Observables for scattering on targets with arbitrary spin

Abstract

Starting from the Weinberg formalism for fields of arbitrary spin, we discuss a method 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. A natural sl(2,C) multipole decomposition emerges, enabling a physical interpretation of non-perturbative objects that multiply spinor bilinears as Generalized Form Factors. 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.