Four-loop relation between the $\overline{\mathrm{MS}}$ and on-shell quark mass

Abstract

In this contribution we discuss the four-loop relation between the on-shell and $\overline{\mathrm{MS}}$ definition of heavy quark masses which is applied to the top, bottom and charm case. We also present relations between the $\overline{\mathrm{MS}}$ quark mass and various threshold mass definitions and discuss the uncertainty at next-to-next-to-next-to-leading order.

Comments: 9 pages, 2 figures, to appear in the proceedings of the 12th International Symposium on Radiative Corrections (Radcor 2015) and LoopFest XIV (Radiative Corrections for the LHC and Future Colliders)