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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2603.12590 |
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| _version_ | 1866910051578413056 |
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| author | Guo, Hengyuan Evslin, Jarah Bolognesi, Stefano |
| author_facet | Guo, Hengyuan Evslin, Jarah Bolognesi, Stefano |
| contents | There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a Pöschl-Teller potential at integer level $σ$. The cases $σ=1$ and $2$ are the well-known Sine-Gordon and $ϕ^4$ double-well models. The $σ=3$ kink has received relatively little attention because it exhibits a $ϕ^{8/3}$ potential, whose third derivative diverges in the vacuum. In old-fashioned perturbation theory this yields a cubic interaction that diverges far from a kink. We nonetheless use this interaction to calculate the amplitudes and probabilities for incoming radiation to excite or de-excite one of the kink's two shape modes. As each shape mode is localized about the kink, the leading order amplitudes are nonetheless finite. This suggests that the $σ=3$ model is not pathological, but rather its mesons are quantum field theoretic extensions of Znojil's bound states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | (De-)Exciting the Third Poschl-Teller Kink Guo, Hengyuan Evslin, Jarah Bolognesi, Stefano High Energy Physics - Theory There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a Pöschl-Teller potential at integer level $σ$. The cases $σ=1$ and $2$ are the well-known Sine-Gordon and $ϕ^4$ double-well models. The $σ=3$ kink has received relatively little attention because it exhibits a $ϕ^{8/3}$ potential, whose third derivative diverges in the vacuum. In old-fashioned perturbation theory this yields a cubic interaction that diverges far from a kink. We nonetheless use this interaction to calculate the amplitudes and probabilities for incoming radiation to excite or de-excite one of the kink's two shape modes. As each shape mode is localized about the kink, the leading order amplitudes are nonetheless finite. This suggests that the $σ=3$ model is not pathological, but rather its mesons are quantum field theoretic extensions of Znojil's bound states. |
| title | (De-)Exciting the Third Poschl-Teller Kink |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.12590 |