Particle masses and the fifth dimension

TL;DR

This paper proposes extending space-time to five dimensions and enlarging the symmetry group to explain elementary particle masses, deriving a mass spectrum that fits certain quarks within experimental bounds.

Contribution

It introduces a five-dimensional framework with an extended symmetry group to naturally generate particle mass spectra, aligning with experimental data.

Findings

A three-point mass spectrum for certain quarks is predicted.

The model's parameters are consistent with known coupling constants.

Compatibility with electroweak theory is discussed.

Abstract

First we argue in an informal, qualitative way that it is natural to enlarge space-time to five dimensions to be able to solve the problem of elementary particle masses. Several criteria are developed for the success of this program. Extending the Poincare group to the group C of all angle-preserving transformations of space-time is one such scheme which satisfies these criteria. Then we show that the field equation for spin 1/2 fermions coupled to a self-force gauge field predicts mass spectra of the desired type: for a certain range of a key parameter (Casimir invariant) a three-point mass spectrum which fits the ``down'' quarks d,s, and b to within their experimental bounds is obtained. Reasonable values of the coupling constant (of QCD magnitude) and the range of the spatial wave function (a few fermis) also result. Compatibility with the electroweak theory is also discussed.