Single perturbative splitting diagrams in double parton scattering

Abstract

We present a detailed study of a specific class of graph that can potentially contribute to the proton-proton double parton scattering (DPS) cross section. These are the '2v1' or 'single perturbative splitting' graphs, in which two 'nonperturbatively generated' ladders interact with two ladders that have been generated via a perturbative 1 → 2 branching process. Using a detailed calculation, we confirm the result written down originally by Ryskin and Snigirev -namely, that the 2v1 graphs in which the two nonperturbatively generated ladders do not interact with one another do contribute to the leading order proton-proton DPS cross section, albeit with a different geometrical prefactor to the one that applies to the '2v2'/'zero perturbative splitting' graphs. We then show that 2v1 graphs in which the 'nonperturbatively generated' ladders exchange partons with one another also contribute to the leading order proton-proton DPS cross section, provided that this 'crosstalk' occurs at a lower scale than the 1 → 2 branching on the other side of the graph. Due to the preference in the 2v1 graphs for the x value at which the branching occurs, and crosstalk ceases, to be very much larger than the x values at the hard scale, the effect of crosstalk interactions is likely to be a decrease in the 2v1 cross section except at exceedingly small x values ( 10 −6 ). At moderate x values ≃ 10 −3 −10 −2 , the x value at the splitting is in the region ≃ 10 −1 where PDFs do not change much with scale, and the effect of crosstalk interactions is likely to be small. We give an explicit formula for the contribution from the 2v1 graphs to the DPS cross section, and combine this with a suggestion that we made in a previous publication, that the 'double perturbative splitting'/'1v1' graphs should be completely removed from the DPS cross section, to obtain a formula for the DPS cross section. It is pointed out that there are two potentially concerning features in this equation, that might indicate that our prescription for handling the 1v1 graphs is not quite correct.

Prompt $${J/\psi }$$-pair production at the LHC: impact of loop-induced contributions and of the colour-octet mechanism

“…Assuming α S ∼ v 2 , the colour-singlet (CS) LI contribution should be of the same magnitude as the leading order (LO) CO contribution (yet both smaller that the bulk of the CS yield in the absence of the possible kinematical enhancement which we are after here). According to the NRQCD velocity scaling rules [52], the former one is indeed O(α 6 S v 3 ) while the latter one is O(α 4 S v 7 ). This justifies why we consider both of them in this study.…”

Two-loop splitting in double parton distributions

“…Developing a theoretical QCD framework for DPS that includes 1 → 2 splitting but avoids double counting between SPS and DPS (and the twist 2 × twist 4 mechanism) is quite nontrivial. First approaches to this problem are given in [13,[40][41][42]. More recently, some of us developed a new formalism [43] that possesses several advantages over the previous approaches.…”

A Monte-Carlo simulation of double parton scattering

“…However, the cross section for GS09 remains smaller than the one found with Equation (19). The main difference is that the 2v1 and 1v1 terms get geometrical enhancements when one uses y-dependent dPDFs [40,47]. This explains why the cross section found for dShower is higher than the one obtained with the GS09 set.…”

“…Unfortunately, no set of mPDFs is available for the moment. However, the case n = 2, referred to as double parton scattering (DPS), has been widely studied [26][27][28][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Despite the lack of experimental data, several groups managed to produce sets of double parton distribution functions (dPDFs) that represent an improvement over the simple product ansatz.…”