Multiloop contributions to the on-shell-$\overline{\mathrm{MS}}$ heavy quark mass relation in QCD and the asymptotic structure of the corresponding series: the updated consideration

Abstract

The asymptotic structure of the QCD perturbative relation between the on-shell and $\overline{\mathrm{MS}}$ heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First, the effective charges motivated approach in two variants is used. Second, the results following from the large-${\beta }_0$ approximation are analyzed. Finally, the consequences of applying the asymptotic renormalon-based formula are investigated. We show that all approaches lead to corrections which are qualitatively consistent in order of magnitude. Their sign-alternating character in powers of the number of massless quarks is demonstrated. We emphasize that there is no contradiction in the behavior of the fine structure of the renormalon-based estimates with other approaches if one use the detailed information about the normalization factor included in the renormalon asymptotic formula. The obtained five- and six-loop estimates indicate that in the case of the $b$-quark the asymptotic character of the studied relation manifests itself above the fourth order of PT, whereas for the $t$-quark it starts to reveal itself after the seventh order. This allows to conclude that like the running masses, the pole masses of the $b$ and especially $t$-quark in principle may be used in the phenomenologically-oriented studies.

arXiv comment21 pages, 4 Tables; title, minor final modifications in the text, version coincides with the one to be published in Euro.Phys. J C

References in corpus (22)

• Parton distributions for the LHC Run II
• Five-Loop Running of the QCD coupling constant
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Updated Values of Running Quark and Lepton Masses
• Infrared Renormalization Group Flow for Heavy Quark Masses
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• On the ultimate uncertainty of the top quark pole mass
• The bottom-quark mass from non-relativistic sum rules at NNNLO
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Measurement of the top-quark mass in $t\bar{t}+1$-jet events collected with the ATLAS detector in $pp$ collisions at $\sqrt{s}=8$ TeV
• Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment
• The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Determination of the top-quark mass from hadro-production of single top-quarks
• Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD
• Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(α_s^4) contributions
• Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment
• Mass of the bottom quark from Upsilon(1S) at NNNLO: an update
• Uncertainties of QCD predictions for Higgs boson decay into bottom quarks at NNLO and beyond
• Comment on "The MSR Mass and the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ Renormalon Sum Rule"

Cited by in corpus (4)

• Precise Values of Running Quark and Lepton Masses in the Standard Model
• Top quark pair production near threshold: single/double distributions and mass determination
• R-parity violating solutions to the $R_{D^{(\ast )}}$ anomaly and their GUT-scale unifications
• High-precision four-loop mass and wave function renormalization in QED