$K^{+}\rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ decays within the Chiral Perturbation Theory

TL;DR

This paper calculates the decay rates and energy spectra of specific kaon decays involving neutrinos using Chiral Perturbation Theory, providing Standard Model predictions for these rare processes.

Contribution

It offers the first leading-order Standard Model predictions for the differential spectra and branching ratios of $K^{+} ightarrow u ar u ext{(lepton)}$ decays within Chiral Perturbation Theory.

Findings

Predicted differential energy spectra for muon and electron channels.

Calculated branching ratios for the rare decays.

Provided theoretical benchmarks for future experimental tests.

Abstract

Decays $K^{+} \rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ are examined to the leading order in momenta in the framework of Chiral Perturbation Theory. Predictions of the Standard Model for the muon and electron differential energy spectra and branching ratios of $K_{\mu 3 \nu}$ and $K_{e 3 \nu}$ are presented.