On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass
Abstract
Here, 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 $$—\atop{MS}$$ mass $$—\atop{m}$$ _{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$$4\atop{s}$$) virtual quark mass corrections in the pole$$—\atop{MS}$$ 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.
 Authors:
 Univ. of Vienna (Austria). Faculty of Physics; Erwin SchrÃÂ¶dinger International Inst. for Mathematical Physics, Vienna (Austria)
 Univ. of Vienna (Austria). Faculty of Physics
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics; Univ. of Vienna (Austria). Faculty of Physics
 Publication Date:
 Research Org.:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); Erwin Schrödinger International Inst. for Mathematical Physics, Vienna (Austria)
 OSTI Identifier:
 1424967
 Grant/Contract Number:
 SC0011090
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 9; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Heavy Quark Physics; Perturbative QCD; Quark Masses and SM Parameters; Renormalization Regularization and Renormalons
Citation Formats
Hoang, André H., Lepenik, Christopher, and Preisser, Moritz. On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass. United States: N. p., 2017.
Web. doi:10.1007/JHEP09(2017)099.
Hoang, André H., Lepenik, Christopher, & Preisser, Moritz. On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass. United States. doi:10.1007/JHEP09(2017)099.
Hoang, André H., Lepenik, Christopher, and Preisser, Moritz. 2017.
"On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass". United States.
doi:10.1007/JHEP09(2017)099. https://www.osti.gov/servlets/purl/1424967.
@article{osti_1424967,
title = {On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass},
author = {Hoang, André H. and Lepenik, Christopher and Preisser, Moritz},
abstractNote = {Here, we provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass m Qpole and shortdistance masses such as the $—\atop{MS}$ mass $—\atop{m}$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$4\atop{s}$) virtual quark mass corrections in the pole$—\atop{MS}$ 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 tpole, 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.},
doi = {10.1007/JHEP09(2017)099},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2017,
place = {United States},
year = 2017,
month = 9
}
Web of Science

The largeorder behavior of perturbation theory of phi/sup 4/ theory in four dimensions in the presence of mass terms is estimated. A new scale comes into the coefficient functions. For mass m and order K this scale is m..sqrt..K.

Asymptotic behavior of the fermion and gluon exchange amplitudes in massive quantum electrodynamics in the Regge limit
We study the e/sup +/e/sup /..> gamma gamma.. amplitude in massive quantum electrodynamics in the larges and fixedt limit. We compute the amplitude in the leadinglogarithm and the nexttotheleadinglogarithm approximations, to all orders in perturbation theory, and also find the general form of the full amplitude up to any nonleadinglogarithm approximation. We do not use any transversemomentum cutoff for our calculation. We find that, up to the nexttotheleadinglogarithm approximation, the contribution to the positivesignature amplitude is given by a single Regge pole. We find the contribution to the Regge trajectory up to twoloop order. The contribution to the negativesignature channelmore »