Vibrational modes of Q-balls

TL;DR

This paper analyzes the vibrational modes of classically stable Q-balls, revealing soft excitations in large Q-balls and identifying specific vibrational modes near critical charge, using analytical methods despite a non-Hermitian boundary value problem.

Contribution

It provides an analytical study of linear perturbations of Q-balls, including soft modes and vibrational modes near critical charge, in theories with flat potentials.

Findings

Large Q-balls have soft vibrational excitations.

A specific vibrational mode exists near the critical charge.

Perturbation analysis confirms stability properties of Q-balls.

Abstract

We study linear perturbations of classically stable Q-balls in theories admitting analytic solutions. Although the corresponding boundary value problem is non-Hermitian, the analysis of perturbations can also be performed analytically in certain regimes. We show that in theories with the flat potential, large Q-balls possess soft excitations. We also find a specific vibrational mode for Q-balls with a near-critical charge, where the perturbation theory for excitations can be developed. Comparing with the results on stability of Q-balls provides additional checks of our analysis.