Supersymmetric Q-balls: A Numerical Study

Abstract

We study numerically a class of non-topological solitons, the Q-balls, arising in supersymmetric extension of the Standard Model with low-energy, gauge-mediated symmetry breaking. % Taking into account the exact form of the supersymmetric potential giving rise to Q-balls, we find that there is a lower limit on the value of the charge $Q$ in order to make them classically stable: $Q\gtrsim 5\times 10^2{Q}_{\mathrm{cr}}$, where $Q_{\mathrm{cr}}$ is constant depending on the parameters defining the potential and can be in the range $1\lesssim Q_{\mathrm{cr}}\lesssim 10^{8÷16}$.If $Q$ is the baryon number, stability with respect to the decay into protons requires $Q\gtrsim 10^{17}{Q}_{\mathrm{cr}}$, while if the gravitino mass is greater then $m_{3/2}\gtrsim 61\text{MeV}$, no stable gauge-mediation supersymmetric Q-balls exist. Finally, we find that energy and radius of Q-balls can be parameterized as $E\sim {\xi }_E{Q}^{3/4}$ and $R\sim {\xi }_R{Q}^{1/4}$, where ${\xi }_E$ and ${\xi }_R$ are slowly varying functions of the charge.

Comments: 6 pages, 2 columns, 6 figures. To appear on Phys. Rev. D