New Determinations of the Charm and Bottom Quark Masses Using QCD Quarkonium Sum Rules
Abstract
We reanalyze the perturbative QCD (pQCD) corrections to quarkonium QCD sum rules and extract the heavy quark masses m̅q(m̅q) (q=c,b). At present, the pQCD corrections to the correlation functions of two heavy-quark pseudoscalar and vector currents at zero momentum transfer, denoted as Mn,qX,th (X = P, V), are calculated up to the 𝒪(αs3) order. These corrections exhibit significant renormalization scheme and scale dependence, which introduces large theoretical uncertainties and deteriorates the precision of heavy quark mass determinations. In this work, we eliminate the renormalization scheme and scale ambiguities in the perturbative part of Mn,qX,th by adopting the Principle of Maximum Conformality (PMC) within the characteristic operator (CO) approach. The CO approach, a novel extension of the standard PMC procedure, simultaneously determines the effective coupling αs(Q*) and the effective quark mass m̅q(Q*). It systematically absorbs the nonconformal {βi}-terms and {γi}-terms via the renormalization group equations, yielding a strictly scheme- and scale-independent conformal perturbative series. Based on the improved PMC conformal series, we further provide reliable estimates for the unknown N4LO contributions using the Padé approximation method. {The final predicted heavy quark masses in the MS̅ scheme read: m̅c(m̅c)=1278.8± 3.9 MeV, extracted from the second moment of the charmed pseudoscalar correlator M2,cP; and m̅b(m̅b) = 4161.0± 9.0 MeV, extracted from the second moment of the bottom vector correlator M2,bV. Both results agree well with the PDG world averages with deviations smaller than 2σ.
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BibTeX
@misc{yu2026determinations,
title = {{New Determinations of the Charm and Bottom Quark Masses Using QCD Quarkonium Sum Rules}},
author = {Qing Yu and Hua Zhou and Xing-Gang Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.07618},
eprint = {2605.07618},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.07618},
}
RIS
TY - UNPB
TI - New Determinations of the Charm and Bottom Quark Masses Using QCD Quarkonium Sum Rules
AU - Qing Yu
AU - Hua Zhou
AU - Xing-Gang Wu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2605.07618
UR - https://arxiv.org/abs/2605.07618
AB - We reanalyze the perturbative QCD (pQCD) corrections to quarkonium QCD sum rules and extract the heavy quark masses m̅_q(m̅_q) (q=c,b). At present, the pQCD corrections to the correlation functions of two heavy-quark pseudoscalar and vector currents at zero momentum transfer, denoted as M_n,q^X,th (X = P, V), are calculated up to the 𝒪(α_s^3) order. These corrections exhibit significant renormalization scheme and scale dependence, which introduces large theoretical uncertainties and deteriorates the precision of heavy quark mass determinations. In this work, we eliminate the renormalization scheme and scale ambiguities in the perturbative part of M_n,q^X,th by adopting the Principle of Maximum Conformality (PMC) within the characteristic operator (CO) approach. The CO approach, a novel extension of the standard PMC procedure, simultaneously determines the effective coupling α_s(Q_*) and the effective quark mass m̅_q(Q_*). It systematically absorbs the nonconformal {β_i}-terms and {γ_i}-terms via the renormalization group equations, yielding a strictly scheme- and scale-independent conformal perturbative series. Based on the improved PMC conformal series, we further provide reliable estimates for the unknown N^4LO contributions using the Padé approximation method. {The final predicted heavy quark masses in the MS̅ scheme read: m̅_c(m̅_c)=1278.8± 3.9 MeV, extracted from the second moment of the charmed pseudoscalar correlator M_2,c^P; and m̅_b(m̅_b) = 4161.0± 9.0 MeV, extracted from the second moment of the bottom vector correlator M_2,b^V. Both results agree well with the PDG world averages with deviations smaller than 2σ.
ER -