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

TL;DR

This paper introduces a frame-independent three-dimensional light-front coordinate $ ilde z$, enabling new insights into hadronic structure and scattering processes by providing a causal, frame-independent spatial coordinate conjugate to light-front momentum.

Contribution

It presents a general method to obtain frame-independent light-front wave functions and derives a new expression for the quark distribution function using this coordinate, with applications in holographic QCD.

Findings

Longitudinal extent of proton eigenfunctions can be very large in $ ilde z$.

The new coordinate simplifies the analysis of hadronic observables.

Model examples demonstrate the utility of the frame-independent wave functions.

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 $\tilde z$.