Lanczos algorithm for lattice QCD matrix elements
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911149420707840 |
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| author | Hackett, Daniel C. Wagman, Michael L. |
| author_facet | Hackett, Daniel C. Wagman, Michael L. |
| contents | Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multi-state fit results than effective masses -- but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of "spurious state filtering" involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lanczos algorithm for lattice QCD matrix elements Hackett, Daniel C. Wagman, Michael L. High Energy Physics - Lattice Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multi-state fit results than effective masses -- but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of "spurious state filtering" involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon. |
| title | Lanczos algorithm for lattice QCD matrix elements |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2407.21777 |