Violation of Casimir scaling for static QCD potential at three-loop order

We compute the full O(αs4) and O(αs4logαs) corrections to the potential VR(r)VR(r) between the static color sources, where VR(r)VR(r) is defined from the Wilson loop in a general representation R of a general gauge group G  . We find a violation of the Casimir scaling of the potential, for the first time, at O(αs4). The effect of the Casimir scaling violation is predicted to reduce the tangent of VR(r)/CRVR(r)/CR proportionally to specific color factors dependent on R. We study the sizes of the Casimir scaling violation for various R  's in the case G=SU(3)G=SU(3). We find that they are well within the present bounds from lattice calculations, in the distance region where both perturbative and lattice computations of VR(r)VR(r) are valid. We also discuss how to test the Casimir scaling violating effect.