Solving the Spectral Problem via the Periodic Boundary Approximation in $\phi^6$ Theory

EPL 147 (2024) 44002 In $\phi^6$ 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 Schr\"{o}dinger...

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Bibliographic Details
Main Authors Long, Lingxiao, Jiang, Yunguo
Format Journal Article
LanguageEnglish
Published 20.04.2024
Subjects
Physics - High Energy Physics - Theory
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Summary:EPL 147 (2024) 44002 In $\phi^6$ 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 Schr\"{o}dinger-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 Schr\"{o}dinger-like equation, and obtain astonishing agreement between them at the long separation regime.
DOI:10.48550/arxiv.2404.13310