On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass
Abstract
We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass m _{ Q } ^{pole} and shortdistance masses such as the \overline{MS} mass {\overline{m}}_Q of a heavy quark Q, coming from virtual loop insertions of massive quarks lighter than Q. 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 to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and m _{ Q }, relate the QCD corrections for different external heavy quarks to each other, predict the O({α}_s^4) virtual quark mass corrections in the pole \overline{MS} mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around 20 MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass m _{ t } ^{pole} , where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is 250 MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the highluminosity phase of the LHC.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2017
 DOI:
 10.1007/JHEP09(2017)099
 arXiv:
 arXiv:1706.08526
 Bibcode:
 2017JHEP...09..099H
 Keywords:

 Heavy Quark Physics;
 Perturbative QCD;
 Quark Masses and SM Parameters;
 Renormalization Regularization and Renormalons;
 High Energy Physics  Phenomenology
 EPrint:
 45 pages + appendix, 6 figures, v2: journal version