Estimate of 4-loop Pole-MSbar Mass Relation from Static QCD Potential

Understand

We estimate the presently unknown constant in the 4-loop relation between the quark pole mass and the MSbar mass, by requiring stability of the perturbative prediction for E_tot(r)=2m_pole+V_QCD(r) in the intermediate-distance region.

• The estimate is fairly sharp due to a severe cancellation between 2m_pole and V_QCD(r).
• This would provide a test, based on general properties of the gauge theory, for the size of ultra-soft contributions to V_QCD(r).