We study the structure of the energy-momentum tensor of radial excitations of $Q$-balls in scalar field theories with U(1) symmetry. The obtained numerical results for the $1\le N\le 23$ excitations allow us to study in detail patterns how the solutions behave with $N$. We show that although the fields $\varphi (r)$ and energy-momentum tensor densities exhibit a remarkable degree of complexity, the properties of the solutions scale with $N$ with great regularity. This is to the best of our knowledge the first study of the $D$-term $d_1$ for excited states, and we demonstrate that it is negative—in agreement with results from literature on the $d_1$ of ground state particles.

• Received 15 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.096002