Valence Double Parton Distributions of the Nucleon in a Simple Model

Abstract

Valence double parton distribution functions of the nucleon are evaluated in the framework of a simple model, where the conservation of the longitudinal momentum is taken into account. The leading-order DGLAP QCD evolution from the low quark-model scale to higher renormalization scales is carried out via the Mellin moments of the distributions. Results of the valence quark correlation function show that in general the double distributions cannot be approximated as a product of the single-particle distributions.Theoretical interest in double parton distributions (dPDFs) in hadrons has been recently renewed (see the reviews [1,2] and the references therein). The activity is largely triggered by the experimental program at the LHC, where the double parton scattering (DPS) may bring substantial contribution in certain production processes [3,4]. Phenomenological aspects of the inclusion of the multi-parton effects have been widely pursued since the early days of the parton model [5], while many formal features of the multiparton evolution [6,7] follow from a pioneering study on fragmentation functions [8]. Elements of the QCD formulation are presented in [9][10][11][12], while a 2 GPD interpretation is provided in [13]. Positivity bounds for dPDFs were recently discussed in [14].Dynamic modeling of dPDFs has been up to now very little explored. In fact, the only calculations which nonperturbatively predict the valence dPDFs of the nucleon have been carried out in the framework of the MIT bag model [15] and in the constituent quark model [16]. In both calculations, the approximate implementation of relativity has the side effect of producing distributions with unphysical support, i.e., extending outside the interval 0 ≤ x 1 , x 2 , x 1 + x 2 ≤ 1. An important aspect of the dPDFs is that they allow to detect tight diquark correlations, in which case the dPDF becomes a function of the sum x 1 + x 2 . In the (x 1 , x 2 ) distribution plot the fingerprints are the straight-line structures inclined by 45 • .The purpose of this talk is to explore the valence dPDF of the proton in a very simple model which includes the exact momentum-conservation constraints and complies to the Lorentz invariance. Satisfaction of these requirements results in proper theoretical features, such as the correct support in the x-variables or the quarknumber and momentum sum rules [17]. In the considered model, the correlations between partons are due Talk presended by WB at the Light Cone 2013 Conference, Skiathos, Greece.

Double parton correlations in Light-Front constituent quark models

“…We notice that, if we use the simple ansatz discussed in Ref. [27] for the evaluation of dPDFs, our code for the pQCD evolution reproduce the results found and discussed in that paper. After having obtained the dPDFs at a generic high energy scale, e.g., Q 2 = 10 GeV 2 , using pQCD, the ratios r 5 and r 6 have been shown again in Figs.…”

Double parton distribution of valence quarks in the pion in chiral quark models

“…To satisfy the GS sum rules, we have argued in [40,41] that a practical approach is the top-down method, where one starts with n-body parton distributions with the longitudinal momentum fractions constrained with δ(1 − x 1 − ... − x n ), and subsequently generates distributions with a lower number of partons via marginal projections. This avoids complications of bottom-up attempts in constructing dPDFs from known sPDFs, which cannot be unique and where one encounters problems [48,50].…”

“…The QCD evolution equations for multi-parton distributions have been derived long ago [21,22]. A simple and numerically efficient method is based on the Mellin moments, similarly to the case of sPDFs (for results of a practical implementation see, e.g., [40] for the nucleon and [41] for the pion). While for ease of notation we do not write explicitly the y dependence, the evolution equations quoted below are still valid for that case [58].…”

“…It is worth noting some other non-perturbative studies of dPDFs in quark models for the nucleon, such as in the MIT bag [34] or in the constituent quark model model [35], also with the light-front wave functions [36,37]. We stress that the longitudinal correlation features in these models are qualitatively understood in the framework of the valon model [38,39], as shown in [40,41]. 2 The paper is organized as follows.…”

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

“…No data are presently available for dPDFs and their calculation using non perturbative methods is cumbersome. A few model calculations, able in principle to grasp the most relevant features of dPDFs, have been therefore performed [12][13][14][15][16]. In particular, in ref.…”