Supersymmetric Q-balls: A Numerical Study

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: $Q \gtrsim 5 \times 10^2 Q_{\rm cr}$, where $Q_{\rm cr}$ is constant depending on the parameters defining the potential and can be in the range $1 \lesssim Q_{\rm cr} \lesssim 10^{8 \div 16}$.If $Q$ is the baryon number, stability with respect to the decay into protons requires $Q \gtrsim 10^{17} Q_{\rm cr}$, while if the gravitino mass is greater then $m_{3/2} \gtrsim 61 \MeV$, 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.