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.

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

References in corpus (70)

• Automatized One-Loop Calculations in 4 and D dimensions
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• PDF4LHC recommendations for LHC Run II
• Factorization for hard exclusive electroproduction of mesons in QCD
• Package-X: A Mathematica package for the analytic calculation of one-loop integrals
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Electroweak Precision Observables in the Minimal Supersymmetric Standard Model
• Amplitudes and Spinor-Helicity in Six Dimensions
• The structure of large logarithmic corrections at small transverse momentum in hadronic collisions
• When radiative corrections are finite but undetermined
• Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry
• Facts of life with gamma(5)
• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Electroweak Sector Under Scrutiny: A Combined Analysis of LHC and Electroweak Precision Data
• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• QED with minimal and nonminimal couplings: on the quantum generation of Lorentz violating terms in the pure photon sector
• Towards gauge theories in four dimensions
• Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• A hint of renormalization
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Equivalence of Dimensional Reduction and Dimensional Regularisation
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• Dimensional Reduction in Non-Supersymmetric Theories
• A four-dimensional approach to quantum field theories
• Consistency Relations for an Implicit n-dimensional Regularization Scheme
• Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting ${\gamma }_5$
• Regularization and supersymmetry-restoring counterterms in supersymmetric QCD
• Symmetry Principle Preserving and Infinity Free Regularization and renormalization of quantum field theories and the mass gap
• Dimensional Reduction applied to QCD at three loops
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
• Consistency in Regularizations of the Gauged NJL Model at One Loop Level
• SCET approach to regularization-scheme dependence of QCD amplitudes
• Regularization Schemes and Higher Order Corrections
• Factorization and Regularization by Dimensional Reduction
• The beta function of N=1 SYM in Differential Renormalization
• Consistent Momentum Space Regularization/Renormalization of Supersymmetric Quantum Field Theories: The 3-loop beta function for the Wess-Zumino Model
• ${\gamma }_5$ in FDH
• Implicit Regularization and Renormalization of QCD
• Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation
• Quantum gravitational contributions to the beta function of quantum electrodynamics
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• (Un)determined finite regularization dependent quantum corrections: the Higgs decay into two photons and the two photon scattering examples
• Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
• Dimensional regularization vs methods in fixed dimension with and without ${\gamma }_5$
• Implicit regularization beyond one loop order: gauge field theories
• The Four Dimensional Helicity Scheme Beyond One Loop
• Momentum routing invariance in Feynman diagrams and quantum symmetry breakings
• An anomalous breaking of supersymmetry in supersymmetric gauge theories with local coupling
• The Infrared Structure of QCD Amplitudes and $H\to gg$ in FDH and DRED
• Arbitrariness in the gravitational Chern-Simons-like term induced radiatively
• Gauge Invariant Treatment of ${\gamma }_5$ in the Scheme of 't Hooft and Veltman
• ${\gamma }_5$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$
• Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints
• The four-dimensional helicity scheme and dimensional reconstruction
• Systematization of Basic Divergent Integrals in Perturbation Theory and Renormalization Group Functions
• Rational Terms of UV Origin at Two Loops
• On the equivalence between Implicit Regularization and Constrained Differential Renormalization
• Supergravity corrections to the $(g-2{)}_l$ factor by Implicit Regularization
• Inconsistency of Naive Dimensional Regularizations and Quantum Correction to Non-Abelian Chern-Simons-Matter Theory Revisited
• Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
• Computation of $H\to gg$ in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
• Shift versus no-shift in local regularizations of Chern-Simons theory
• Renormalization Ambiguities in Chern-Simons Theory
• Symmetries and Ambiguities in the linear sigma model with light quarks
• Subtleties in the beta function calculation of N=1 supersymmetric gauge theories
• On the Bose symmetry and the left- and right-chiral anomalies
• Guises and Disguises of Quadratic Divergences
• Ambiguities in the gravitational correction of quantum electrodynamics
• Maintaining Gauge Symmetry in Renormalizing Chiral Gauge Theories

Cited by in corpus (11)

• Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting ${\gamma }_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory
• Formula for two-loop divergent part of 4-D Yang-Mills effective action
• 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