The Frame-Independent Spatial Coordinate $\tilde{z}$: Implications for Light-Front Wave Functions, Deep Inelastic Scattering, Light-Front Holography, and Lattice QCD Calculations

Abstract

A general procedure for obtaining frame-independent, three-dimensional light-front coordinate-space wave functions is introduced. The third spatial coordinate, $\tilde{z}$ , is the frame independent coordinate conjugate to the light-front momentum coordinate $x=\frac{k^{+}}{P^{+}}$ which appears in the momentum-space light-front wave functions underlying generalized parton distributions, structure functions, distribution amplitudes, form factors, and other hadronic observables. These causal light-front coordinate-space wave functions are used to derive a general expression for the quark distribution function of hadrons as an integral over the frame-independent longitudinal distance (the Ioffe time) between virtual-photon absorption and emission appearing in the forward virtual photon-hadron Compton scattering amplitude. Specific examples using models derived from light-front holographic QCD show that the spatial extent of the proton eigenfunction in the longitudinal direction can have very large extent in $\tilde{z}$.

6 pages, 6 figures, this version adds references, corrects a typographical error and contains more explanations regarding the use of the variable $\tilde{z}$

References in corpus (6)

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• Leading twist GTMDs at nonzero skewness and Wigner distributions in boost-invariant longitudinal position space
• Confinement in Two-Dimensional QCD and the Infinitely Long Pion
• Quark generalized TMDs at skewness and Wigner Distribution in boost invariant longitudinal space
• Longitudinal dynamics for mesons on the light cone
• Chiral sum rule on the light front and the 3D image of the pion
• The Mystery of Bloom-Gilman Duality: A Light Front Holographic QCD Perspective
• Proton image and momentum distributions from light-front dynamics
• Polarized and unpolarized gluon PDFs: generative machine learning applications for lattice QCD matrix elements at short distance and large momentum
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• Six-dimensional light-front Wigner distributions of the proton
• Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in (1+1) dimensions
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• Analysis of virtual meson production in solvable (1+1) dimensional scalar field theory
• Quantum entanglement between partons in a strongly coupled quantum field theory
• T-odd Wigner Distributions in boost-invariant longitudinal position space and Spin-momentum correlation in proton
• Hadron spectroscopy using the light-front holographic Schrödinger equation and the 't Hooft equation