Low energy moments of heavy quark current correlators at four loops

Abstract

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charm- and bottom-quark mass from experimental data for σ(e^+ e^- -> hadrons).

21 pages

References in corpus (14)

• Algorithm FIRE -- Feynman Integral REduction
• Heavy Quark Masses from Sum Rules in Four-Loop Approximation
• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Charm and Bottom Quark Masses from Perturbative QCD
• Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD
• 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
• Heavy-quark QCD vacuum polarisation function: analytical results at four loops
• An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations
• Hypergeometric representation of a four-loop vacuum bubble

Cited by in corpus (24)

• Heavy quarkonium: progress, puzzles, and opportunities
• FLAG Review 2021
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• FLAG Review 2024
• QCD sum rule determination of the charm-quark mass
• Addendum to arXiv:0907.2110: "Charm and Bottom Quark Masses: An Update"
• Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
• Lattice determinations of the strong coupling
• Expected Precision of Higgs Boson Partial Widths within the Standard Model
• Charm-quark mass from weighted finite energy QCD sum rules
• Charm Quark Mass with Calibrated Uncertainty
• The role of low-energy observables in precision Higgs analysis
• Analytical determination of the QCD quark masses
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions
• Precise Charm- and Bottom-Quark Masses: Recent Updates
• Charm quark mass determined from a pair of sum rules
• Bottom Quark Mass with Calibrated Uncertainty
• Renormalization Group Improvement and QCD Sum Rules
• Singlet and non-singlet three-loop massive form factors
• Perturbative heavy quark contributions to the anomalous magnetic moment of the muon
• Renormalization of bilinear and four-fermion operators through temporal moments