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Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight

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Abstract

We evaluate analytically higher terms of the ϵ-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g − 2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin-Barnes representation, and the PSLQ algorithm.

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Authors and Affiliations

  1. Budker Institute of Nuclear Physics and Novosibirsk State University, 630090, Novosibirsk, Russia

    R. N. Lee

  2. Skobeltsyn Institute of Nuclear Physics of Moscow State University, 119992, Moscow, Russia

    V. A. Smirnov

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  1. R. N. Lee
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  2. V. A. Smirnov
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Correspondence to R. N. Lee.

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Lee, R.N., Smirnov, V.A. Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight. J. High Energ. Phys. 2011, 102 (2011). https://doi.org/10.1007/JHEP02(2011)102

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