The Further Estimations of the Q-Balls with One-Loop Motivated Effective Potential

Abstract

The analytical estimations on the Friedberg-Lee-Sirlin typed Q-balls is performed. The two-field Q-balls are also discussed under the one-loop motivated effective potential subject to the temperature. We argue under the analytical consideration that the parameters from the potential can be regulated to lead the energy per unit charge of Q-balls to be lower to keep the model stable. If the energy density is low enough, the Q-balls can become candidates of dark matter. It is also shown rigorously that the two-field Q-balls can generate in the first-order phase transition and survive while they are affected by the expansion of the universe. The analytical evaluations show that the Q-balls with one-loop motivated effective potential can exist with the adjustment of coefficients of terms. We cancel the infinity in the energy to obtain the necessary conditions consist with those imposed in the previous work. According to the approximate expressions instead of curves versus the model parameters with a series of fixed values, the lower temperature will reduce the energy density, so there probably have been more and more stable Friedberg-Lee-Sirlin typed Q-balls to become the dark matter in the expansion of the universe.