Modified Lüscher zeta-function and the modified effective range expansion in the presence of a long-range force
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908464626794496 |
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| author | Bubna, Rishabh Hammer, Hans-Werner Hoid, Bai-Long Pang, Jin-Yi Rusetsky, Akaki Wu, Jia-Jun |
| author_facet | Bubna, Rishabh Hammer, Hans-Werner Hoid, Bai-Long Pang, Jin-Yi Rusetsky, Akaki Wu, Jia-Jun |
| contents | An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in Ref.~\cite{Bubna:2024izx} for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modified Lüscher zeta-function and the modified effective range expansion in the presence of a long-range force Bubna, Rishabh Hammer, Hans-Werner Hoid, Bai-Long Pang, Jin-Yi Rusetsky, Akaki Wu, Jia-Jun High Energy Physics - Lattice An efficient numerical algoritm is proposed for the calculation of the modified Lüscher zeta-function in the presence of a long-range force. Using the formalism developed in Ref.~\cite{Bubna:2024izx} for the analysis of synthetic data on the finite-volume energy levels in a toy model, it is demonstrated that, in contrast to the standard Lüscher approach, the truncation of the higher partial waves has very little effect on the final result. Furthermore, the regularization and renormalization of the modified Lüscher zeta-function is discussed in detail, as well as the problems arising within the cutoff regularization. It is shown that, using the renormalization scheme proposed in the present paper, one obtains modified effective range expansion parameters of natural size in all partial waves. |
| title | Modified Lüscher zeta-function and the modified effective range expansion in the presence of a long-range force |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2507.18399 |