R2SM: a package for the analytic computation of the R2 Rational terms in the Standard Model of the Electroweak interactions

Abstract

The analytical package written in FORM presented in this paper allows the computation of the complete set of Feynman Rules producing the Rational terms of kind R2 contributing to the virtual part of NLO amplitudes in the Standard Model of the Electroweak interactions. Building block topologies filled by means of generic scalars, vectors and fermions, allowing to build these Feynman Rules in terms of specific elementary particles, are explicitly given in the Rxi gauge class, together with the automatic dressing procedure to obtain the Feynman Rules from them. The results in more specific gauges, like the 't Hooft Feynman one, follow as particular cases, in both the HV and the FDH dimensional regularization schemes. As a check on our formulas, the gauge independence of the total Rational contribution (R1 + R2) to renormalized S-matrix elements is verified by considering the specific example of the H --> gamma-gamma decay process at 1-loop. This package can be of interest for people aiming at a better understanding of the nature of the Rational terms. It is organized in a modular way, allowing a further use of some its files even in different contexts. Furthermore, it can be considered as a first seed in the effort towards a complete automation of the process of the analytical calculation of the R2 effective vertices, given the Lagrangian of a generic gauge theory of particle interactions.

References in corpus (53)

• Automatized One-Loop Calculations in 4 and D dimensions
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• 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
• Reduction schemes for one-loop tensor integrals
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Full one-loop amplitudes from tree amplitudes
• Assault on the NLO Wishlist: pp -> tt bb
• On the Rational Terms of the one-loop amplitudes
• Scalar one-loop 4-point integrals
• 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
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• NLO QCD corrections to pp -> t anti-t b anti-b + X at the LHC
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• 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
• 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
• NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results
• 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
• Next-to-Leading Order QCD Predictions for Z,gamma^*+3-Jet Distributions at the Tevatron
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Feynman Rules for the Rational Part of the QCD 1-loop amplitudes
• W+3 jet production at the Tevatron
• 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
• Next-to-leading order QCD predictions for W+W+jj production at the LHC
• Recursive numerical calculus of one-loop tensor integrals
• The SM and NLO multileg working group: Summary report
• Next-to-leading order QCD corrections to pp --> b b_bar b b_bar + X at the LHC: the quark induced case
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• Numerical Evaluation of Six-Photon Amplitudes
• Tensorial Reconstruction at the Integrand Level
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes
• NLO QCD corrections to five-jet production at LEP and the extraction of alpha_s(M_Z)
• Multi-gluon one-loop amplitudes using tensor integrals
• W+3 jet production at the LHC as a signal or background
• The rational parts of one-loop QCD amplitudes I: The general formalism
• The FORM project
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes in the R_xi gauge and in the Unitary gauge
• Electroweak corrections to hadronic event shapes and jet production in e+e- annihilation
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• NLO QCD calculations with HELAC-NLO

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• Multi-leg One-loop Massive Amplitudes from Integrand Reduction via Laurent Expansion
• 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
• Feynman Rules for the Rational Part of One-loop QCD Corrections in the MSSM
• Automated computation of scattering amplitudes
• Phenomenological studies of top-pair production at Next-to-Leading order