Adjoint string breaking in 4d SU(2) Yang–Mills theory

We compute the static potential of adjoint sources in SU(2) Yang–Mills theory in four dimensions by numerical Monte Carlo simulations. Following a recent calculation in 2+1 dimensions, we employ a variational approach involving string and gluelump operators and obtain clear evidence for string breaking and the saturation of the potential at large distances. For the string breaking scale we find rb≈1.25 fm, 2.3r0, or in units of the lightest glueball, rbm0++≈9.7. We furthermore resolve the first excitation of the flux-tube and observe its breaking as well. The result for rb is in remarkable quantitative agreement with the three-dimensional one.