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

Abstract

Abstract 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 ∼ 0.106M2, where the ℤ2 symmetry is still broken.