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

Abstract

The valence double parton distribution of the pion is analyzed in the framework of chiral quark models, where in the chiral limit factorization between the longitudinal and transverse degrees of freedom occurs. This feature leads, at the quark-model scale, to a particularly simple distribution of the form $D(x_1,x_2,\vec{q})=\delta (1-x_1-x_2)F(\vec{q})$, where $x_{1,2}$ are the longitudinal momentum fractions carried the valence quark and antiquark and $\vec{q}$ is their relative transverse momentum. For $\vec{q}=\vec{0}$ this result complies immediately to the Gaunt-Sterling sum rules. The DGLAP evolution to higher scales is carried out in terms of the Mellin moments. We then explore its role on the longitudinal correlation quantified with the ratio of the double distribution to the product of single distributions, $D(x_1,x_2,\vec{q}=\vec{0})/D(x_1)D(x_2)$. We point out that the ratios of moments $⟨x_1^n{x}_2^m⟩/⟨x_1^n⟩⟨x_2^m⟩$ are independent of the evolution, providing particularly suitable measures to be tested in the upcoming lattice simulations. The transverse form factor $F(\vec{q})$ and its Fourier conjugate in the relative transverse coordinate $\vec{b}$ are obtained in variants of the Nambu--Jona-Lasinio model with the spectral and Pauli-Villars regularizations.The results are valid in the soft-momentum domain. Interestingly, with the spectral regularization of the model, the effective cross section for the double parton scattering of pions is exactly equal to the geometric cross section, ${\sigma }_{\mathrm{eff}}=\pi ⟨{\vec{b}}^2⟩$ and yields about 20~mb.

arXiv commentdiscussion added, typos corrected, 12 pages, 6 figures

References in corpus (34)

• Pionic Parton Distributions Revisited
• Double Parton Distributions Incorporating Perturbative QCD Evolution and Momentum and Quark Number Sum Rules
• Measurement of hard double-parton interactions in W->lv+ 2 jet events at sqrt(s)=7 TeV with the ATLAS detector
• pQCD Physics of multiparton interactions
• Perturbative QCD correlations in multi-parton collisions
• A QCD Analysis of Double Parton Scattering: Color Correlations, Interference Effects and Evolution
• Generalized parton distributions of the pion in chiral quark models and their QCD evolution
• Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model
• What is Double Parton Scattering?
• Double parton correlations in constituent quark models
• Spectral quark model and low-energy hadron phenomenology
• The Transverse Momentum Dependent Fragmentation Function at NNLO
• Production of two $c\bar{c}$ pairs in double-parton scattering
• Double Parton Correlations in the Bag Model
• Correlations in double parton distributions: effects of evolution
• Parton Distributions in the Valon Model
• Hadron Structure Functions in a Chiral Quark Model: Regularization, Scaling and Sum Rules
• Scale Factor in Double Parton Collisions and Parton Densities in Transverse Space
• Double parton correlations and constituent quark models: a Light Front approach to the valence sector
• Valence double parton distributions of the nucleon in a simple model
• Same-sign WW production in proton-nucleus collisions at the LHC as a signal for double parton scattering
• Constraining the double gluon distribution by the single gluon distribution
• Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model
• Hadronic structure from double parton scattering
• Proof of sum rules for double parton distributions in QCD
• How to impose initial conditions for QCD evolution of double parton distributions?
• Generalized Valon Model for Double Parton Distributions
• The effective cross section for double parton scattering within a holographic AdS/QCD approach
• A model calculation of double parton distribution functions of the pion
• Double parton distributions in the pion in the Nambu and Jona-Lasinio model
• Two-current correlations in the pion on the lattice
• Constraining double parton correlations and interferences
• Unintegrated double parton distributions
• Numerical analysis of the unintegrated double gluon distribution

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• Two-current correlations in the pion in the Nambu and Jona-Lasinio model
• Double parton distributions of the proton from basis light-front quantization
• Applications of the Nambu--Jona-Lasinio model to the partonic structure of the pion
• Double parton distributions with flavor interference from lattice QCD
• The Schwinger and Chiral Schwinger Models in a Non-perturbative Spectral Regularization
• On sum rules for double and triple parton distribution functions and Pythia's model of multiple parton interactions