Cutting-Edge Tools for Cutting Edges

Abstract

We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We consolidate this knowledge, summarize how cuts are used in various computational strategies, and explain their relations to other quantities including imaginary parts, discontinuities, and monodromies. Differences and nuances are illustrated on explicit examples.

23 pages, invited contribution to the Encyclopedia of Mathematical Physics

References in corpus (40)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Causality, Analyticity and an IR Obstruction to UV Completion
• Higgs boson production at hadron colliders in NNLO QCD
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Differential Equations for Feynman Graph Amplitudes
• Higgs boson gluon-fusion production in N3LO QCD
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Electroweak corrections to charged-current e+e- --> 4 fermion processes - technical details and further results
• Amplitudes, Observables, and Classical Scattering
• Predictions for all processes e^+e^- -> 4 fermions + gamma
• Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD
• From polygons and symbols to polylogarithmic functions
• PolyLogTools - Polylogs for the masses
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• The complex-mass scheme for perturbative calculations with unstable particles
• Schwinger mechanism revisited
• Feynman Integrals and Intersection Theory
• The Drell-Yan cross section to third order in the strong coupling constant
• On the maximal cut of Feynman integrals and the solution of their differential equations
• Pulling the straps of polygons
• Cuts of Feynman Integrals in Baikov representation
• Cutkosky Rules for Superstring Field Theory
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Three-mass triangle integrals and single-valued polylogarithms
• Loop Tree Duality for multi-loop numerical integration
• Charged Current Drell-Yan Production at N3LO
• Higgs production in bottom-quark fusion to third order in the strong coupling
• Lepton-pair production at hadron colliders at N${}^3$LO in QCD
• Cuts from residues: the one-loop case
• CFT Unitarity and the AdS Cutkosky Rules
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Scattering Amplitudes in Quantum Field Theory
• Differential equations for loop integrals in Baikov representation
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Unitarity Cuts of the Worldsheet
• Snowmass White Paper: UV Constraints on IR Physics
• Generalized Cuts of Feynman Integrals in Parameter Space
• Four Lectures on Euler Integrals

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• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• The spectrum of Feynman-integral geometries at two loops