Abstract
This work introduces a new method for computing correlation functions on the light front. Starting from Bethe-Salpeter equations, the authors present calculations using contour deformation and analytic continuation, finding good agreement with established methods. This approach shows promise as an efficient and generalizable technique with applications to parton distribution functions and related constructions.
Highlights
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
Ongoing and future experiments at the LHC, Jefferson Lab, RHIC, the Electron-Ion Collider, COMPASS/AMBER and other facilities aim to establish a three-dimensional spatial imaging of hadrons and measure structure observables such as the spin and orbital angular momentum distributions inside hadrons and their longitudinal and transverse momentum structure. These properties are encoded in parton distribution functions (PDFs), generalized parton distributions (GPDs) and transverse momentum distributions (TMDs), see e.g., [1–5] and references therein, whose matrix elements
Summary
Understanding the quark-gluon structure of hadrons is a major goal in strong interaction studies. There remain questions regarding the formulation of generalized spectral representations for gauge theories, and the singularity structure of the remaining parts of the integrands (propagators, vertices, etc.) must still be known explicitly which poses practical limitations The combination of such techniques, occasionally together with a reconstruction using moments, has found widespread recent applications in the calculation of parton distributions and related quantities [20–25,36–56]. Instead of the hadron-to-hadron correlator (1), we consider the simpler case of the vacuum-to-hadron amplitude shown, Ψðz; PÞ 1⁄4 h0jTΦðzÞΦð0ÞjPi: ð2Þ This is the generic form of a two-body Bethe-Salpeter wave function (BSWF) for a hadron carrying momentum P, which can be dynamically calculated from its BetheSalpeter equation (BSE). Two Appendixes provide details on the Nakanishi representation and the general properties of the singularities that appear in the integrands
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