Validity of Padé approximations in vacuum polarization at three- and four-loop order

The heavy-quark contribution to the polarization function Π 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 numerica...

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Bibliographic Details
Published in:Physical review. D 2018-03, Vol.97 (5), Article 056016
Main Authors: Maier, Andreas, Marquard, Peter
Format: Article
Language:English
Subjects:
Kinematics
Pade approximation
Polarization
Quarks
State of the art
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Summary:The heavy-quark contribution to the polarization function Π 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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.97.056016