Masses and Interactions of q-Fermionic Knots

TL;DR

This paper proposes a model where elementary particles are represented as knots labeled by SU_q(2) representations, predicting new fermions and neutrino spectra, and connecting knot theory with electroweak interactions.

Contribution

It introduces a novel knot-based model for elementary particles, linking fermion families to specific knots and predicting additional generations and neutrino spectra.

Findings

Predicts a fourth fermion generation

Forecasts a specific neutrino spectrum

Compatible with the Kobayashi-Maskawa matrix when q~1

Abstract

The q-electroweak theory suggests a description of elementary particles as solitons labelled by the irreducible representations of SU_q(2). Since knots may also be labelled by the irreducible representations of SU_q(2), we study a model of elementary particles based on a one-to-one correspondence between the four families of Fermions (leptons, neutrinos, (-1/3) quarks, (2/3) quarks) and the four simplest knots (trefoils). In this model the three particles of each family are identified with the ground and first two excited states of their common trefoil. Guided by the standard electroweak theory we calculate conditions restricting the masses of the fermions and the interactions between them. In its present form the model predicts a fourth generation of fermions as well as a neutrino spectrum. The same model with q almost equal to 1 is compatible with the Kobayashi-Maskawa matrix. Depending on the test of these predictions, the model may be refined.