Inverse Problem Approach for Non-Perturbative QCD: Theoretical Foundation

Fuente: arXiv
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Auteurs principaux: Xiong, Ao-Sheng, Yu, Fu-Sheng, Zheng, Yong, Wei, Ting
Format: Preprint
Publié: 2022
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author Xiong, Ao-Sheng
Yu, Fu-Sheng
Zheng, Yong
Wei, Ting
author_facet Xiong, Ao-Sheng
Yu, Fu-Sheng
Zheng, Yong
Wei, Ting
contents A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown low-energy non-perturbative quantities from known high-energy perturbative inputs via solving an inverse problem. The resulting inverse problem is rigorously proven to be ill-posed, with the solutions being unique but unstable. To address this instability, the well-established Tikhonov regularization is employed, yielding stable approximate solutions that converge to the true values as input errors vanish. The key features of this approach are illustrated through three toy models, demonstrating that solution precision can be systematically improved through reduced input errors and optimized regularization strategies.
format Preprint
id arxiv_https___arxiv_org_abs_2211_13753
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Inverse Problem Approach for Non-Perturbative QCD: Theoretical Foundation
Xiong, Ao-Sheng
Yu, Fu-Sheng
Zheng, Yong
Wei, Ting
High Energy Physics - Theory
High Energy Physics - Experiment
High Energy Physics - Lattice
High Energy Physics - Phenomenology
Nuclear Theory
A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown low-energy non-perturbative quantities from known high-energy perturbative inputs via solving an inverse problem. The resulting inverse problem is rigorously proven to be ill-posed, with the solutions being unique but unstable. To address this instability, the well-established Tikhonov regularization is employed, yielding stable approximate solutions that converge to the true values as input errors vanish. The key features of this approach are illustrated through three toy models, demonstrating that solution precision can be systematically improved through reduced input errors and optimized regularization strategies.
title Inverse Problem Approach for Non-Perturbative QCD: Theoretical Foundation
topic High Energy Physics - Theory
High Energy Physics - Experiment
High Energy Physics - Lattice
High Energy Physics - Phenomenology
Nuclear Theory
url https://arxiv.org/abs/2211.13753