Kinetic Heavy Quark Mass to Three Loops

Abstract

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¯ quark masses, we can establish precise relations between the kinetic and 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 |Vcb| at Belle II.