Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods

Abstract

We compute the two-loop $\beta$-function of scalar and spinorial quantum electrodynamics as well as pure Yang-Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using Implicit Regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.

Section 2 expanded, references revised, misprints corrected. Final results unchanged. Comply with published version

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• Explicit Cutoff Regularization in Coordinate Representation
• Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• A brief review of Implicit Regularization and its connection with the BPHZ theorem
• A step towards a consistent treatment of chiral theories at higher loop order: the abelian case
• Higgs boson decay into gluons in a 4D regularization: IR cancellation without evanescent fields to NLO
• Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions
• Infrared Subtleties and Chiral Vertices at NLO: An Implicit Regularization Analysis
• Ambiguities in the generation of CFJ-terms in a QED with dimension-5 operators in one loop