The Static Potential in the SU ( 2 ) Higgs Model

The static potential in the confinement “phase” of the SU(2) Higgs model is studied. In particular, the observation of the screening (called string breaking) of the static quarks by the dynamical light quarks leading to the formation of two static-light mesons was not observed before my work in non-Abelian gauge theories. The tool that I employ is lattice gauge simulation. The observable from which the spectrum of the Hamiltonian in presence of two static quarks can be extracted, is a matrix correlation whose elements are constructed not only from string-type states represented by Wilson loops (like in pure gauge theories). Additional matrix elements representing transitions from string-type to meson-type states and the propagation of meson-type states are taken into account. From this basis of states it is possible to extract the ground state and first excited state static potentials employing a variational method. The crossing of these two energy levels in the string breaking region is clearly visible and the inadequacy of the Wilson loops alone can be demonstrated. I also address the question of the lattice artifacts. For this purpose lines of constant physics in the confinement “phase” of the model have to be constructed. This problem has only partially been solved. Nevertheless it is possible to show that the static potentials have remarkable scaling properties under a variation of the lattice spacing by a factor two and are almost independent of the quartic Higgs coupling.