Solitons in an effective theory of CP violation

TL;DR

This paper explores soliton solutions in an effective scalar meson theory with CP violation, revealing stable Q-ball-like excitations and instantons, with implications for long-lived domain walls and anomalous meson processes.

Contribution

It introduces a novel scalar field theory with a specific CP-violating interaction and analytically finds soliton and instanton solutions, expanding understanding of non-perturbative effects in meson sectors.

Findings

Analytic soliton solutions with Q-balls exhibiting Q^{2/3} energy scaling.

Existence of finite-action instanton solutions in the theory.

Potential long-lived domain wall excitations in the model.

Abstract

We study an effective field theory describing CP-violation in a scalar meson sector. We write the simplest interaction that we can imagine, $${\cal L}\sim \epsilon_{i_1\cdots i_5}\epsilon^{\mu_1\cdots\mu_4}\phi_{i_1}\partial_{\mu_1}\phi_{i_2}\partial_{\mu_2}\phi_{i_3}\partial_{\mu_3}\phi_{i_4}\partial_{\mu_4}\phi_{i_5}$$ which involves 5 scalar fields. The theory describes CP-violation only when it contains scalar fields representing mesons such as the $K^*_0$, sigma, $f_0$ or $a_0$. If the fields represent pseudo-scalar mesons, such as B, K and $\pi$ mesons then the Lagrangian describes anomalous processes such as $KK\to \pi\pi\pi$. We speculate that the field theory contains long lived excitations corresponding to $Q$-ball type domain walls expanding through space-time. In an 1+1 dimensional, analogous, field theory we find an exact, analytic solution corresponding to such solitons. The solitons have a U(1) charge $Q$, which can be arbitrarily high, but oddly, the energy behaves as $Q^{2/3}$ for large charge, thus the configurations are stable under disintegration into elementary charged particles of mass $m$ with $Q=1$. We also find analytic complex instanton solutions which have finite, positive Euclidean action.