Unintegrated double parton distributions

TL;DR

This paper develops unintegrated double parton distribution functions incorporating transverse momentum dependence, extending previous single distributions, and analyzes their behavior across different energy scales with implications for parton correlations.

Contribution

It introduces a novel construction of unintegrated double parton distributions including transverse momentum dependence and different scale regimes, extending existing frameworks.

Findings

Three distinct forms of unintegrated double distributions for different energy scales

Non-trivial correlations in parton momenta due to Sudakov form factors

Analysis of splitting contributions to transverse momentum dependence

Abstract

We present the construction of unintegrated double parton distribution functions which include dependence on transverse momenta of partons. We extend the formulation which was used to obtain the single unintegrated parton distributions from the standard, integrated parton distribution functions. Starting from the homogeneous part of the evolution equations for the integrated double parton distributions, we construct the unintegrated double parton distributions as the convolutions of the integrated double distributions and the splitting functions, multiplied by the Sudakov form factors. We show that there exist three domains of external hard scales which require three distinct forms of the unintegrated double distributions. The additional transverse momentum dependence which arises through the Sudakov form factors leads to non-trivial correlations in the parton momenta. We also discuss the non-homogeneous contribution to the unintegrated double parton distributions, which arises due to the splitting of a single parton into daughter partons with high transverse momenta. We analyze two cases, the unfolding of the transverse momenta dependence from the last step of the evolution of two partons, and the case where the transverse momenta are generated directly from the single parton splitting.