One-Loop Gluon Scattering Amplitudes in Theories with $N<4$ Supersymmetries

Abstract

Generalised unitarity techniques are used to calculate the coefficients of box and triangle integral functions of one-loop gluon scattering amplitudes in gauge theories with $N<4$ supersymmetries. We show that the box coefficients in N=1 and N=0 theories inherit the same coplanar and collinear constraints as the corresponding N=4 coefficients. We use triple cuts to determine the coefficients of the triangle integral functions and present, as an example, the full expression for the one-loop amplitude $A^{N=1}(1^{-},2^{-},3^{-},4^{+},..,n^{+})$.

15 pages, minor typos corrected

References in corpus (30)

• 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
• Multi-Parton Amplitudes in Gauge Theories
• MHV Vertices And Tree Amplitudes In Gauge Theory
• One-Loop Amplitudes for e^+ e^- to Four Partons
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• One-Loop Corrections to Five-Gluon Amplitudes
• On the Tree-Level S-Matrix of Yang-Mills Theory
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• One-Loop Self-Dual and N=4 Super Yang-Mills
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Factorization in One-Loop Gauge Theory
• Tree Amplitudes in Gauge Theory as Scalar MHV Diagrams
• One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• String-Based Methods in Perturbative Gravity
• Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory
• A Two-Loop Four-Gluon Helicity Amplitude in QCD
• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• Non-MHV Tree Amplitudes in Gauge Theory
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
• The Googly Amplitudes in Gauge Theory
• N=1 Supersymmetric One-loop Amplitudes and the Holomorphic Anomaly of Unitarity Cuts
• MHV Vertices and Scattering Amplitudes in Gauge Theory
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Counterterms in type I Supergravities
• Supertwistor Orbifolds: Gauge Theory Amplitudes and Topological Strings

Cited by in corpus (74)

• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• On-Shell Methods in Perturbative QCD
• A direct proof of the CSW rules
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• One-Loop Amplitudes Of Gluons In SQCD
• Uniqueness of two-loop master contours
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• The Cut-Constructible Part of QCD Amplitudes
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• The Last of the Finite Loop Amplitudes in QCD
• Maximal Unitarity at Two Loops
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Scattering Amplitudes
• Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions
• The No-Triangle Hypothesis for N=8 Supergravity
• Recursive Calculation of One-Loop QCD Integral Coefficients
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Algebraic evaluation of rational polynomials in one-loop amplitudes
• MHV-Vertices for Gravity Amplitudes
• Multi-Gluon Collinear Limits from MHV diagrams
• Integral Coefficients for One-Loop Amplitudes
• From Trees to Loops and Back
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Two-loop five-point all plus helicity Yang-Mills amplitude
• Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes
• Scalar diagrammatic rules for Born amplitudes in QCD
• Two-Loop Maximal Unitarity with External Masses
• Two-loop six gluon all plus helicity amplitude
• A comparison of efficient methods for the computation of Born gluon amplitudes
• The rational parts of one-loop QCD amplitudes I: The general formalism
• Structure of the MHV-rules Lagrangian
• MHV Techniques for QED Processes
• Analytic Structure of Three-Mass Triangle Coefficients
• Collinear Limits in QCD from MHV Rules
• Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• Multivariate Residues and Maximal Unitarity
• $n$-point amplitudes with a single negative-helicity graviton
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• The two-loop n-point all-plus helicity amplitude
• Maximal Unitarity for the Four-Mass Double Box
• Unitarity Cuts of Integrals with Doubled Propagators
• S-Matrix Equivalence Theorem Evasion and Dimensional Regularisation with the Canonical MHV Lagrangian
• Building Bases of Loop Integrands
• The Unitarity Method using a Canonical Basis Approach
• Global Residues and Two-Loop Hepta-Cuts
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory
• Perturbative expansion of N<8 Supergravity
• Chiral Squaring
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Massive Nonplanar Two-Loop Maximal Unitarity
• Recursion relations, Helicity Amplitudes and Dimensional Regularization
• Two-Loop Gravity amplitudes from four dimensional Unitarity
• The MHV Lagrangian for a spontaneously broken gauge theory
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude
• Next-to-Leading-Order Corrections to Weak Boson Production with a Massive Quark Jet Pair at Hadron Colliders
• Hard QCD at hadron colliders
• Illustrations of Integrand-Basis Building at Two Loops
• Automated calculations for multi-leg processes
• Generating MHV super-vertices in light-cone gauge
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• The MHV lagrangian vertices and the Parke-Taylor formula
• Developments in perturbative QCD
• Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities
• On perturbative field theory and twistor string theory
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Recursive structures in string field theory
• Quantum MHV Diagrams
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD