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Analytic Computing Methods for Precision Calculations in Quantum Field Theory

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arxiv 1809.02889 v1 pith:WW46RHD7 submitted 2018-09-08 hep-ph hep-thmath-phmath.MP

classification hep-phhep-thmath-phmath.MP
keywords loopmethodsorderquantitiesscalesingletheorycalculated
verification ladder T0 review T1 audit T2 compute T3 formal

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An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present massless single scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The variable flavor number scheme to three-loop order

    hep-ph 2026-07 accept novelty 6.0 of 10

    The variable flavor number scheme is completed to three-loop order with single- and two-mass effects, validated by renormalization-group analysis to match asymptotic heavy-flavor corrections, plus numerical Wilson-coe...

  2. The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements

    hep-ph 2019-08 conditional novelty 5.0 of 10

    The authors recompute the T_F-proportional pieces of the polarized three-loop QCD anomalous dimensions using massive operator matrix elements and find full agreement with the published 2014 results.

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