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Radially excited $U\left(1\right)$ gauged $Q$-balls

Radially excited $U(1)$ gauged $Q$-balls are studied using both analytical and numerical methods. Unlike the nongauged case, there exists only a finite number of radially excited gauged $Q$-balls at given values of the model's parameters. Similarly to the unexcited gauged $Q$-ball, the radially excited one cannot possess the Noether charge exceeding some limiting value. This limiting Noether charge decreases with an increase in the radial excitation of the gauged $Q$-ball. For $n$-th radial excitation, there is a maximum allowable value of the gauge coupling constant, and the existence of the $n$-th radially excited gauged $Q$-ball becomes impossible if the gauge coupling constant exceeds this limiting value. Similarly to the limiting Noether charge, the limiting gauge coupling constant decreases with an increase in the radial excitation. At a fixed Noether charge, the energy of the gauged $Q$-ball increases with an increase in the radial excitation, and thus the radially excited gauged $Q$-ball is unstable against transit into a less excited or unexcited one.