Two-loop scalar kinks

2021

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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.

“…The two-loop vacuum energy does suffer from an infrared (IR) divergence, which is removed in ref. [15] via the inclusion of an…”

Section: Review Of the φ 4 Kinkmentioning

confidence: 99%

Section: Jhep09(2021)009mentioning

confidence: 99%

“…This standard exercise is performed in detail in refs. [15] and [16] for the two kink states. Subtracting the two energies yields (3.1).…”

Section: Jhep09(2021)009mentioning

confidence: 99%

“…[14] has been extended, from one loop to arbitrary numbers of loops, in a series of papers summarized in ref. [15]. At one loop, it has been known since ref.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

2021

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Cut-off kinks

Royston

Zhang

2023

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We answer the question: If a vacuum sector Hamiltonian is regularized by an energy cutoff, how is the one-kink sector Hamiltonian regularized? We find that it is not regularized by an energy cutoff, indeed normal modes of all energies are present in the kink Hamiltonian, but rather the decomposition of the field into normal mode operators yields coefficients which lie on a constrained surface that forces them to become small for energies above the cutoff. This explains the old observation that an energy cutoff of the kink Hamiltonian leads to an incorrect one-loop kink mass. To arrive at our conclusion, we impose that the regularized kink sector Hamiltonian is unitarily equivalent to the regularized vacuum sector Hamiltonian. This condition implies that the two regularized Hamiltonians have the same spectrum and so guarantees that the kink Hamiltonian yields the correct kink mass.

A reduced inner product for kink states

Liu

2023

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Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized via wave packets or by compactification. However, in some applications both possibilities are undesirable. In the present note, we introduce a finite inner product on translation-invariant kink states that allows us to compute probabilities involving these nonnormalizable states. Essentially, it is the quotient of the usual inner product by the translation group. We present a surprisingly simple formula for the reduced inner product, which requires no knowledge of the zero-mode dependence of the states but includes a correction which accounts for the mixing between zero modes and normal modes as the kink moves. As an application, we show that initial and final state corrections to meson multiplication vanish. However, we find that the pole of the subleading term in the initial state requires an infinitesimal imaginary shift.