Observables for scattering on targets with arbitrary spin*

Starting from the Weinberg formalism for fields for arbitrary spin, we discuss a construction for the decomposition of matrix elements of QCD operators (local currents, quark/gluon bilinears) for targets with arbitrary spin. This procedure is advantageous for the systematic study of the structure of hadrons and nuclei, particularly in the case of spin-dependent observables. As higher spin targets exhibit new features in their hadronic structure, the investigation of these properties can enhance our understanding of the strong force.

The construction allows for a unified framework to discuss spin > 1/2 very similar to the spin 1/2 case, without subsidiary conditions for the wave functions. Different types of spinors (canonical, helicity, light-front helicity) can be easily accommodated.  Its numerical implementation is simple and can be entirely reduced to objects familiar from the rotation group.  An sl(2,C) multipole decomposition naturally appears and allows for a physical interpretation of non-perturbative objects multiplying spinor bilinears.

To demonstrate the efficacy of this method, we apply it to the description of  a spin 1 target, such as the deuteron. We discuss extensions of the formalism to hard exclusive processes on the deuteron and beyond.