Quark masses: N3LO bridge from ${\rm RI/SMOM}$ to ${\rm \overline{MS}}$ scheme

Abstract

We analytically compute the three-loop corrections to the relation between the renormalized quark masses defined in the minimal-subtraction (${\rm \overline{MS}}$) and the regularization-invariant symmetric momentum-subtraction (${\rm RI/SMOM}$) schemes. Our result is valid in the Landau gauge and can be used to reduce the uncertainty in a lattice determination of the ${\rm \overline{MS}}$ quark masses.