The Relation of Constraints on Particle Statistics for Different Species of Particles

TL;DR

This paper explores how particle statistics constraints, modeled by quons with a parameter q, relate different particle species and suggests all particles are nearly fermions or bosons based on these constraints.

Contribution

It extends the conservation of statistics to quons with mixed couplings and relates bounds on particle statistics parameters across different particle types.

Findings

Relation q_f^2 = q_b for fermion-like and boson-like particles

Bound on photon q relates to bound on electron q

All particles are nearly fermions or bosons according to high-precision bounds

Abstract

Quons are particles characterized by the parameter $q$, which permits smooth interpolation between Bose and Fermi statistics; $q=1$ gives bosons, $q=-1$ gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form $\bar{f}fb$, where $f$ is fermion-like and $b$ is boson-like. We show that $q_f^2=q_b$. In particular, we relate the bound on $q_{\gamma}$ for photons to the bound on $q_e$ for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to high precision.