A Novel Algorithm for Extracting the Parton Distribution Amplitude from the Euclidean Bethe-Salpeter Wave Function

TL;DR

This paper introduces a new numerical approach using the maximum entropy method to extract parton distribution amplitudes from Euclidean Bethe-Salpeter wave functions, improving the determination of the Nakanishi weight function and light-front PDA.

Contribution

The paper presents a novel numerical technique for extracting the Nakanishi weight function and PDA from Euclidean Bethe-Salpeter wave functions using MEM, addressing an ill-posed inversion problem.

Findings

Successful extraction of the Nakanishi weight function

Accurate determination of the light-front PDA

Validation against previous PDA computation methods

Abstract

We propose a new numerical method to compute parton distribution amplitude(PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method(MEM). The Nakanishi weight function as well as the corresponding light-front PDA can be well determined. We confirm the previous works on PDA computation therein the different method has been performed.