Electromagnetic Properties for Arbitrary Spin Particles: Part 1 $-$ Electromagnetic Current and Multipole Decomposition

In a set of two papers, we propose to study an old-standing problem, namely the electromagnetic interaction for particles of arbitrary spin. Based on the assumption that light-cone helicity at tree level and $Q^2=0$ should be conserved non-trivially by the electromagnetic interaction, we are able to derive \emph{all} the natural electromagnetic moments for a pointlike particle of \emph{any} spin. In this first paper, we propose a transparent decomposition of the electromagnetic current in terms of covariant vertex functions. We also define in a general way the electromagnetic multipole form factors, and show their relation with the electromagnetic moments. Finally, by considering the Breit frame, we relate the covariant vertex functions to multipole form factors.