Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions

Abstract

We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-${\beta }_0$ limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, ${\alpha }_s$, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can guide the design of combinations of moments with improved perturbative behaviour.

27 pages, 7 figures. References added. Version to appear in JHEP

References in corpus (18)

• The five-loop beta function of Yang-Mills theory with fermions
• Heavy Quark Masses from Sum Rules in Four-Loop Approximation
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Charm and Bottom Quark Masses from Perturbative QCD
• Five-loop renormalisation of QCD in covariant gauges
• Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
• Low energy moments of heavy quark current correlators at four loops
• The second physical moment of the heavy quark vector correlator at O(alpha_s^3)
• Higher Moments of Heavy Quark Correlators in the Low Energy Limit at O(alpha_s^2)
• Four-Loop Tadpoles: Applications in QCD
• Moments of Heavy Quark Current Correlators at Four-Loop Order in Perturbative QCD
• Addendum to arXiv:0907.2110: "Charm and Bottom Quark Masses: An Update"
• REvolver: Automated running and matching of couplings and masses in QCD
• Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
• Strong coupling constant from moments of quarkonium correlators revisited
• Renormalons in integrated spectral function moments and ${\alpha }_s$ extractions

Cited by in corpus (2)

• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• $H\to \gamma \gamma$ to all orders in ${\alpha }_s$ in the large-${\beta }_0$ limit of QCD