Estimate of 4-loop pole-MS¯ mass relation from static QCD potential

We estimate the presently unknown constant in the 4-loop relation between the quark pole mass and the MS¯ mass, by requiring stability of the perturbative prediction for Etot(r)=2mpole+VQCD(r)Etot(r)=2mpole+VQCD(r) in the intermediate-distance region. The estimate is fairly sharp due to a severe cancellation between 2mpole2mpole and VQCD(r)VQCD(r). This would provide a test, based on general properties of the gauge theory, for the size of ultra-soft contributions to VQCD(r)VQCD(r).