Multi-loop Amplitudes and Resummation

Abstract

We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each order of perturbation theory. For these amplitudes, previously-observed relations between single and double poles in different 2 to 2 processes can now be interpreted in terms of universal functions associated with external partons and process-dependent anomalous dimensions that describe coherent soft radiation. Catani's proposal for multiple poles in dimensionally-continued amplitudes emerges naturally.

14 pages, LateX2e using elsart.cls (included). Typographical errors corrected and expansion in renormalized coupling clarified. Thanks added to Z. Bern and L. Dixon for critical readings of the original version

References in corpus (1)

• Two-Loop QCD Helicity Amplitudes for $e^{+}{e}^{-}\to 3$~Jets

Cited by in corpus (287)

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• The Sivers Asymmetry in Hadronic Dijet Production
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• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
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• Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering
• Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Going beyond Soft plus Virtual
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Coordinate-space singularities of massless gauge theories
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• Two loop QCD amplitudes for di-pseudo scalar production in gluon fusion
• Form factors with two operator insertions and the principle of maximal transcendentality
• Two-Loop QCD Correction to massive spin-2 resonance $\to$ 3 gluons
• Resummation prediction on the jet mass spectrum in one-jet inclusive production at the LHC
• Momentum mappings for subtractions at higher orders in QCD
• Hidden Beauty in Multiloop Amplitudes
• Factorization of low-energy gluons in exclusive processes
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• Infrared Singularities and Soft Gluon Resummation with Massive Partons
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• The Asymptotic Structure of Cosmological Integrals
• Alphabet of one-loop Feynman integrals
• Iterating QCD scattering amplitudes in the high-energy limit
• The Two-Loop Infrared Structure of Amplitudes with Mixed Gauge Groups
• A Surprise in the Amplitude/Wilson Loop Duality
• Locally finite two-loop amplitudes for electroweak production through gluon fusion
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Three-loop helicity amplitudes for photon+jet production
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Two-Loop Diagrammatics in a Self-Dual Background
• Spin-2 Form Factors at Three Loop in QCD
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• Dimensional Regularization and Dimensional Reduction in the Light Cone
• Two-loop amplitudes for di-Higgs and di-pseudo-Higgs productions through quark annihilation in QCD
• Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator
• The two-loop Higgs impact factor
• Two-Loop Four-Fermion Scattering Amplitude in QED
• Universal structure of subleading infrared poles at strong coupling
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• Two-loop QCD Correction to Massive Spin-2 Resonance $\to q\bar{q}g$
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
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• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• Sudakov Resummations at Higher Orders
• Dijet Event Shapes as Diagnostic Tools
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• All-order results for soft and collinear gluons
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• Two-loop Splitting Amplitudes
• Two-parton contribution to the heavy-quark A_FB at NNLO QCD in e+e- collisions
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• Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Boomerang webs up to three-loop order
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit
• Two-loop mixed QCD-EW corrections to neutral current Drell-Yan
• Refining threshold resummations
• Progress on soft gluon exponentiation and long-distance singularities