Two-Loop Integrals for Planar Five-Point One-Mass Processes

Abstract

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at leading color in QCD. We provide a set of pure integrals together with differential equations in canonical form. We obtain analytic differential equations efficiently from numerical samples over finite fields, fitting an ansatz built from symbol letters. The symbol alphabet itself is constructed from cut differential equations and we find that it can be written in a remarkably compact form. We comment on the analytic properties of the integrals and confirm the extended Steinmann relations, which govern the double discontinuities of Feynman integrals, to all orders in $\epsilon$. We solve the differential equations in terms of generalized power series on single-parameter contours in the space of Mandelstam invariants. This form of the solution trivializes the analytic continuation and the integrals can be evaluated in all kinematic regions with arbitrary numerical precision.

arXiv commentv2: minor typos corrected

References in corpus (58)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Feynman Graph Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dimensionally Regulated Pentagon Integrals
• Kira - A Feynman Integral Reduction Program
• 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
• Bootstrapping the three-loop hexagon
• FIESTA 4: optimized Feynman integral calculations with GPU support
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Full top quark mass dependence in Higgs boson pair production at NLO
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Bootstrapping an NMHV amplitude through three loops
• Heptagons from the Steinmann Cluster Bootstrap
• Hexagon functions and the three-loop remainder function
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Pentagon functions for massless planar scattering amplitudes
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Pulling the straps of polygons
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• The two-loop helicity amplitudes for $q{\bar{q}}^{\prime }\to V_1{V}_2\to 4\mathrm{leptons}$
• NLO QCD corrections to Higgs boson plus jet production with full top-quark mass dependence
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Ntuples for NLO Events at Hadron Colliders
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Analytic result for a two-loop five-particle amplitude
• Loop Tree Duality for multi-loop numerical integration
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Cuts from residues: the one-loop case
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Rationalizing Loop Integration
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Numerical Loop-Tree Duality: contour deformation and subtraction
• Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• The complete set of two-loop master integrals for Higgs + jet production in QCD
• Differential equations on unitarity cut surfaces
• Differential equations for loop integrals in Baikov representation
• Internal Reduction method for computing Feynman Integrals
• Evaluating multi-loop Feynman integrals numerically through differential equations
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory

Cited by in corpus (55)

• Collider Physics at the Precision Frontier
• Pentagon Functions for Scattering of Five Massless Particles
• Multiloop corrections for collider processes using auxiliary mass flow
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Cluster algebras for Feynman integrals
• Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Jet Angularities in Z+jet production at the LHC
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel
• Antipodal Self-Duality for a Four-Particle Form Factor
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• Symbol Alphabets from the Landau Singular Locus
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Symbology for elliptic multiple polylogarithms and the symbol prime
• One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$
• Bootstrapping a Two-Loop Four-Point Form Factor
• A first look at the function space for planar two-loop six-particle Feynman integrals
• Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop
• Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
• Pentagon integrals to arbitrary order in the dimensional regulator
• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• One-loop hexagon integral to higher orders in the dimensional regulator
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• Computational challenges for multi-loop collider phenomenology
• SOFIA: Singularities of Feynman Integrals Automatized
• Resummation methods for Master Integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• A Two-Loop Four-Point Form Factor at Function Level
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• Illustrations of Integrand-Basis Building at Two Loops
• Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• On non-factorisable contributions to $t$-channel single-top production
• Two-loop non-planar hexa-box integrals with one massive leg
• One-Loop QCD Corrections to $\bar{u}d\to t\bar{t}W$ at $\mathcal{O}({\epsilon }^2)$
• Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes
• Two-loop amplitude for mixed QCD-EW corrections to $gg\to Hg$
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit
• Analytic results for two-loop planar master integrals for Bhabha scattering
• Two-loop tensor integral coefficients in OpenLoops
• Recent progress for five-particle two-loop scattering amplitudes with an off-shell leg
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons