  It is known that after Affleck-Dine baryogenesis, spatial inhomogeneities of
Affleck-Dine field grow into non-topological solitons called Q-balls. In gauge
mediated SUSY breaking models, sufficiently large Q-balls with baryon charge
are stable while Q-balls with lepton charge can always decay into leptons. For
a Q-ball that carries nonzero $B$ and $L$ charges, the difference between the
baryonic component and the leptonic component in decay rate may induce nonzero
electric charge on the Q-ball. This implies that charged Q-ball, also called
gauged Q-ball, may emerge in our universe. In this paper, we investigate two
complex scalar fields, a baryonic scalar field and a leptonic one, in an
Abelian gauge theory. We find stable solutions of gauged Q-balls for different
baryon and lepton charges. Those solutions shows that a Coulomb potential
arises and the Q-ball becomes electrically charged as expected. It is
energetically favored that some amount of leptonic component decays, but there
is an upper bound on its amount due to the Coulomb force. The baryonic decay
also becomes possible by virtue of electrical repulsion and we find the
condition to suppress it so that the charged Q-balls can survive in the
universe.
