Finally, we consider new physics with $\Delta I =3/2$ interactions to go beyond the Grossman-Nir bound. We find that the rare kaon rates are only sensitive to new physics scales up to a few GeV for this scenario.