The heavy-quark contribution to the polarization function $\mathrm{\Pi }$ at higher perturbative orders is presently only known approximately. We scrutinize 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 nonsinglet heavy-quark vacuum polarization in order to test the prediction for this moment based on the Padé approximation.

• Received 4 December 2017

DOI:https://doi.org/10.1103/PhysRevD.97.056016

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society