Primitive Pythagorean triples and neutrino mixing

TL;DR

This paper constructs neutrino mixing models based on primitive Pythagorean triples, successfully fitting observed neutrino oscillation data within experimental uncertainties.

Contribution

It introduces a novel approach linking primitive Pythagorean triples to neutrino mixing models that align with current experimental observations.

Findings

Models fit the observed mixing angles within 3 sigma

Successfully incorporate the Dirac CP phase

Provide a new mathematical framework for neutrino mixing

Abstract

The primitive Pythagorean triples are the three natural numbers $(a, b, c)$ that satisfy $c^2=a^2+b^2$ in a right triangle. We constructed a neutrino mixing models related to primitive Pythagorean triples that satisfy the observed values within the $3 \sigma$ region for the reactor, solar, and atmospheric neutrino mixing angles, as well as the Dirac CP phase.