Partial wave decomposition on the lattice and its applications to the HAL QCD method
| العنوان: | Partial wave decomposition on the lattice and its applications to the HAL QCD method |
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| المؤلفون: | Takumi Doi, Takaya Miyamoto, Sinya Aoki, Shinya Gongyo, Kenji Sasaki, Yutaro Akahoshi, Tatsumi Aoyama |
| المصدر: | Physical Review |
| بيانات النشر: | American Physical Society (APS), 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Quantum chromodynamics, Physics, 010308 nuclear & particles physics, Scattering, High Energy Physics::Lattice, High Energy Physics - Lattice (hep-lat), High Energy Physics::Phenomenology, FOS: Physical sciences, Lattice QCD, Lambda, 01 natural sciences, Computer Science::Digital Libraries, Lattice constant, High Energy Physics - Lattice, Lattice (order), 0103 physical sciences, 010306 general physics, Wave function, Laplace operator, Mathematical physics |
| الوصف: | The approximated partial wave decomposition method to the discrete data on a cubic lattice, developed by C. W. Misner, is applied to the calculation of $S$-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet $\Lambda_c N$ system calculated in the $(2+1)$-flavor QCD on a $(32a~\mathrm{fm})^3$ lattice at the lattice spacing $a\simeq0.0907$ fm and $m_\pi \simeq 700$ MeV. We find that the $l=0$ component can be successfully extracted by Misner's method from the NBS wave function projected to $A_1^+$ representation of the cubic group, which contains small $l\ge 4$ components. Furthermore, while the higher partial wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian approximated by the usual second order difference is applied to the NBS wave function, such structures are found to be absent in the potential extracted by Misner's method, where the Laplacian can be evaluated analytically for each partial wave component. Despite the difference in the potentials, two methods give almost identical results on the central values and on the magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates not only that Misner's method works well in lattice QCD with the HAL QCD method but also that the contaminations from higher partial waves in the study of $S$-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial wave channels in the HAL QCD method with Misner's decomposition, where the utility of this new technique may become clearer. Comment: 22 pages, 10 figures |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 2470-0010 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f9c47f2b1086d4de1c54f87fca14d45c http://hdl.handle.net/2433/254058 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....f9c47f2b1086d4de1c54f87fca14d45c |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 24700010 |
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