From Decay to Complete Breaking: Pulling the Strings in $SU(2)$ Yang-Mills Theory

We study $\{2Q+1\}$ strings connecting two static charges $Q$ in $(2+1)\mathrm{D}$ $SU(2)$ Yang-Mills theory. While the fundamental $\{2\}$ string between two charges $Q=\frac{1}{2}$ is unbreakable, the adjoint $\{3\}$ string connecting two charges $Q=1$ can break. When a $\{4\}$ string is stretched beyond a critical length, it decays into a $\{2\}$ string by gluon pair creation. When a $\{5\}$ string is stretched, it first decays into a $\{3\}$ string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.

Figure 1

Top: Potential $V(r)$ of two static color charges with $Q=\frac{1}{2}$ (squares) and $Q=\frac{3}{2}$ (stars), shifted by a constant for a more convenient comparison of the slopes. Bottom: The same for $Q=1$ (squares) and $Q=2$ (stars). The lines are a fit of the multichannel model to the Monte Carlo data. The horizontal band at $2M_{0,2}=4.84(2)$ corresponds to twice the mass of a source of charge $Q=2$ obtained from the measurement of a single Polyakov loop.

Figure 2

Top: Forces $F(r)$ that the $\{2\}$ and $\{4\}$ strings exert on the external charges $Q=\frac{1}{2}$ (squares) and $Q=\frac{3}{2}$ (stars), respectively. Bottom: The same for the $\{3\}$ and $\{5\}$ strings connecting external charges $Q=1$ (squares) and $Q=2$ (stars), respectively. The lines represent the fit of the multichannel model to the Monte Carlo data.