Diagrams and Parastatistical Factors for Cascade Emission of a Pair of Paraparticles

TL;DR

This paper investigates the theoretical framework and diagrammatic analysis of cascade emission processes involving paraparticles obeying order p=2 parastatistics, highlighting their potential role in dark matter and energy.

Contribution

It derives and compares parastatistical factors for paraparticle emission diagrams within a supersymmetric-like model, advancing perturbative analysis methods for paraparticle processes.

Findings

Parastatistical factors differ from normal statistics in emission diagrams.

Diagrammatic analysis can be applied to paraparticle processes.

Paraparticles could be stable and relevant to dark matter/energy.

Abstract

The empirical absence to date of particles obeying parastatistics in high energy collider experiments might be due to their large masses, weak scale couplings, and lack of gauge couplings. Paraparticles of order p=2 must be pair produced, so the lightest such particles are absolutely stable and so are excellent candidates to be associated with dark matter and/or dark energy. If there is a portal to such particles, from a new scalar A1 boson they might be cascade emitted as a pair of para-Majorana neutrinos as in A1 ---> A2 para-nu para-nu or as a pair of neutral spin-zero paraparticles such as in A1 ---> A2 para-A para-B, where para-B is the anti-paraparticle to para-A. In this paper, for an assumed supersymmetric-like "statistics portal" Lagrangian, the associated connected tree diagrams and their parastatistical factors are obtained for the case of order p=2 parastatistics. These factors are compared with the corresponding statistical factors for the analogous emission of a non-degenerate or a 2-fold degenerate pair which obey normal statistics. This shows that diagrams, and diagrammatic thinking, can be use in perturbatively analyzing paraparticle processes. The parastatistical factor associated with each diagram does require explicit calculation.