Inverse Problem Approach for Non-Perturbative QCD: Applications
Abstract
In arXiv:2211.13753 we proposed a novel theoretical approach for non-perturbative QCD, named the inverse problem approach. It extracts non-perturbative quantities by solving a dispersion integral equation as an inverse problem, using perturbative QCD and operator product expansion as inputs. In this work, we apply this approach to the pion and a1(1260) decay constants, as well as the continuum spectral function. The extracted fπ= 130.8 ± 8.1 MeV agrees with the experimental value, and the reconstructed spectral function reproduces the ALEPH τ-decay data from threshold up to s ≃ 3 GeV2. The advantages of this approach are as follows: (i) the whole non-perturbative range is solved simultaneously, yielding the ground state, excited states, and the continuum spectrum within a single framework; (ii) it is based on rigorous mathematics, with not only statistical but also systematic uncertainties well controlled and quantifiable; (iii) the regularized solutions exhibit convergence, allowing the precision to be systematically improved with better inputs; (iv) quark-hadron duality emerges naturally at high energy scales, avoiding the low-energy duality assumption and the Borel transformation, and eliminating their associated uncertainties. Finally, the successful physical application of the inverse problem approach demonstrates its broad applicability to non-perturbative quantities.
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BibTeX
@misc{zheng2026inverse,
title = {{Inverse Problem Approach for Non-Perturbative QCD: Applications}},
author = {Yong Zheng and Ao-Sheng Xiong and Fu-Sheng Yu and Ting Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40111},
eprint = {2610.40111},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40111},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inverse Problem Approach for Non-Perturbative QCD: Applications
AU - Yong Zheng
AU - Ao-Sheng Xiong
AU - Fu-Sheng Yu
AU - Ting Wei
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40111
UR - https://arxiv.org/abs/2610.40111
AB - In arXiv:2211.13753 we proposed a novel theoretical approach for non-perturbative QCD, named the inverse problem approach. It extracts non-perturbative quantities by solving a dispersion integral equation as an inverse problem, using perturbative QCD and operator product expansion as inputs. In this work, we apply this approach to the pion and a_1(1260) decay constants, as well as the continuum spectral function. The extracted f_π= 130.8 ± 8.1 MeV agrees with the experimental value, and the reconstructed spectral function reproduces the ALEPH τ-decay data from threshold up to s ≃ 3 GeV^2. The advantages of this approach are as follows: (i) the whole non-perturbative range is solved simultaneously, yielding the ground state, excited states, and the continuum spectrum within a single framework; (ii) it is based on rigorous mathematics, with not only statistical but also systematic uncertainties well controlled and quantifiable; (iii) the regularized solutions exhibit convergence, allowing the precision to be systematically improved with better inputs; (iv) quark-hadron duality emerges naturally at high energy scales, avoiding the low-energy duality assumption and the Borel transformation, and eliminating their associated uncertainties. Finally, the successful physical application of the inverse problem approach demonstrates its broad applicability to non-perturbative quantities.
ER -