Double parton distributions out of bounds in colour space

TL;DR

This paper examines the positivity constraints of double parton distributions considering colour dependence, revealing that positivity is not maintained under evolution at higher scales, unlike the colour-summed case.

Contribution

It demonstrates that colour-dependent double parton distributions lose positivity during leading-order evolution, contrasting with the colour-summed scenario, and analyzes their properties at small distances.

Findings

Positivity is not preserved under evolution for colour-dependent distributions.

At small distances, distributions can be computed using perturbative kernels.

Positivity holds when parton colour is summed over, but not when explicitly considered.

Abstract

We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour. It turns out that positivity is not preserved by leading-order evolution from lower to higher scales, in contrast to the case in which parton colour is summed over. We also study the positivity properties of the distributions at small distance between the two partons, where they can be computed in terms of perturbative splitting kernels and ordinary parton densities.