The Coulomb-branch S-matrix from massless amplitudes

Abstract

We present a systematic method to extract the entire tree-level S-matrix on the Coulomb branch of N=4 SYM from soft-scalar limits of on-shell amplitudes at the origin of moduli space. Massive amplitudes in the spontaneously-broken theory can thus be computed from on-shell amplitudes in the massless, unbroken theory. To check this correspondence, we first prove that soft and collinear divergences in the required massless amplitudes cancel for a judicious choice of soft-scalar momenta. We then explicitly verify our proposal in examples with arbitrarily many external legs and to all orders in the mass. As a byproduct, the construction leads to a massive CSW-like expansion that reproduces several known all-n results for Coulomb-branch amplitudes in an effortless way. We briefly discuss the extension of our method to loop integrands.

23 pages, 1 table, many figures

References in corpus (44)

• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• A direct proof of the CSW rules
• Scattering into the fifth dimension of N=4 super Yang-Mills
• The Grassmannian Origin Of Dual Superconformal Invariance
• Weyl-van-der-Waerden formalism for helicity amplitudes of massive particles
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• The singular behavior of massive QCD amplitudes
• Generalized unitarity for N=4 super-amplitudes
• Generalized Unitarity and Six-Dimensional Helicity
• All tree-level amplitudes in massless QCD
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Massive amplitudes on the Coulomb branch of N=4 SYM
• All-Multiplicity Amplitudes with Massive Scalars
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• An ambitwistor Yang-Mills Lagrangian
• No triangles on the moduli space of maximally supersymmetric gauge theory
• Compact multigluonic scattering amplitudes with heavy scalars and fermions
• One-loop MHV Rules and Pure Yang-Mills
• Multigluonic scattering amplitudes of heavy quarks
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• Dual conformal symmetry at loop level; massive regularization
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Symmetries of the N=4 SYM S-matrix
• CSW rules for a massive scalar
• On-shell supersymmetry for massive multiplets
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• A super MHV vertex expansion for N=4 SYM theory
• MHV Diagrams from an All-Line Recursion Relation
• Scattering on the Moduli Space of N=4 Super Yang-Mills
• First-quantized N=4 Yang-Mills
• The MHV Lagrangian for a spontaneously broken gauge theory

Cited by in corpus (8)

• Massive amplitudes on the Coulomb branch of N=4 SYM
• On-shell Higgsing for EFTs
• Twistor actions for gauge theory and gravity
• The two-loop six-point amplitude in ABJM theory
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• Holonomies of gauge fields in twistor space 5: amplitudes of gluons and massive scalars
• General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion
• Holonomies of gauge fields in twistor space 7: an electroweak model