The Tunneling Potential Approach to Q-Balls

Q-balls are bound-state configurations of complex scalars stabilized by conserved Noether charge Q. They are solutions to a second-order differential equation that is structurally identical to Euclidean vacuum-decay bounce solutions in three dimensions. This enables us to translate the recent tunneling potential approach to Q-balls, which amounts to a reformulation of the problem: instead of treating the field as a dynamical variable one rewrites the equation in the language of the "total energy" and minimizes it. That can dramatically simplify the task of finding approximate and even exact Q-ball solutions. This allows orders of magnitude speed up in numerical calculations for certain parts of a parameter space while sacrificing less than 1% accuracy.