Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity

Abstract

In previous work, the two-loop five-point amplitudes in $\mathcal{N}=4$ super Yang-Mills theory and $\mathcal{N}=8$ supergravity were computed at symbol level. In this paper, we compute the full functional form. The amplitudes are assembled and simplified using the analytic expressions of the two-loop pentagon integrals in the physical scattering region. We provide the explicit functional expressions, and a numerical reference point in the scattering region. We then calculate the multi-Regge limit of both amplitudes. The result is written in terms of an explicit transcendental function basis. For certain non-planar colour structures of the $\mathcal{N}=4$ super Yang-Mills amplitude, we perform an independent calculation based on the BFKL effective theory. We find perfect agreement. We comment on the analytic properties of the amplitudes.

arXiv comment60 pages, 4 figures; v2: typos corrected, functional expressions of the hard functions provided

References in corpus (85)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Magic identities for conformal four-point integrals
• Numerical evaluation of multiple polylogarithms
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• High energy QCD as a completely integrable model
• Kira - A Feynman Integral Reduction Program
• Local Integrals for Planar Scattering Amplitudes
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Multi-loop Amplitudes and Resummation
• One-Loop Corrections to Five-Gluon Amplitudes
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• From polygons and symbols to polylogarithmic functions
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Bootstrapping the three-loop hexagon
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Factorization Properties of Soft Graviton Amplitudes
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Pentagon functions for massless planar scattering amplitudes
• On the highest transcendentality in N=4 SUSY
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• All master integrals for three-jet production at NNLO
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Analytic form of the full two-loop five-gluon all-plus helicity amplitude
• Collinear and Soft Divergences in Perturbative Quantum Gravity
• The infrared structure of gauge theory amplitudes in the high-energy limit
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Evidence for a Nonplanar Amplituhedron
• Analytic result for a two-loop five-particle amplitude
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Eikonal methods applied to gravitational scattering amplitudes
• Infinities within graviton scattering amplitudes
• Bootstrapping pentagon functions
• Soft gluons at large angles in hadron collisions
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Analytic result for the nonplanar hexa-box integrals
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Two-parton scattering in the high-energy limit
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
• Soft-collinear gravity
• Iterated amplitudes in the high-energy limit
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• The R*-operation for Feynman graphs with generic numerators
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Logarithmic forms and differential equations for Feynman integrals
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• Dual Conformal Structure Beyond the Planar Limit
• Implications of nonplanar dual conformal symmetry
• Amplitudes at Infinity
• Amplitudes from superconformal Ward identities
• Subleading Regge limit from a soft anomalous dimension
• UV cancelations in gravity loop integrands

Cited by in corpus (13)

• Pentagon Functions for Scattering of Five Massless Particles
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$
• Bootstrapping a Two-Loop Four-Point Form Factor
• Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The two-loop Higgs impact factor
• Recent progress for five-particle two-loop scattering amplitudes with an off-shell leg
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point