Feynman rules for the rational part of the Electroweak 1-loop amplitudes in the R_xi gauge and in the Unitary gauge

Abstract

We present the complete set of Feynman rules producing the rational terms of kind R_2 needed to perform any 1-loop calculation in the Electroweak Standard Model. Our formulae are given both in the R_xi gauge and in the Unitary gauge, therefore completing the results in the 't Hooft-Feynman gauge already presented in a previous publication. As a consistency check, we verified, in the case of the process H -> gamma gamma and in a few other physical cases, the independence of the total Rational Part R_1+R_2 on the chosen gauge. In addition, we explicitly checked the equivalence of the limits xi -> infinity after or before the loop momentum integration in the definition of the Unitary gauge at 1-loop.

16 pages,3 figures

References in corpus (45)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• New features of FORM
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Massive Loop Amplitudes from Unitarity
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• Assault on the NLO Wishlist: pp -> tt bb
• On the Rational Terms of the one-loop amplitudes
• Precise Predictions for W + 4 Jet Production at the Large Hadron Collider
• D-dimensional unitarity cut method
• Automated one-loop calculations: a proof of concept
• One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200
• Masses, fermions and generalized D-dimensional unitarity
• Dominant QCD Backgrounds in Higgs Boson Analyses at the LHC: A Study of pp -> t anti-t + 2 jets at Next-To-Leading Order
• One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• A proposal for a standard interface between Monte Carlo tools and one-loop programs
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Feynman Rules for the Rational Part of the QCD 1-loop amplitudes
• NLO QCD corrections to tri-boson production
• The Last of the Finite Loop Amplitudes in QCD
• Next-to-leading order QCD predictions for W+W+jj production at the LHC
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 1. quark-antiquark annihilation
• Recursive numerical calculus of one-loop tensor integrals
• Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production
• The SM and NLO multileg working group: Summary report
• Regularization Scheme Independence and Unitarity in QCD Cross Sections
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• Numerical Evaluation of Six-Photon Amplitudes
• Tensorial Reconstruction at the Integrand Level
• Optimizing the Reduction of One-Loop Amplitudes
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC
• The FORM project
• Formulae for a numerical computation of one-loop tensor integrals
• Testing and improving the numerical accuracy of the NLO predictions

Cited by in corpus (27)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• UFO - The Universal FeynRules Output
• OpenLoops 2
• Automation of one-loop QCD corrections
• Automated One-Loop Calculations with GoSam
• A framework for Higgs characterisation
• Helac-nlo
• Electroweak Radiative Corrections for Collider Physics
• Weak corrections to Higgs hadroproduction in association with a top-quark pair
• Hadronic top-quark pair production in association with two jets at Next-to-Leading Order QCD
• The gluon-fusion production of Higgs boson pair: N${}^3$LO QCD corrections and top-quark mass effects
• Multi-leg One-loop Massive Amplitudes from Integrand Reduction via Laurent Expansion
• A four-dimensional approach to quantum field theories
• NLO QCD+EW predictions for HV and HV+jet production including parton-shower effects
• Feynman Rules for the Rational Part of the Standard Model One-loop Amplitudes in the 't Hooft-Veltman ${\gamma }_5$ Scheme
• NLO QCD Predictions for off-shell $t\bar{t}$ and $t\bar{t}H$ Production and Decay at a Linear Collider
• Primary Feynman rules to calculate the epsilon-dimensional integrand of any 1-loop amplitude
• R2SM: a package for the analytic computation of the R2 Rational terms in the Standard Model of the Electroweak interactions
• R2 vertices for the effective ggH theory
• Feynman Rules for the Rational Part of One-loop QCD Corrections in the MSSM
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Status of MadLoop/aMC@NLO
• Automated computation of scattering amplitudes
• UFO 2.0 -- The Universal Feynman Output format
• Phenomenological studies of top-pair production at Next-to-Leading order