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

Maier, Andreas; Marquard, Peter

Abstract

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.

Citation

Maier, A., & Marquard, P. (2018). Validity of Padé approximations in vacuum polarization at three- and four-loop order. Physical Review D, 97(5), Article 056016. https://doi.org/10.1103/physrevd.97.056016

• Journal Article Type: Article
• Online Publication Date: Mar 22, 2018
• Publication Date: Mar 22, 2018
• Deposit Date: Apr 13, 2018
• Publicly Available Date: Apr 13, 2018
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 97
• Issue: 5
• Article Number: 056016
• DOI: https://doi.org/10.1103/physrevd.97.056016