Covariant multipole expansion of local currents for massive states of any spin

TL;DR

This paper develops a covariant multipole expansion framework to systematically analyze local currents for massive particles of any spin, clarifying the structure and counting of form factors involved.

Contribution

It introduces a universal covariant multipole expansion method to identify independent form factors for particles of arbitrary spin, extending previous results to higher spins.

Findings

Identifies fundamental structures for form factors across spins

Provides counting rules linking form factors to total spin

Matches known results up to spin 2

Abstract

We study the structure of scalar, vector, and tensor currents for on-shell massive particles of any spin. When considering higher values for the spin of the particle, the number of form factors (FFs) involved in the decomposition of the matrix elements associated with these local currents increases. We identify all the fundamental structures that give rise to the independent FFs, systematically for any spin value. These structures can be conveniently organised using an expansion in covariant multipoles, built solely from the Lorentz generators. This approach allows one to uniquely identify the terms which are universal and those that arise because of spin. We derive counting rules which relate the number of FFs to the total spin $j$ of the state, showing explicitly that these rules match all the well-known cases up to spin 2.