Implications of Neutrino Masses on the $K_{L}\to\pi^{0}\nu\bar{\nu}$ Decay

TL;DR

This paper investigates how neutrino masses influence the decay $K_{L} o \pi^{0} uar{ u}$, finding that such effects are negligible, but identifying new potential contributions involving lepton flavor mixing that could be comparable to Standard Model predictions.

Contribution

The study provides a detailed calculation of neutrino mass effects on the decay, revealing their negligible size and introducing new contributions involving lepton flavor mixing.

Findings

Neutrino mass contributions are suppressed by factors of order 10^{-12} to 10^{-29}.

New contributions with lepton flavor mixing can be comparable to Standard Model CP conserving modes.

Neutrino mass effects are negligible despite chiral enhancement.

Abstract

We calculate the different contributions to the decay $K_{L}\to \pi ^{0}\nu \bar{\nu}$ that arise if the neutrinos are massive. In spite of a chiral enhancement factor, we find that these contributions are negligibly small. Compared to the CP violating leading contributions, the CP conserving contributions related to Dirac masses are suppressed by a factor of order $(m_K m_\nu/m_W^2)^2\lesssim10^{-12}$, and those related to Majorana masses are suppressed by a factor of order $(\alpha_W m_K m_s^2 m_\nu/m_W^4)^2\lesssim10^{-29}$. With lepton flavor mixing we find new contributions with a single CP violating coupling leading to a final CP even state or with two CP violating couplings leading to a final CP odd state. These contributions can be of the order of the Standard Model CP conserving contributions to the flavor diagonal modes.