Double Parton Distributions Incorporating Perturbative QCD Evolution and Momentum and Quark Number Sum Rules

TL;DR

This paper develops a new set of leading order double parton distributions (dPDFs) incorporating QCD evolution and sum rules, enabling more accurate predictions for double scattering processes at the LHC.

Contribution

It introduces a novel method to construct and evolve dPDFs that satisfy sum rules, improving upon previous approaches and providing publicly available grids for high-energy physics applications.

Findings

Derived momentum and quark number sum rules for dPDFs

Constructed improved input dPDFs at Q_0^2=1 GeV^2

Created a numerical program for dPDF evolution and generated extensive dPDF grids

Abstract

It is anticipated that hard double parton scatterings will occur frequently in the collisions of the LHC, producing interesting signals and significant backgrounds to certain single scattering processes. For double scattering processes in which the same hard scale t = ln(Q^2) is involved in both collisions, we require the double parton distributions (dPDFs) D_h^{j_1j_2}(x_1,x_2;t) in order to make theoretical predictions of their rates and properties. We describe the development of a new set of leading order dPDFs that represents an improvement on approaches used previously. First, we derive momentum and number sum rules that the dPDFs must satisfy. The fact that these must be obeyed at any scale is used to construct improved dPDFs at the input scale Q_0, for a particular choice of input scale (Q_0^2 = 1 GeV^2) and corresponding single PDFs (the MSTW2008LO set). We then describe a novel program which uses a direct x-space method to numerically integrate the LO DGLAP equation for the dPDFs, and which may be used to evolve the input dPDFs to any other scale. This program has been used along with the improved input dPDFs to produce a set of publicly available dPDF grids covering the ranges 10^{-6}<x_1<1, 10^{-6}<x_2<1, and 1<Q^2<10^9 GeV^2.