Going to the light front with contour deformations

TL;DR

This paper introduces a novel contour deformation technique combined with analytic continuation to accurately compute light-front wave functions from the Bethe-Salpeter equation, demonstrating its effectiveness in scalar models and potential for QCD applications.

Contribution

The paper presents a new contour deformation method for projecting Bethe-Salpeter wave functions onto the light front, capable of handling complex singularities and extensions relevant to QCD.

Findings

Excellent agreement with Nakanishi method

Handles complex singularities and unequal masses

Potential for computing parton distributions

Abstract

We explore a new method to calculate the valence light-front wave function of a system of two interacting particles, which is based on contour deformations combined with analytic continuation methods to project the Bethe-Salpeter wave function onto the light front. In this proof-of-concept study, we solve the Bethe-Salpeter equation for a scalar model and find excellent agreement between the light-front wave functions obtained with contour deformations and those obtained with the Nakanishi method frequently employed in the literature. The contour-deformation method is also able to handle extensions of the scalar model that mimic certain features of QCD such as unequal masses and complex singularities. In principle the method is suitable for computing parton distributions on the light front such as PDFs, TMDs and GPDs in the future.