Q-balls in polynomial potentials*

Bosons carrying a conserved charge can form stable bound states if their Lagrangian contains

attractive self-interactions. Bound-state configurations with a large charge Q can be described

classically and are denoted as Q-balls, their properties encoded in a non-linear differential equation.

Here, we study Q-balls in arbitrary polynomial single-scalar-field potentials both numerically and

via various analytical approximations. We highlight some surprising universal features of Q-balls

that barely depend on the details of the potential. The polynomial potentials studied here can be

realized in renormalizable models involving additional heavy or light scalars, as we illustrate with

several examples.