All master integrals for three-jet production at NNLO

Abstract

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in $D$ space-time dimensions. These integrals evaluate to $\mathbb{Q}$-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter, and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless $2\to 3$ scattering process, thereby opening up a new level of precision collider phenomenology.

arXiv comment6 pages, 1 figure, 5 ancillary files; v2: references added; full boundary values in s12 physical region included; v3: values of the master integrals in the ancillary files updated

References in corpus (45)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithm FIRE -- Feynman Integral REduction
• Local Integrals for Planar Scattering Amplitudes
• Lectures on differential equations for Feynman integrals
• A novel approach to integration by parts reduction
• From polygons and symbols to polylogarithmic functions
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Explicit solutions of the 3--loop vacuum integral recurrence relations
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Pentagon functions for massless planar scattering amplitudes
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Cuts of Feynman Integrals in Baikov representation
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A first look at two-loop five-gluon scattering in QCD
• Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Evidence for a Nonplanar Amplituhedron
• Measurement of the inclusive 3-jet production differential cross section in proton-proton collisions at 7 TeV and determination of the strong coupling constant in the TeV range
• Measurement of the ratio of the inclusive 3-jet cross section to the inclusive 2-jet cross section in pp collisions at sqrt(s) = 7 TeV and first determination of the strong coupling constant in the TeV range
• Analytic result for a two-loop five-particle amplitude
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Bootstrapping pentagon functions
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Analytic result for the nonplanar hexa-box integrals
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Maximal Cuts in Arbitrary Dimension
• Baikov-Lee Representations Of Cut Feynman Integrals
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Determination of the strong coupling constant ${\alpha }_s$ from transverse energy-energy correlations in multijet events at $\sqrt{s}=8$ TeV using the ATLAS detector
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Measurement of transverse energy-energy correlations in multi-jet events in $pp$ collisions at $\sqrt{s}=7$ TeV using the ATLAS detector and determination of the strong coupling constant ${\alpha }_{\mathrm{s}}(m_Z)$
• Implications of nonplanar dual conformal symmetry
• Amplitudes from superconformal Ward identities
• Measurement of dijet azimuthal decorrelations in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector and determination of the strong coupling

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