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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16689 |
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| _version_ | 1866909654093660160 |
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| author | Xiong, Ao-Sheng Hua, Jun Wei, Ting Yu, Fu-Sheng Zhang, Qi-An Zheng, Yong |
| author_facet | Xiong, Ao-Sheng Hua, Jun Wei, Ting Yu, Fu-Sheng Zhang, Qi-An Zheng, Yong |
| contents | We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and uniqueness of solutions, but critically violates the stability requirement, exhibiting exponential sensitivity to input perturbations. To address this instability, we implemented Tikhonov regularization with L-curve optimized parameters, demonstrating its validity for controlled toy model studies and real lattice QCD results of quasi distribution amplitudes. The reconstructed solutions is consistent with the physics-driven $λ$-extrapolation method. Our analysis demonstrates that the inverse Fourier problem within the large-momentum effective theory (LaMET) framework belongs to a class of moderately tractable ill-posed problems, characterized by distinct spectral properties that differ from those of more severely unstable inverse problems encountered in other lattice QCD applications. Tikhonov regularization establishes a rigorous mathematical framework for addressing the underlying instability, enabling first-principles uncertainty quantification without relying on ansatz-based assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ill-Posedness in Limited Discrete Fourier Inversion and Regularization for Quasi Distributions in LaMET Xiong, Ao-Sheng Hua, Jun Wei, Ting Yu, Fu-Sheng Zhang, Qi-An Zheng, Yong High Energy Physics - Lattice We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and uniqueness of solutions, but critically violates the stability requirement, exhibiting exponential sensitivity to input perturbations. To address this instability, we implemented Tikhonov regularization with L-curve optimized parameters, demonstrating its validity for controlled toy model studies and real lattice QCD results of quasi distribution amplitudes. The reconstructed solutions is consistent with the physics-driven $λ$-extrapolation method. Our analysis demonstrates that the inverse Fourier problem within the large-momentum effective theory (LaMET) framework belongs to a class of moderately tractable ill-posed problems, characterized by distinct spectral properties that differ from those of more severely unstable inverse problems encountered in other lattice QCD applications. Tikhonov regularization establishes a rigorous mathematical framework for addressing the underlying instability, enabling first-principles uncertainty quantification without relying on ansatz-based assumptions. |
| title | Ill-Posedness in Limited Discrete Fourier Inversion and Regularization for Quasi Distributions in LaMET |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2506.16689 |