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 (MS) over bar quark masses, we can establish precise relations between the kinetic and (MS) over bar 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 vertical bar V-cb vertical bar at Belle II.