New Determinations of the Charm and Bottom Quark Masses Using QCD Quarkonium Sum Rules

TL;DR

This paper refines heavy quark mass determinations using QCD sum rules by applying the Principle of Maximum Conformality to eliminate scheme and scale ambiguities, resulting in more precise and reliable results.

Contribution

It introduces the CO approach, an extension of PMC, to systematically remove renormalization ambiguities in heavy quark mass calculations from QCD sum rules.

Findings

Predicted charm quark mass: 1275.8 ± 0.4 MeV.

Predicted bottom quark mass: 4177.0 ± 7.2 MeV.

Results agree with PDG averages within 1σ.

Abstract

We reanalyze the perturbative QCD (pQCD) corrections to quarkonium QCD sum rules and extract the heavy quark masses $\overline{m}_{q}(\overline{m}_{q})$ ($q=c,b$). At present, the pQCD corrections to the correlation functions of two heavy-quark pseudoscalar and vector currents at zero momentum transfer, denoted as $M_{n,q}^{X,\rm th}$ ($X = P, V$), are calculated up to the $\mathcal{O}(\alpha_s^3)$ 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 $M_{n,q}^{X,\rm th}$ 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 $\alpha_s(Q_*)$ and the effective quark mass $\overline{m}_q(Q_*)$. It systematically absorbs the nonconformal $\{\beta_i\}$-terms and $\{\gamma_i\}$-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 $\mathrm{N^4LO}$ contributions using the Pad\'e approximation method. The final predicted heavy quark masses in the $\overline{\mathrm{MS}}$ scheme read: $\overline{m}_c(\overline{m}_c)=1275.8\pm 0.4~\text{MeV}$, extracted from the second moment of the charmed pseudoscalar correlator $M_{2,c}^{P}$; and $\overline{m}_b(\overline{m}_b) = 4177.0 \pm 7.2~\text{MeV}$, extracted from the first moment of the bottom vector correlator $M_{1,b}^{V}$. Both results agree well with the PDG world averages with deviations smaller than $1\sigma$.