Four-gluon scattering at three loops, infrared structure and Regge limit

Abstract

We compute the three-loop four-gluon scattering amplitude in maximally supersymmetric Yang-Mills theory, including its full color dependence. Our result is the first complete computation of a non-planar four-particle scattering amplitude to three loops in four-dimensional gauge theory and consequently provides highly non-trivial data for the study of non-planar scattering amplitudes. We present the amplitude as a Laurent expansion in the dimensional regulator to finite order, with coefficients composed of harmonic poly-logarithms of uniform transcendental weight, and simple rational prefactors. Our computation provides an independent check of a recent result for three-loop corrections to the soft anomalous dimension matrix that predicts the general infrared singularity structure of massless gauge theory scattering amplitudes. Taking the Regge limit of our result, we determine the three-loop gluon Regge trajectory. We also find agreement with very recent predictions for sub-leading logarithms.

References in corpus (19)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Three-Loop Superfiniteness of N=8 Supergravity
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Iterated amplitudes in the high-energy limit
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Subleading-color contributions to gluon-gluon scattering in N=4 SYM theory and relations to N=8 supergravity
• Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory

Cited by in corpus (15)

• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Bootstrapping the QCD soft anomalous dimension
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Full-color three-loop three-point form factors in N=4 SYM
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
• The two-loop Higgs impact factor
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• The long road from Regge poles to the LHC
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• QCD Beyond Leading Power