Oscillons from $Q$-balls in generalized models

Abstract

We study the oscillon/$Q$-ball relation in an extended model with non-canonical kinematics. The model contains a single real scalar field whose kinetic term is enlarged to include a generalizing function. We approximate the real sector up to the third order in a book-keeping parameter. In this context, we implement the Renormalization Group Perturbation Expansion (RGPE), from which we conclude that the relation between oscillons and underlying $Q$-balls holds even in the presence of nontrivial kinematics. We apply our results to the study of three different effective cases. In all of them, our expressions mimic the numerical evolution of nonstandard oscillons with great accuracy, especially for small and moderate amplitudes. As the initial amplitude increases, the numerical profile develops a modulated behavior, and we use a two $Q$-balls solution to seed our analytical oscillon. We discuss how our non-canonical construction allows the existence of a well-behaved oscillon in connection to the simplest $φ^2$-potential. This novel profile behaves in the same general way as the previous ones. So, we argue that they belong to the same universality class. Finally, we extend our analysis to consider those contributions up to the fifth order in the approximation expansion. We explore an exotic $φ^6$-scenario, and conclude that the relation between generalized oscillons and underlying $Q$-balls now belongs to a different universality class.

Figures (17)

• Figure 1: Results for the $\phi^3$-potential Eq. (\ref{['p3']}). The numerical oscillon (black line) is compared to the renormalized analytical one (red line). Here, we have chosen $\eta=0.10$ (upper line) and $\eta=0.80$ (lower line), with $\lambda=0.10$ (left column) and $\lambda=0.20$ (right column).
• Figure 2: Results for the inverse $\phi^4$-potential Eq. (\ref{['pi4']}). Conventions as in Fig. \ref{['fig_1A']}.
• Figure 3: Results for the prototypical double-well $\phi^4$-potential Eq. (\ref{['pdwp']}). Conventions as in Fig. \ref{['fig_1A']}.
• Figure 4: Results for the $\phi^3$-potential Eq. (\ref{['p3']}), with $\lambda_2=-0.05$ fixed. The numerical oscillon (black line) is compared to the renormalized analytical one (red line). Here, we have chosen $\eta=0.10$ (upper line) and $\eta=0.80$ (lower line), with $\lambda_1=0.10$ (left column) and $\lambda_1=0.20$ (right column).
• Figure 5: Results for the $\phi^3$-potential Eq. (\ref{['p3']}), with $\lambda_1=0.15$ fixed. The numerical oscillon (black line) is compared to the renormalized analytical one (red line). Here, we have chosen $\eta=0.10$ (upper line) and $\eta=0.80$ (lower line), with $\lambda_2=-0.08$ (left column) and $\lambda_2=-0.20$ (right column).