Positivity bounds on double parton distributions

TL;DR

The paper derives model-independent positivity bounds for double parton distributions by interpreting them as probability densities of finding two partons with specified polarization inside an unpolarized proton. It constructs spin-density matrices for quark, antiquark, and gluon pairs and extracts inequalities that bound polarized DPDs and spin correlations. The authors then show that these bounds are preserved under leading-order DGLAP-type evolution by formulating suitable linear combinations of DPDs whose positivity is maintained, providing a practical framework to constrain spin effects in double hard scattering. These results offer guidance for modeling polarized DPDs and for setting upper limits on spin correlations in proton-proton collisions at high energies.

Abstract

Double hard scattering in proton-proton collisions is described in terms of double parton distributions. We derive bounds on these distributions that follow from their interpretation as probability densities, taking into account all possible spin correlations between two partons in an unpolarized proton. These bounds constrain the size of the polarized distributions and can for instance be used to set upper limits on the effects of spin correlations in double hard scattering. We investigate the stability of the bounds under leading-order DGLAP evolution to higher scales.