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

TL;DR

This paper extends the fundamental positivity bounds on parton distribution functions from spin-1/2 nucleons to spin-3/2 hadrons, providing a comprehensive set of constraints for higher-spin systems.

Contribution

It derives the complete positivity bounds for leading-twist PDFs of spin-3/2 hadrons, generalizing the Soffer bound to higher-spin particles for the first time.

Findings

Established positivity bounds for spin-3/2 PDFs.

Connected scattering amplitudes with PDFs via spin density matrices.

Defined PDFs in terms of helicity amplitudes.

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.