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On the quantum stability of Q-balls

We consider the evolution and decay of Q-balls under the influence of quantum fluctuations. We argue that the most important effect resulting from these fluctuations is the modification of the effective potential in which the Q-ball evolves. This is in addition to spontaneous decay into elementary particle excitations and fission into smaller Q-balls previously considered in the literature, which -- like most tunnelling processes -- are likely to be strongly suppressed. We illustrate the effect of quantum fluctuations in a particular model $ϕ^6$ potential, for which we implement the inhomogeneous Hartree approximation to quantum dynamics and solve for the evolution of Q-balls in 3+1 dimensions. We find that the stability range as a function of (field space) angular velocity $ω$ is modified significantly compared to the classical case, so that small-$ω$ Q-balls are less stable than in the classical limit, and large-$ω$ Q-balls are more stable. This can be understood qualitatively in a simple way.