Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach

TL;DR

This paper introduces a novel large-momentum effective theory approach to compute light-front wave functions from Euclidean lattice QCD, avoiding traditional light-front quantization issues like zero modes and divergences.

Contribution

It proposes a new method to calculate light-front wave functions via large-momentum expansion of Euclidean correlators, bypassing the subtleties of direct light-front quantization.

Findings

Successfully applied to a pseudo-scalar meson wave function

Provides a systematic lattice QCD-based framework for light-front physics

Circumvents zero-mode and divergence problems in light-front calculations

Abstract

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultra-violet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small $k^+$ modes have been effectively ``integrated out'', with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudo-scalar meson wave function.