Evolution equations for the double parton distributions. Initial conditions and transverse momentum dependence

Anna M Staśto,Krzysztof Golec-Biernat,I.-K Yoo

doi:10.1051/epjconf/201714106001

Abstract

In the first part of this contribution we discuss the problem of the initial conditions for the evolution of double parton distribution functions (PDFs). We show that one can construct a framework based on the expansion in terms of the Dirichlet functions in which both single and double PDFs satisfy momentum sum rules. In the second part, we propose how to include the transverse momentum dependence for the double parton distribution functions using the extension of the Kimber-Martin-Ryskin framework previously applied to the single PDFs.

Highlights

Hard processes in hadron collisions are usually described by the collinear factorization
One needs to compute the exact form of the vertex including the transverse momentum dependence, and treat the splitting beyond the collinear approximation. In this presentation we have discussed two issues related with the double parton distribution functions
We have proposed the framework for the construction of the initial conditions for the double parton distribution functions (PDFs) using the information from the single PDFs and the constraints from the sum rules

Summary

Introduction

Hard processes in hadron collisions are usually described by the collinear factorization. This factorization can be schematically written as follows dσ = D1f (x1, Q2) ⊗ σf f (s, Q2) ⊗ D1f (x1, Q2) + O(1/Q2) ,. The single PDFs are non-perturbative quantities, but their evolution with the hard scale can be described by the DGLAP evolution equations, with the splitting functions which can be calculated perturbatively. The physical interpretation of these evolution equations is as follows: the first two terms describe the situation where one of the two partons undergoes the collinear splitting, and the third term describes the situation when one parton collinearly splits into two. The above equations were first discussed in the context of the jet structure, and later on derived for the the parton distribution functions

Momentum sum rules

Initial conditions

Unintegrated double PDFs

Summary