An update on the evolution of double parton distributions

TL;DR

This work extends double parton distribution evolution to the general case of unequal parton virtualities, deriving the LL evolution equation for the higher scale and presenting a compact, two-step approach that incorporates correlations up to the lower scale. It advances the theoretical framework by outlining the next-to-leading logarithmic accuracy structure, including how two-loop splitting and fracture-function kernels enter the inhomogeneous term, and discusses how to map known kernels to the DPS context. The results validate prior conjectures about unequal-scale evolution and offer guidance for numerical implementations, while highlighting the need for an ab initio NLLA derivation. Overall, the paper broadens the predictive power of DPS by accommodating realistic scale hierarchies and outlining the path toward higher-precision evolution.

Abstract

We consider double parton distributions in the general case in which the virtualities of the interacting partons are different. We elaborate the corresponding evolution equations and their extension to next-to-leading logarithmic accuracy.

Figures (1)

• Figure 1: Pictorial representation of both terms on right hand side of eq. (\ref{['Ddef']}). Black dots symbolize the parton-to-parton evolution function, $E$ .