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We compute the full ${\cal O}(\alpha_s^4)$ and ${\calO}(\alpha_s^4\log\alpha_s)$ corrections to the potential $V_R(r)$ between thestatic color sources, where $V_R(r)$ is defined from the Wilson loop in ageneral representation $R$ of a general gauge group $G$. We find a violation ofthe Casimir scaling of the potential, for the first time, at ${\calO}(\alpha_s^4)$. The effect of the Casimir scaling violation is predicted toreduce the tangent of $V_R(r)/C_R$ proportionally to specific color factorsdependent on $R$. We study the sizes of the Casimir scaling violation forvarious $R$'s in the case $G=SU(3)$. We find that they are well within thepresent bounds from lattice calculations, in the distance region where bothperturbative and lattice computations of $V_R(r)$ are valid. We also discusshow to test the Casimir scaling violating effect.

Violation of Casimir Scaling for Static QCD Potential at Three-loop Order