Life of Π

Abstract

The heavy-quark contribution to the polarisation function $\Pi$ at higher perturbative orders is presently only known approximately. We scrutinise the accuracy of state-of-the-art approximations at three- and four-loop order. At three loops, we present for the first time a result with arbitrary numerical precision for general kinematics and compare to the best Padé estimate. At four loops, we calculate the fourth (inverse) moment of the non-singlet heavy-quark vacuum polarisation in order to test the prediction for this moment based on Padé approximation.

21 pages, 2 figures. Equivalent to journal version

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• Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
• Hypergeometric representation of a four-loop vacuum bubble
• Charm Quark Mass with Calibrated Uncertainty
• Top-quark pair production at next-to-next-to-leading order QCD in electron positron collisions

Cited by in corpus (10)

• Top-Quark Physics at the CLIC Electron-Positron Linear Collider
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Hadronic vacuum polarization using gradient flow
• Precise determination of ${\alpha }_s$ from relativistic quarkonium sum rules
• Top quark mass measurement in radiative events at electron-positron colliders
• Precise ${\alpha }_s$ determination from charmonium sum rules
• The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions
• Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions
• Bottom Quark Mass with Calibrated Uncertainty