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.