Left-hand cut and the HAL QCD method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909468794552320 |
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| author | Aoki, Sinya Doi, Takumi Lyu, Yan |
| author_facet | Aoki, Sinya Doi, Takumi Lyu, Yan |
| contents | We investigate how the left-hand cut (LHC) problem is treated in the HAL QCD method. For this purpose, we first consider the effect of the LHC to the scattering problem in non-relativistic quantum mechanics with potentials. We show that the $S$-matrix or the scattering phase shift obtained from the potential including the Yukawa term ($e^{- m_πr}/r$) with the infra-red (IR) cutoff $R$ is well-defined even for the complex momentum $k$ as long as $R$ is finite, and they are compared with those obtained by the analytic continuation without the IR cutoff. In the $R\to\infty$ limit, the phase shift approaches the result from the analytic continuation at ${\rm Im}\, k < m_π/2$, while they differ at ${\rm Im}\, k > m_π/2$, except $k= k_b$, where $k_b$ is the binding momentum. We also observe that $k_b$ can be correctly obtained even at finite but large $R$. Using knowledge obtained in the non-relativistic quantum mechanics, we present how we should treat the LHC in the HAL QCD potential method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left-hand cut and the HAL QCD method Aoki, Sinya Doi, Takumi Lyu, Yan High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory We investigate how the left-hand cut (LHC) problem is treated in the HAL QCD method. For this purpose, we first consider the effect of the LHC to the scattering problem in non-relativistic quantum mechanics with potentials. We show that the $S$-matrix or the scattering phase shift obtained from the potential including the Yukawa term ($e^{- m_πr}/r$) with the infra-red (IR) cutoff $R$ is well-defined even for the complex momentum $k$ as long as $R$ is finite, and they are compared with those obtained by the analytic continuation without the IR cutoff. In the $R\to\infty$ limit, the phase shift approaches the result from the analytic continuation at ${\rm Im}\, k < m_π/2$, while they differ at ${\rm Im}\, k > m_π/2$, except $k= k_b$, where $k_b$ is the binding momentum. We also observe that $k_b$ can be correctly obtained even at finite but large $R$. Using knowledge obtained in the non-relativistic quantum mechanics, we present how we should treat the LHC in the HAL QCD potential method. |
| title | Left-hand cut and the HAL QCD method |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2501.16804 |