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

Understand

We compute the full ${\cal O}(\alpha_s^4)$ and ${\cal O}(\alpha_s^4\log\alpha_s)$ corrections to the potential $V_R(r)$ between the static color sources, where $V_R(r)$ 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 ${\cal O}(\alpha_s^4)$.
• The effect of the Casimir scaling violation is predicted to reduce the tangent of $V_R(r)/C_R$ proportionally to specific color factors dependent on $R$.
• We study the sizes of the Casimir scaling violation for various $R$'s in the case $G=SU(3)$.