S@M, a Mathematica Implementation of the Spinor-Helicity Formalism

Abstract

In this paper we present the package S@M (Spinors@Mathematica) which implements the spinor-helicity formalism in Mathematica. The package allows the use of complex-spinor algebra along with the multi-purpose features of Mathematica. The package defines the spinor objects with their basic properties along with functions to manipulate them. It also offers the possibility of evaluating the spinorial objects numerically at every computational step. The package is therefore well suited to be used in the context of on-shell technology, in particular for the evaluation of scattering amplitudes at tree- and loop-level.

52 pages, the package can be downloaded from http://www.slac.stanford.edu/grp/th/software/#Mathematica_Packages_

References in corpus (100)

• ALPGEN, a generator for hard multiparton processes in hadronic collisions
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Multi-Parton Amplitudes in Gauge Theories
• Automatic Generation of Tree Level Helicity Amplitudes
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Dimensionally Regulated Pentagon Integrals
• Reduction schemes for one-loop tensor integrals
• Next-to-leading order calculation of three-jet observables in hadron-hadron collision
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Higgs Radiation off Top Quarks at the Tevatron and the LHC
• NLO QCD corrections to t anti-t H production in hadron collisions
• One-Loop Corrections to Five-Gluon Amplitudes
• Next-to-leading order corrections to W+2 jet and Z+2 jet production at hadron colliders
• Massive Loop Amplitudes from Unitarity
• Dimensionally Regulated One-Loop Integrals
• AMEGIC++ 1.0, A Matrix Element Generator In C++
• Reduction of one-loop tensor 5-point integrals
• Associated Higgs production with top quarks at the Large Hadron Collider: NLO QCD corrections
• Progress in One-Loop QCD Computations
• Three-jet cross sections in hadron-hadron collisions at next-to-leading order
• On-Shell Methods in Perturbative QCD
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• One-Loop Splitting Amplitudes in Gauge Theory
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• One-Loop Self-Dual and N=4 Super Yang-Mills
• D-dimensional unitarity cut method
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Factorization in One-Loop Gauge Theory
• A direct proof of the CSW rules
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• HELAC: a package to compute electroweak helicity amplitudes
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• An algebraic/numerical formalism for one-loop multi-leg amplitudes
• One-Loop Amplitudes Of Gluons In SQCD
• An Algorithm to Compute Born Scattering Amplitudes without Feynman Graphs
• Next-to-leading order QCD predictions for W+2j and Z+2j production at the CERN LHC
• Is N = 8 Supergravity Ultraviolet Finite?
• Next-to-Leading order Higgs + 2 jet production via gluon fusion
• A new approach to multi-jet calculations in hadron collisions
• Associated Top Quark-Higgs Boson Production at the LHC
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• The Cut-Constructible Part of QCD Amplitudes
• A Two-Loop Four-Gluon Helicity Amplitude in QCD
• Consistency Conditions on the S-Matrix of Massless Particles
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Non-Supersymmetric Loop Amplitudes and MHV Vertices
• General subtraction method for numerical calculation of one-loop QCD matrix elements
• Algebraic reduction of one-loop Feynman graph amplitudes
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• The Last of the Finite Loop Amplitudes in QCD
• Unexpected Cancellations in Gravity Theories
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• Two-loop splitting functions in QCD
• Recursive numerical calculus of one-loop tensor integrals
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions
• Tree Level Recursion Relations In General Relativity
• Recursive Calculation of One-Loop QCD Integral Coefficients
• One-Loop Gluon Scattering Amplitudes in Theories with $N<4$ Supersymmetries
• Reduction method for dimensionally regulated one-loop N-point Feynman integrals
• On Triple-Cut of Scattering Amplitudes
• All-Purpose Numerical Evaluation of One-Loop Multi-Leg Feynman Diagrams
• N=1 Supersymmetric One-loop Amplitudes and the Holomorphic Anomaly of Unitarity Cuts
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• NLO QCD corrections to WW+jet production at hadron colliders
• On the computation of multigluon amplitudes
• MHV-Vertices for Gravity Amplitudes
• Higgs Production in Association with Bottom Quarks at Hadron Colliders
• A Calculational Formalism for One-Loop Integrals
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• Semi-Numerical Evaluation of One-Loop Corrections
• All-Multiplicity Amplitudes with Massive Scalars
• Next-to-Leading Order Gluonic Three Jet Production at Hadron Colliders
• Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes
• NLO QCD corrections to W boson production with a massive b-quark jet pair at the Fermilab Tevatron p-pbar collider
• On-shell recursion relations for all Born QCD amplitudes
• A simple method for multi-leg loop calculations
• Virtual QCD corrections to Higgs boson plus four parton processes
• All-Multiplicity One-Loop Corrections to MHV Amplitudes in QCD
• The one-loop amplitude for six-gluon scattering
• Next-to-leading order numerical calculations in Coulomb gauge
• QCD event generators with next-to-leading order matrix-elements and parton showers
• Unitarity-based Techniques for One-Loop Calculations in QCD
• Scattering amplitudes with massive fermions using BCFW recursion
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• A simple method for multi-leg loop calculations 2: a general algorithm
• NLO QCD corrections to the production of t-tbar-Z in gluon fusion
• Recursion Relations for One-Loop Gravity Amplitudes
• Massive Quark-Gluon Scattering Amplitudes at Tree Level
• Formulae for a numerical computation of one-loop tensor integrals
• Top quark pair + jet production at next-to-leading order: NLO QCD corrections to gg -> t tbar g

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• Off-shell Currents and Color-Kinematics Duality
• Next-to-leading order predictions for Z gamma+jet and Z gamma gamma final states at the LHC
• Extracting analytical one-loop amplitudes from numerical evaluations
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Boundary Contributions Using Fermion Pair Deformation
• Spinors: a Mathematica package for doing spinor calculus in General Relativity
• Off-shell single-top-quark production in the Standard Model Effective Field Theory
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• A unitarity compatible approach to one-loop amplitudes with massive fermions
• Unitarity Method with Spurious Pole
• ${\chi }_{cJ}$ production associated with a $c\bar{c}$ pair at hadron colliders
• External leg corrections in the unitarity method
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• Next-to-leading order predictions for WW+jet production
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Double-Soft Limits of Gluons and Gravitons
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• BCJ Relations for One-Loop QCD Integral Coefficients
• One-loop electroweak radiative corrections to lepton pair production in polarized electron-positron collisions
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Maximal transcendental weight contribution of scattering amplitudes
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Electroweak effects in polarized muon-electron scattering
• Learning the Simplicity of Scattering Amplitudes
• Analytical amplitudes from numerical solutions of the scattering equations
• Higher Derivative Theories for Interacting Massless Gravitons in Minkowski Spacetime
• SpinorsExtras - Mathematica implementation of massive spinor-helicity formalism
• A new Wilson line-based action for gluodynamics
• An Introduction to the Massive Helicity Formalism with applications to the Electroweak SM
• Four photon production at the LHC: an application of 2->4 analytic unitarity
• Generalised unitarity for dimensionally regulated amplitudes within FDF
• All one-loop NMHV gluon amplitudes in N=1 SYM
• W+W- + jet: compact analytic results
• General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion
• Generalised Unitarity for Dimensionally Regulated Amplitudes
• A Tale Of Two Amplitudes In High Energy Physics
• Shifts in BCFW method for QED
• Helicity Spinor Methods and Tree Level QCD Corrections in Higgs Production via Weak Boson Fusion
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes
• Recursion in multiplet bases for tree-level MHV gluon amplitudes
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit