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

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.