Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
arXiv:1303.4734
Abstract
We revisit the familiar construction of one-loop scattering amplitudes via generalized unitarity in light of the recently understood properties of loop integrands prior to their integration. We show how in any four-dimensional quantum field theory, the integrand-level factorization of infrared divergences leads to twice as many constraints on integral coefficients than are visible from the integrated expressions. In the case of planar, maximally supersymmetric Yang-Mills amplitudes, we demonstrate that these constraints are both sufficient and necessary to imply the finiteness and dual-conformal invariance of the ratios of scattering amplitudes. We present a novel regularization of the scalar box integrals which makes dual-conformal invariance of finite observables manifest term by term, and describe how this procedure can be generalized to higher loop-orders. Finally, we describe how the familiar scalar boxes at one-loop can be upgraded to `chiral boxes' resulting in a manifestly infrared-factorized, box-like expansion for all one-loop integrands in planar, N=4 super Yang-Mills. Accompanying this note is a Mathematica package which implements our results, and allows for the efficient numerical evaluation of any one-loop amplitude or ratio function.
arXiv comment42 pages, 43 figures, and 4 tables. Included with the submission is a Mathematica package "loop_amplitudes" which implements our results
References in corpus (32)
- 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
- Dimensionally Regulated Pentagon Integrals
- Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
- What is the Simplest Quantum Field Theory?
- Magic identities for conformal four-point integrals
- Local Integrals for Planar Scattering Amplitudes
- On planar gluon amplitudes/Wilson loops duality
- Dimensionally Regulated One-Loop Integrals
- Dual Superconformal Invariance, Momentum Twistors and Grassmannians
- Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
- On-Shell Methods in Perturbative QCD
- Factorization in One-Loop Gauge Theory
- One-Loop N Gluon Amplitudes with Maximal Helicity Violation via Collinear Limits
- Scattering into the fifth dimension of N=4 super Yang-Mills
- The Grassmannian Origin Of Dual Superconformal Invariance
- All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
- Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
- Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
- Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
- Generalized unitarity for N=4 super-amplitudes
- Sharpening The Leading Singularity
- Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
- Dissolving N=4 loop amplitudes into QCD tree amplitudes
- The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
- Simple loop integrals and amplitudes in N=4 SYM
- Eliminating spurious poles from gauge-theoretic amplitudes
- Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
- Positroids, Plabic Graphs, and Scattering Amplitudes in Mathematica
- The box integrals in momentum-twistor geometry
- Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
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- Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
- Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
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- Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
- OPE for all Helicity Amplitudes
- Nonsinglet pentagons and NMHV amplitudes
- OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
- Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
- On factorization of multiparticle pentagons
- Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
- On-shell diagrammatics and the perturbative structure of planar gauge theories
- Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes