Quark Mass Relations to Four-Loop Order in Perturbative QCD

We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS heavy quark masses