The Kinetic Heavy Quark Mass to Three Loops

We compute three-loop corrections to the relation between the heavy quark masses defined in the pole and kinetic schemes. Using known relations between the pole and $\overline{\mathrm{M}\mathrm{S}}$ quark masses we can establish precise relations between the kinetic and $\overline{\mathrm{M}\mathrm{S}}$ charm and bottom masses. As compared to two loops, the precision is improved by a factor two to three. Our results constitute important ingredients for the precise determination of the Cabibbo-Kobayashi-Maskawa matrix element $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ at Belle~II.