Generalized quasi, Ioffe-time, and pseudo quark distributions of the pion in the Nambu--Jona-Lasinio model

Abstract

We analyze the generalized quasi, Ioffe-time, and pseudo distributions of the valence quarks in the pion at the quark model scale. We use the framework of the Nambu-Jona-Lasinio model and investigate the basic question of how fast the pion has to move to effectively reach the infinite momentum limit, where the approach can provide the information on the generalized parton distribution functions. We consider both the vector distributions and the transversity distributions, related to the spin densities. With the developed analytic expressions, we conclude that to effectively approach the infinite momentum limit, one roughly needs the pion momenta of the order of $\sim 3$GeV. We also explore polynomiality of the quasi distributions and study the generalized quasi form factors. The issue of separability of the transverse and longitudinal dynamics in the model is studied with the help of the generalized Ioffe-time distributions, with the conclusion that the breaking is not substantial, unless the momentum transfer $t$ is large. We also provide an estimate of the range of the Ioffe-time values needed to obtain the generalized parton distributions with a reasonable accuracy. Our model results, which are analytic or semi-analytic, provide a valuable insight into the theoretical formalism and illustrate the intricate features of the investigated distributions.

extended discussion and a reference added, 23 pages, 12 figures

References in corpus (26)

• Large-Momentum Effective Theory
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• A Lattice Calculation of Parton Distributions
• Nonperturbative Evolution of Parton Quasi-Distributions
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Generalized parton distributions of the pion in chiral quark models and their QCD evolution
• Basic features of the pion valence-quark distribution function
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• Pion and kaon valence-quark parton distribution functions
• Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point
• Gravitational and higher-order form factors of the pion in chiral quark models
• Generalized Parton Distributions and Pseudo-Distributions
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions
• Nonperturbative partonic quasidistributions of the pion from chiral quark models
• Quasi-parton distribution functions: a study in the diquark spectator model
• Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike
• Pion and Kaon parton distributions in the QCD instanton vacuum
• Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions
• Generalized parton distributions and spin structures of light mesons from a light-front Hamiltonian approach
• Double parton distribution of valence quarks in the pion in chiral quark models
• Bayesian-Wilson coefficients in lattice QCD computations of valence PDFs and GPDs
• Vector-axial vector lattice cross section and valence parton distribution in the pion from a chiral quark model
• Baryonic form factors of the pion and kaon in a chiral quark model
• Parton physics of the large-$N_c$ mesons
• The quark quasi Sivers function and quasi Boer-Mulders function in a spectator diquark model

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