Two-Loop Rational Terms in Yang-Mills Theories

Abstract

Scattering amplitudes in $D$ dimensions involve particular terms that originate from the interplay of UV poles with the $D-4$ dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the $D-4$ dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to $n_f$ fermions with arbitrary masses.

arXiv commentTypo fixed in (4.83). References added. Version to appear in JHEP

References in corpus (33)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• OpenLoops 2
• Automation of one-loop QCD corrections
• Group theory factors for Feynman diagrams
• Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
• Full one-loop amplitudes from tree amplitudes
• On the Rational Terms of the one-loop amplitudes
• The Multithreaded version of FORM
• Automated one-loop calculations: a proof of concept
• Recola2: REcursive Computation of One-Loop Amplitudes 2
• Two-loop mixing of dimension-five flavor-changing operators
• Beta functions and anomalous dimensions up to three loops
• MATAD: a program package for the computation of MAssive TADpoles
• Feynman Rules for the Rational Part of the QCD 1-loop amplitudes
• General subtraction method for numerical calculation of one-loop QCD matrix elements
• Techniques for QCD calculations by numerical integration
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 1. quark-antiquark annihilation
• From loops to trees by-passing Feynman's theorem
• Recursive numerical calculus of one-loop tensor integrals
• Numerical NLO QCD calculations
• Four-dimensional unsubtraction from the loop-tree duality
• Open loop amplitudes and causality to all orders and powers from the loop-tree duality
• A four-dimensional approach to quantum field theories
• Removing infrared divergences from two-loop integrals
• Numerical Loop-Tree Duality: contour deformation and subtraction
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
• Direct numerical integration for multi-loop integrals
• Factorization and Regularization by Dimensional Reduction
• Two-loop off-shell QCD amplitudes in FDR
• Primary Feynman rules to calculate the epsilon-dimensional integrand of any 1-loop amplitude
• The Four Dimensional Helicity Scheme Beyond One Loop
• Rational Terms of UV Origin at Two Loops

Cited by in corpus (10)

• Collider Physics at the Precision Frontier
• Event Generators for High-Energy Physics Experiments
• May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations
• Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
• Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme
• Computational challenges for multi-loop collider phenomenology
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Two-loop amplitude generation in OpenLoops
• Two-Loop Rational Terms for Spontaneously Broken Theories
• Two-loop tensor integral coefficients in OpenLoops