title: Quark mass relations to four-loop order in perturbative QCD.
abstract: We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) 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[over ¯] 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[over ¯] heavy quark masses.
authors.affiliation: Deutsches Elektronen Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany.
authors.forename: Peter
authors.initials: P
authors.lastname: Marquard
authors.affiliation: Scientific Research Computing Center, Moscow State University, 119991 Moscow, Russia.
authors.forename: Alexander V
authors.initials: AV
authors.lastname: Smirnov
authors.affiliation: Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991 Moscow, Russia.
authors.forename: Vladimir A
authors.initials: VA
authors.lastname: Smirnov
authors.affiliation: Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Steinhauser