Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions

TL;DR

This paper investigates a (1+1)-dimensional scalar field model with a logarithmic potential, analyzing kink solutions, their excitation spectra, and scattering behavior, revealing no vibrational modes or resonance phenomena in collisions.

Contribution

It introduces and analyzes kink solutions in a logarithmic scalar field theory, detailing their excitation spectra and scattering dynamics, with novel insights into their collision regimes.

Findings

Kinks have no vibrational excitation modes.

Kink-antikink collisions exhibit two regimes based on initial velocity.

No resonance phenomena observed in scattering events.

Abstract

We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with spontaneous symmetry breaking and mass generation. We demonstrate that this model allows topological solutions -- kinks. We analyze the kink excitation spectrum, and show that it does not contain any vibrational modes. We also study the scattering dynamics of kinks for a wide range of initial velocities. The critical value of the initial velocity occurs in kink-antikink collisions, which thus differentiates two regimes. Below this value, we observe the capture of kinks and their fast annihilation; while above this value, the kinks bounce off and escape to spatial infinities. Numerical studies show no resonance phenomena in the kink-antikink scattering.