Higher partial waves in femtoscopy
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915025888739328 |
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| author | Murase, Koichi Hyodo, Tetsuo |
| author_facet | Murase, Koichi Hyodo, Tetsuo |
| contents | Femtoscopy is recently gaining more attention as a new approach complementary to scattering experiments for constraining hadron-hadron interactions. We discuss the effect of higher partial waves on the two-particle correlation function, which has been neglected in traditional formulae used in the femtoscopy analyses. We consider the partial-wave expansion of the wave function in the Koonin-Pratt formula to give the correction to the correlation function by a sum of the contributions from each partial wave. We also generalize the Lednicky-Lyuboshitz formula, which was originally derived for the s-wave interaction, for higher partial waves. We find a compact representation of the generalized Lednicky-Lyuboshitz formula given by the backward scattering amplitude $f(θ= π)$ and the Fourier-Laplace transform of the relative source function, which gives an insight into the structure of the Lednicky-Lyuboshitz formula and its relation to the optical theorem. We numerically demonstrate the significance of higher partial waves with resonances using the square potential well. Also, the generalized Lednicky-Lyuboshitz formula turned out to be broken for higher partial waves, which suggests the importance of the centrifugal force for the higher partial waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher partial waves in femtoscopy Murase, Koichi Hyodo, Tetsuo Nuclear Theory High Energy Physics - Phenomenology Femtoscopy is recently gaining more attention as a new approach complementary to scattering experiments for constraining hadron-hadron interactions. We discuss the effect of higher partial waves on the two-particle correlation function, which has been neglected in traditional formulae used in the femtoscopy analyses. We consider the partial-wave expansion of the wave function in the Koonin-Pratt formula to give the correction to the correlation function by a sum of the contributions from each partial wave. We also generalize the Lednicky-Lyuboshitz formula, which was originally derived for the s-wave interaction, for higher partial waves. We find a compact representation of the generalized Lednicky-Lyuboshitz formula given by the backward scattering amplitude $f(θ= π)$ and the Fourier-Laplace transform of the relative source function, which gives an insight into the structure of the Lednicky-Lyuboshitz formula and its relation to the optical theorem. We numerically demonstrate the significance of higher partial waves with resonances using the square potential well. Also, the generalized Lednicky-Lyuboshitz formula turned out to be broken for higher partial waves, which suggests the importance of the centrifugal force for the higher partial waves. |
| title | Higher partial waves in femtoscopy |
| topic | Nuclear Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2411.08541 |