Anti-Screening by Quarks and the Structure of the Inter-Quark Potential

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The inter-quark potential is dominated by anti-screening effects which underly asymptotic freedom. We calculate the order g⁶ anti-screening contribution from light fermions and demonstrate that these effects introduce a non-local divergence. These divergences are shown to make it impossible to define a coupling renormalisation scheme that renormalises this minimal, anti-screening potential. Hence the beta function cannot be divided into screening and anti-screening parts beyond lowest order. However, we then demonstrate that renormalisation can be carried out in terms of the anti-screening potential.