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The Frame-Independent Spatial Coordinate $\tilde{z}$: Implications for Light-Front Wave Functions, Deep Inelastic Scattering, Light-Front Holography, and Lattice QCD Calculations
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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 $x={k^+\over P^+}$ 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 $\tilde z$.
Forward citations
Cited by 3 Pith papers
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Six-dimensional light-front Wigner distributions of the proton
All 16 leading-twist six-dimensional light-front quark Wigner distributions for the proton are computed in a spectator-diquark model, extending earlier five-dimensional and unpolarized-only results.
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Gluon skewed generalized parton distributions of proton from a light-front Hamiltonian approach
Using light-front wave functions with one dynamical gluon, the authors obtain all leading-twist gluon GPDs of the proton at nonzero skewness and find diffraction-like patterns in longitudinal position space.
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Nucleon relativistic weak-neutral axial-vector four-current distributions
The 3D axial charge density of a spin-1/2 hadron is parity-odd and controlled by the induced pseudotensor form factor G_T^Z, while the second-class current drops out of the mean-square axial and spin radii.
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