Generalizing the Soffer Bound: Positivity Constraints on Parton Distributions of Spin-3/2 Particles

Abstract

We derive the complete set of positivity bounds for the leading-twist parton distribution functions (PDFs) of a spin-3/2 hadron for the first time. This work generalizes the Soffer bound, a fundamental constraint for spin-1/2 nucleons, to quark and gluon distribution functions in higher-spin systems. Expressing the antiparton-hadron scattering amplitudes in terms of the PDFs and the spin density matrix, we establish the connections between the PDFs and the scattering amplitudes in the tensor product space of the parton and hadron spins. Moreover, we obtain the definitions of the PDFs in terms of the helicity amplitudes. Positive definiteness of the scattering amplitude matrix yields a set of inequalities that define the physically allowed parameter space for the helicity amplitudes and a set of constraints for the PDFs. The Cauchy-Schwartz inequality determines the constrains between the PDFs and generalized parton distributions.