Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model

TL;DR

This paper explores the geometric structure of the Standard Model using noncommutative geometry, showing that current experimental data supports a specific duality condition if neutrinos have mass.

Contribution

It demonstrates that the Hodge duality condition in noncommutative geometry is compatible with the Standard Model given massive neutrinos, linking geometry with particle physics data.

Findings

Hodge duality supports the Standard Model with massive neutrinos

Neutrino and quark mass-mixing are necessary for the duality

Current experimental data aligns with the geometric condition

Abstract

We investigate whether the Standard Model, within the accuracy of current experimental measurements, satisfies the Hodge duality condition introduced and studied in Dabrowski, D'Andrea, Sitarz, Lett Math Phys (2018) 108:1323. We show that the neutrino and quark mass-mixing and the difference of fermion masses is necessary for this property. We demonstrate that the current data supports the new geometric feature of the Standard Model, Hodge duality, provided that all neutrinos are massive.