Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions

TL;DR

This paper explores scalar field models with polynomial potentials, introducing a parameter that modifies kink solutions' tails and stability properties, revealing transitions from exponential to power-law decay and complex fluctuation spectra.

Contribution

It presents analytical solutions for modified kink structures in scalar fields, linking tail behavior to a tunable parameter and analyzing stability features in detail.

Findings

Kink solutions exhibit adjustable tail behaviors from exponential to power-law.

The classical mass vanishes as the parameter tends to infinity, affecting solution properties.

Stability potentials can support multiple bound states or volcano-like profiles.

Abstract

We investigate a class of scalar field models which engender kink-like solutions in the presence of polynomial potentials that allows for modifications of the tails of the localized configurations. We introduce a parameter in the potential that controls the classical mass associated to its minima. By using the first-order framework developed by Bogomol'nyi, we obtain analytical solutions that become more and more interactive as we increase such parameter. By investigating the limit in which the parameter tends to infinite, the kink solution gets power law tails, and we show that this feature is related to the behavior of the classical mass, which vanishes in the aforementioned limit. We also investigate the stability against small fluctuations, with the results unveiling that, depending on the values of the parameter, the stability potential may support several bound states and also, it may attain a volcano-like profile.