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A bstract The  4  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 . 106 M  2 , where the  ℤ  2  symmetry is still broken.

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