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.

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径向激发的 U(1) 测量 Q 球

使用解析和数值方法研究径向激发的 $U(1)$ 测量的 $Q$ 球。与非测量情况不同，在模型参数的给定值下，仅存在有限数量的径向激发测量的 $Q$ 球。与未激发的测量 $Q$-球类似，径向激发的球不能拥有超过某个极限值的诺特电荷。这种限制性 Noether 电荷随着测量的 $Q$ 球的径向激发的增加而减少。对于第n$个径向激励，规范耦合常数有一个最大允许值，如果规范耦合常数超过这个极限值，第n$个径向激励规范的$Q$-球就不可能存在. 与限制 Noether 电荷类似，限制规范耦合常数随着径向激励的增加而减小。