Gauged Q ball in a piecewise parabolic potential

Q-ball solutions are considered within the theory of a complex scalar field with a gauged U (1) symmetry and a parabolic-type potential. In the thin-w alled limit, we show explicitly that there is a maximum size for these obje cts because of the repulsive Coulomb force. The size of the Q ball will inc rease with decreasing local minimum of the potential. And when the two mini ma degenerate, the energy stored within the surface of the Q ball becomes s ignificant. Furthermore, we find an analytic expression for a gauged Q ball , which is beyond the conventional thin-walled limit.