Correlations in double parton distributions: perturbative and non-perturbative effects

Abstract

The correct description of Double Parton Scattering (DPS), which represents a background in several channels for the search of new Physics at the LHC, requires the knowledge of double parton distribution functions (dPDFs). These quantities represent also a novel tool for the study of the three-dimensional nucleon structure, complementary to the possibilities offered by electromagnetic probes. In this paper we analyze dPDFs using Poincaré covariant predictions obtained by using a Light-Front constituent quark model proposed in a recent paper, and QCD evolution. We study to what extent factorized expressions for dPDFs, which neglect, at least in part, two-parton correlations, can be used. We show that they fail in reproducing the calculated dPDFs, in particular in the valence region. Actually measurable processes at existing facilities occur at low longitudinal momenta of the interacting partons; to have contact with these processes we have analyzed correlations between pairs of partons of different kind, finding that, in some cases, they are strongly suppressed at low longitudinal momenta, while for other distributions they can be sizeable. For example, the effect of gluon-gluon correlations can be as large as 20 %. We have shown that these behaviors can be understood in terms of a delicate interference of non-perturbative correlations, generated by the dynamics of the model, and perturbative ones, generated by the model independent evolution procedure. Our analysis shows that at LHC kinematics two-parton correlations can be relevant in DPS, and therefore we address the possibility to study them experimentally.

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].…”

Double parton correlations in mesons within AdS/QCD soft-wall models: a first comparison with lattice data

“…Refs. [15,57], the evolution procedure can reduce the impact of x 1 − x 2 correlations. However, since the pQCD evolution equations of dPDFs do not involve the k ⊥ dependence, correlations between x and k ⊥ can be relevant also at high energy scales.…”

Sum rule improved double parton distributions in position space

“…It is hence essential to develop realistic models for DPDs. Considerable efforts have been made to compute them in quark models [51][52][53][54][55][56][57][58][59][60][61][62], and lattice calculations of Mellin moments of DPDs are underway [63,64]. In addition, there are important theoretical constraints on DPDs.…”

“…In addition, there are important theoretical constraints on DPDs. On the one hand, there is the perturbative splitting of one parton into two [34][35][36][37][38][39]41,42,45,57,[65][66][67][68][69][70][71][72][73][74][75][76], which determines the behaviour of DPDs at small y and likewise puts constraints on DPDs depending on Δ. On the other hand, there are sum rules [77,78], which involve DPDs integrated over y (or evaluated at Δ = 0) and express the conservation of momentum and quark number.…”