Sum rule improved double parton distributions in position space

Abstract

Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of small transverse distance between the partons can be improved step by step, such as to fulfil the sum rules for double parton distributions with an accuracy around 10%.

Double parton distributions in the pion from lattice QCD

“…It is therefore important to have as much theoretical guidance as possible about the properties and behaviour of DPDs. Apart from approaches that focus on fulfilling theoretical constraints [47][48][49][50], there exists a large number of model calculations for the DPDs of the nucleon [51][52][53][54][55][56][57][58] and a smaller number for those of the pion [59][60][61][62].…”

Two-loop splitting in double parton distributions: the colour non-singlet case

“…There is a large number of calculations of DPDs in quark models [39][40][41][42][43][44][45][46][47][48][49], and information about the Mellin moments of DPDs can be obtained in lattice QCD [50,51]. One may also try to construct an ansatz for DPDs that fulfils non-trivial theory constraints [52][53][54][55].…”

Combining single and double parton scatterings in a parton shower

“…The dPDFs should be "aware" of the constraints associated with the finite number of valence quarks in the proton (and the fact that its composition is uud) and the fact that the momentum of all partons should add up to the proton momentum. Formally this information is encoded in the number and momentum sum rules for the dPDFs [53,[68][69][70][71][72], which place non-trivial constraints on their structure. The MPI model in Pythia 8 in fact takes account of number and momentum sum-rule constraints in an approximate way, by ordering the interactions in scale and rescaling the PDFs following each hard interaction [37].…”