Frame-independent spatial coordinate z̃ : Implications for light-front wave functions, deep inelastic scattering, light-front holography, and lattice QCD calculations

Gerald A Miller,Stanley J Brodsky

doi:10.1103/physrevc.102.022201

Gerald A Miller, Stanley J Brodsky

Open Access

https://doi.org/10.1103/physrevc.102.022201

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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 $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{z}$ is the boost and Lorentz 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 a very large extent in $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{z}$.

Highlights

Much recent effort has been devoted to understanding and measuring the generalized parton distributions [1,2,3] which encode the fundamental structure of hadrons in terms of the three-dimensional momentum-space coordinates of their quark and gluon constituents
Recent lattice calculations of quasi-parton distribution functions evaluate a Fourier transform of a matrix element which depends on the spatial separation between the points of virtual-photon absorption and emission that appears in the virtual photon-proton Compton scattering amplitude
Of considerable interest to understand the spatial longitudinal dependence of the virtual Compton amplitude from a causal frame-independent perspective. In this Rapid Communication, we show that the frame-independent eigensolutions of the Quantum Chromodynamics (QCD) light-front (LF) Hamiltonian that underly hadronic observables can be expressed in terms of a longitudinal spatial coordinate zthat is related to the spatial separation between a struck quark and the spectators

Summary

Rapid Communications

Frame-independent spatial coordinate z: Implications for light-front wave functions, deep inelastic scattering, light-front holography, and lattice QCD calculations. Miller Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA. A general procedure for obtaining frame-independent three-dimensional light-front coordinate-space wave functions is introduced. 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 frameindependent 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 a very large extent in z

Introduction

Published by the American Physical Society

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