A Generic Analysis of Nucleon Decay Branching Fractions in Flipped SU(5) Grand Unification

TL;DR

This paper analyzes how unknown parameters affect nucleon decay predictions in flipped SU(5) grand unified theories and proposes methods to determine these parameters through specific decay measurements.

Contribution

It introduces a parametrization of uncertainties in nucleon decay branching ratios and suggests experimental tests to validate flipped SU(5) models.

Findings

Uncertainty in decay branching ratios can be parametrized with two parameters.

Measurement of specific decay channels can determine these parameters.

Upper limits on decay width ratios provide tests for flipped SU(5).

Abstract

In flipped SU(5) grand unified theories, the partial decay lifetimes of certain nucleon decay channels depend generically on an unknown unitary matrix, which arises when left-handed lepton fields are embedded into anti-fundamental representations of SU(5). This dependency is particularly relevant when the neutrino mass matrix has a generic structure, introducing uncertainty in the prediction of nucleon decay branching fractions within flipped SU(5). In this paper, we demonstrate that this uncertainty can be parametrized using two parameters, which can be determined by measuring the partial lifetimes of $p \to \pi^0 e^+$, $p \to \pi^0 \mu^+$, and $n \to \pi^0 \bar{\nu}$. In addition, we establish upper limits on the ratios of the decay widths of these channels, offering a potential method to test flipped SU(5) in future nucleon decay experiments.