Quark mass relations to four-loop order

Abstract

We present results for the relation between a heavy quark mass defined in the on-shell and $\overline{\mathrm{MS}}$ 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 $\overline{\mathrm{MS}}$ quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the $\overline{\mathrm{MS}}$ heavy quark masses.

6 pages, v2: references added, typos in eq.(16) fixed, matches published version

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