The Standard Model within Non-associative Geometry

TL;DR

This paper constructs the Standard Model within non-associative geometry, deriving tree-level predictions for particle masses and mixing angles, highlighting differences from non-commutative geometry approaches.

Contribution

It introduces a novel non-associative geometric framework for the Standard Model, providing specific predictions for particle masses and mixing parameters.

Findings

Predicts $m_W=0.5 m_t$ and $m_H=1.5 m_t$ at tree level

Derives $ ext{sin}^2 heta_W=3/8$

Shows differences from non-commutative geometry predictions

Abstract

We present the construction of the standard model within the framework of non--associative geometry. For the simplest scalar product we get the tree--level predictions $m_W=\frac{1}{2} m_t\,,$ $m_H=\frac{3}{2} m_t$ and $\sin^2 \theta_W= \frac{3}{8}.$ These relations differ slightly from predictions derived in non--commutative geometry.