Could Leptons, Quarks or both be Highly Relativistic Bound States of Minimally Interacting Fermion and Scalar?

TL;DR

This paper explores the theoretical possibility that leptons and quarks could be highly relativistic bound states of a fermion and scalar particle, potentially explaining their spin properties within minimal electrodynamics.

Contribution

It demonstrates that strongly bound solutions with realistic coupling constants can exist, offering a novel explanation for the spin-1/2 nature of leptons and quarks.

Findings

Bound states with realistic coupling constants are possible.

Such states must have spin one half.

This may explain the absence of higher-spin leptons and quarks.

Abstract

The possibility that leptons, quarks or both might be highly relativistic bound states of a spin-0 and spin-1/2 constituent bound by minimal electrodynamics is discussed. Typically, strongly bound solutions of the Bethe-Salpeter equation exist only when the coupling constant is on the order of or greater than unity. For the bound-state system discussed here, there exist two classes of boundary conditions that could yield strongly bound solutions with coupling constants on the order of the electromagnetic fine structure constant. In both classes the bound state must have spin one half, thus providing a possible explanation for the absence of higher-spin leptons and quarks.