Solving the Spectral Problem via the Periodic Boundary Approximation in $ϕ^6$ Theory
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916374397321216 |
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| author | Long, Lingxiao Jiang, Yunguo |
| author_facet | Long, Lingxiao Jiang, Yunguo |
| contents | In $ϕ^6$ theory, the resonance scattering structure is triggered by the so-calls delocalized modes trapped between the $\bar{K}K$ pair. The frequencies and configurations of such modes depend on the $\bar{K}K$ half-separation 2$a$, can be derived from the Schrödinger-like equation. We propose to use the periodic boundary conditions to connect the localized and delocalized modes, and use periodic boundary approximation (PBA) to solve the spectrum analytically. In detail, we derive the explicit form of frequencies, configurations and spectral wall locations of the delocalized modes. We test the analytical prediction with the numerical simulation of the Schrödinger-like equation, and obtain astonishing agreement between them at the long separation regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving the Spectral Problem via the Periodic Boundary Approximation in $ϕ^6$ Theory Long, Lingxiao Jiang, Yunguo High Energy Physics - Theory In $ϕ^6$ theory, the resonance scattering structure is triggered by the so-calls delocalized modes trapped between the $\bar{K}K$ pair. The frequencies and configurations of such modes depend on the $\bar{K}K$ half-separation 2$a$, can be derived from the Schrödinger-like equation. We propose to use the periodic boundary conditions to connect the localized and delocalized modes, and use periodic boundary approximation (PBA) to solve the spectrum analytically. In detail, we derive the explicit form of frequencies, configurations and spectral wall locations of the delocalized modes. We test the analytical prediction with the numerical simulation of the Schrödinger-like equation, and obtain astonishing agreement between them at the long separation regime. |
| title | Solving the Spectral Problem via the Periodic Boundary Approximation in $ϕ^6$ Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.13310 |