Feynman Rules for the Rational Part of the QCD 1-loop amplitudes

Abstract

We compute the complete set of Feynman Rules producing the Rational Terms of kind R_2 needed to perform any QCD 1-loop calculation. We also explicitly check that in order to account for the entire R_2 contribution, even in case of processes with more than four external legs, only up to four-point vertices are needed. Our results are expressed both in the 't Hooft Veltman regularization scheme and in the Four Dimensional Helicity scheme, using explicit color configurations as well as the color connection language.

18 pages, 11 figures. Misprints corrected in Appendix A. Version to be published in JHEP

References in corpus (48)

• Automatized One-Loop Calculations in 4 and D dimensions
• 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
• 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
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• One-Loop Corrections to Five-Gluon Amplitudes
• Massive Loop Amplitudes from Unitarity
• Reduction of one-loop tensor 5-point integrals
• Full one-loop amplitudes from tree amplitudes
• On-Shell Methods in Perturbative QCD
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• On the Rational Terms of the one-loop amplitudes
• One-Loop Self-Dual and N=4 Super Yang-Mills
• D-dimensional unitarity cut method
• Automated one-loop calculations: a proof of concept
• One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
• ZFITTER v.6.21 - A Semi-Analytical Program for Fermion Pair Production in e+e- Annihilation
• HELAC: a package to compute electroweak helicity amplitudes
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200
• Helac-Phegas: a generator for all parton level processes
• Masses, fermions and generalized D-dimensional unitarity
• An algebraic/numerical formalism for one-loop multi-leg amplitudes
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• The Last of the Finite Loop Amplitudes in QCD
• 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
• All-Purpose Numerical Evaluation of One-Loop Multi-Leg Feynman Diagrams
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• Numerical Evaluation of Six-Photon Amplitudes
• Optimizing the Reduction of One-Loop Amplitudes
• Integral Coefficients for One-Loop Amplitudes
• Closed-Form Decomposition of One-Loop Massive Amplitudes
• O(alpha) corrections to e+e- --> WW --> 4fermions(+gamma): first numerical results from RACOONWW
• The NLO multileg working group: summary report
• The rational parts of one-loop QCD amplitudes I: The general formalism
• A complete reduction of one-loop tensor 5- and 6-point integrals
• One-loop Integral Coefficients from Generalized Unitarity
• Multi-gluon one-loop amplitudes numerically
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• Precise predictions for LHC using a GOLEM
• Formulae for a numerical computation of one-loop tensor integrals
• Supernova Neutrino Process and its Impact on the Galactic Chemical Evolution of the Light Elements

Cited by in corpus (95)

• 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
• MadGraph 5 : Going Beyond
• UFO - The Universal FeynRules Output
• Scattering Amplitudes with Open Loops
• OpenLoops 2
• QCD and strongly coupled gauge theories: challenges and perspectives
• Automation of one-loop QCD corrections
• Automated One-Loop Calculations with GoSam
• Assault on the NLO Wishlist: pp -> tt bb
• A framework for Higgs characterisation
• Automatic evaluation of UV and R2 terms for beyond the Standard Model Lagrangians: a proof-of-principle
• Helac-nlo
• RECOLA: REcursive Computation of One-Loop Amplitudes
• One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
• Automated one-loop calculations: a proof of concept
• Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order
• Recola2: REcursive Computation of One-Loop Amplitudes 2
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report
• Dominant QCD Backgrounds in Higgs Boson Analyses at the LHC: A Study of pp -> t anti-t + 2 jets at Next-To-Leading Order
• Electroweak Radiative Corrections for Collider Physics
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results
• Recursive generation of one-loop amplitudes in the Standard Model
• Polarizing the Dipoles
• On-the-fly reduction of open loops
• Higgs characterisation at NLO in QCD: CP properties of the top-quark Yukawa interaction
• Constraining BSM Physics at the LHC: Four top final states with NLO accuracy in perturbative QCD
• Hadronic top-quark pair production in association with two jets at Next-to-Leading Order QCD
• Standard Model Higgs boson production in association with a top anti-top pair at NLO with parton showering
• Top quark pair production in association with a Z-boson at NLO accuracy
• Tensorial Reconstruction at the Integrand Level
• Numerical NLO QCD calculations
• spinney: A Form Library for Helicity Spinors
• Event Generators for High-Energy Physics Experiments
• Analytic one-loop amplitudes for a Higgs boson plus four partons
• Top Quark Pair Production in Association with a Jet with NLO QCD Off-Shell Effects at the Large Hadron Collider
• Top quark pair production in association with a jet with NLO parton showering
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes
• The gluon-fusion production of Higgs boson pair: N${}^3$LO QCD corrections and top-quark mass effects
• Off-shell Top Quarks with One Jet at the LHC: A comprehensive analysis at NLO QCD
• Multi-leg One-loop Massive Amplitudes from Integrand Reduction via Laurent Expansion
• Complete Nagy-Soper subtraction for next-to-leading order calculations in QCD
• Multi-gluon one-loop amplitudes using tensor integrals
• A four-dimensional approach to quantum field theories
• NLO electroweak corrections in extended Higgs Sectors with RECOLA2
• Probing triple-Higgs productions via $4b2\gamma$ decay channel at a 100 TeV hadron collider
• Pseudo-observables in electroweak Higgs production
• Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
• NNLO QCD subtraction for top-antitop production in the $q\bar{q}$ channel
• Tensor integrand reduction via Laurent expansion
• Gauge invariance at work in FDR: H -> gamma gamma
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes in the R_xi gauge and in the Unitary gauge
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Hard Photons in Hadroproduction of Top Quarks with Realistic Final States
• Feynman Rules for the Rational Part of the Standard Model One-loop Amplitudes in the 't Hooft-Veltman ${\gamma }_5$ Scheme
• New Physics in multi-Higgs boson final states
• NLO QCD Predictions for off-shell $t\bar{t}$ and $t\bar{t}H$ Production and Decay at a Linear Collider
• Hadroproduction of t anti-t pair with a b anti-b pair with PowHel
• 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
• Triple collinear splitting functions at NLO for scattering processes with photons
• Two-Loop Rational Terms in Yang-Mills Theories
• One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity
• Phenomenology of $t\bar{t}j+X$ production at the LHC
• Rational Terms of UV Origin at Two Loops
• On the next-to-leading order QCD K-factor for top anti-top bottom anti-bottom production at the TeVatron
• NLO QCD corrections to full off-shell production of $t\bar{t}Z$ including leptonic decays
• Quantifying quark mass effects at the LHC: A study of pp -> b anti-b b anti-b + X at next-to-leading order
• NLO QCD calculations with HELAC-NLO
• R2 vertices for the effective ggH theory
• Electroweak Higgs production with HiggsPO at NLO QCD
• Random polarisations of the dipoles
• A study of additional jet activity in top quark pair production and decay at the LHC
• 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
• Testing and improving the numerical accuracy of the NLO predictions
• Discovery potential of Higgs boson pair production through 4$\ell$+$E/$ final states at a 100 TeV collider
• Anomalies without an action
• Four top final states with NLO accuracy in perturbative QCD: 4 lepton channel
• Hadroproduction of $W^{+}{W}^{-}b\bar{b}$ at NLO accuracy matched with shower Monte Carlo programs
• Four top final states with NLO accuracy in perturbative QCD: 3 lepton channel
• Calculating off-shell one-loop amplitudes for $k_T$-dependent factorization: a proof of concept
• New developments in MadLoop
• Precise evaluation of the Cut Constructible part of one loop amplitudes within D-dimensional unitarity
• Automated computation of scattering amplitudes
• Two-loop amplitude generation in OpenLoops
• Two-Loop Rational Terms for Spontaneously Broken Theories
• Phenomenological studies of top-pair production at Next-to-Leading order
• $t\bar{t}jj$ -- NLO QCD corrections to top quark pair production and decays at the LHC
• Rational terms in two-loop calculations
• Automated NLO/NLL Monte Carlo programs for the LHC
• UFO 2.0 -- The Universal Feynman Output format
• Two-loop tensor integral coefficients in OpenLoops
• Next-to-leading order QCD corrections to ttbb production at the LHC