Evidence for the unbinding of the 𝜙4 kink’s shape mode

Jarah Evslin (Institute of Modern Physics, NanChangLu 509, Lanzhou, 730000, China; University of the Chinese Academy of Sciences, YuQuanLu 19A, Beijing, 100049, China)

The 𝜙4 double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is −0.115567λ/M in terms of the coupling λ/4 and the meson mass M evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is −0.433λ/M. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of λ/4 ∼ 0.106M 2, where the ℤ 2 symmetry is still broken.

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      "source": "Springer", 
      "value": "The \ud835\udf194 double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is \u22120.115567\u03bb/M in terms of the coupling \u03bb/4 and the meson mass M evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is \u22120.433\u03bb/M. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of \u03bb/4 \u223c 0.106M 2, where the \u2124 2 symmetry is still broken."
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Published on:
02 September 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 9
Pages 1-13
DOI:
https://doi.org/10.1007/JHEP09(2021)009
arXiv:
2104.14387
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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