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 $\overline{\mathrm{MS}}$ quark masses, we can establish precise relations between the kinetic and $\overline{\mathrm{MS}}$ charm and bottom masses. As compared to two loops, the precision is improved by a factor of 2 to 3. Our results constitute important ingredients for the precise determination of the Cabibbo-Kobayashi–Maskawa matrix element |V$_{cb}$| at Belle II.