On the Light Massive Flavor Dependence of the Top Quark Mass

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass and short-distance masses such as the MS mass of a heavy quark Q, coming from virtual loop insertions of massive quarks lighter than Q with the main focus on the top quark. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and also to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and heavy quark mass, predict the virtual quark mass corrections in the pole- mass relation and calculate the pole mass differences for the top, bottom and charm quarks with a precision of around 20 MeV.