| Strong interactions can be described by quantum chromodynamics, a model of quarks based on the SU(3) gauge theory. However isolated quarks have never been observed. This is known as confinement and in particular a linearly rising potential between quarks is expected at large distances. The lattice formulation of quantum chromodynamics combined with Monte Carlo methods, has provided data in support of confinement. In this work we consider SU(2) lattice gauge theory. By Monte Carlo techniques we evaluate the energy between heavy sources---the static potential---in different representations of the group and find that at large distances it rises linearly. We verify the Casimir scaling hypothesis: the ratio between the potential in some representation and the potential in the fundamental representation at the same distance is equal to the ratio of the corresponding Casimir operators. As the separation of the sources and the dimension of the representations increase, Wilson loops, the quantities used to measure static potentials, become increasingly smaller and hard to measure because statistical fluctuations cover their signal. We employed the smearing and multilevel algorithms to improve the signal and reduce the statistical fluctuations respectively. Analysis of the data supports the Casimir scaling hypothesis and highlights the multilevel algorithm as a powerful technique to evaluate Wilson loops. |
