A non-planar two-loop three-point function beyond multiple polylogarithms

Abstract

We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t\bar{t}$ production and $\gamma \gamma$ production in gluon fusion through a massive top-quark loop. All subtopology integrals can be written in terms of multiple polylogarithms over an irrational alphabet and we employ a new method for the integration of the differential equations which does not rely on the rationalization of the latter. The top topology integrals, instead, in spite of the absence of a massive three-particle cut, cannot be evaluated in terms of multiple polylogarithms and require the introduction of integrals over complete elliptic integrals and polylogarithms. We provide one-fold integral representations for the solutions and continue them analytically to all relevant regions of the phase space in terms of real function, extracting all imaginary parts explicitly. The numerical evaluation of our expressions becomes straightforward in this way.

27 pages, 1 figure, 1 ancillary file

References in corpus (6)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• The kite integral to all orders in terms of elliptic polylogarithms
• The Two-Loop Master Integrals for $q\bar{q}\to VV$
• The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

Cited by in corpus (59)

• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Feynman Integrals and Intersection Theory
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• Collider Physics at the Precision Frontier
• Elliptic Feynman integrals and pure functions
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• An Elliptic Generalization of Multiple Polylogarithms
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• An Analytical Method for the NLO QCD Corrections to Double-Higgs Production
• Elliptic polylogarithms and Feynman parameter integrals
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the non-planar graphs
• An analytic solution for the equal-mass banana graph
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• RationalizeRoots: Software Package for the Rationalization of Square Roots
• Maximal Cuts in Arbitrary Dimension
• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
• Algorithms and tools for iterated Eisenstein integrals
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• Towards a new approximation for pair-production and associated-production of the Higgs boson
• The electron self-energy in QED at two loops revisited
• Two-loop helicity amplitudes for $gg\to ZZ$ with full top-quark mass effects
• The complete set of two-loop master integrals for Higgs + jet production in QCD
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• NNLO QCD Corrections to $\gamma +{\eta }_c({\eta }_b)$ Exclusive Production in Electron-Positron Collision
• Top-quark effects in diphoton production through gluon fusion at NLO in QCD
• Two-loop mixed QCD-EW corrections to $gg\to Hg$
• Three-loop contributions to the $\rho$ parameter and iterated integrals of modular forms
• Analytic approximations of $2\to 2$ processes with massive internal particles
• Master integrals for the NNLO virtual corrections to $q\bar{q}\to t\bar{t}$ scattering in QCD: the non-planar graphs
• Evaluating multi-loop Feynman integrals numerically through differential equations
• Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Evaluation of multi-loop multi-scale Feynman integrals for precision physics
• Symmetric $\epsilon$- and $(\epsilon +1/2)$-forms and quadratic constraints in "elliptic" sectors
• Two-loop master integrals for the mixed QCD-electroweak corrections for $H\to b\bar{b}$ through a $Ht\bar{t}$-coupling
• Constructing multi-loop scattering amplitudes with manifest singularity structure
• Cuts and Isogenies
• Total cross sections of $e\gamma \to eX\bar{X}$ processes with $X=\mu ,\gamma ,e$ via multiloop methods
• Systematic approximation of multi-scale Feynman integrals
• Non-planar elliptic vertex
• The Higgs-gluon form factor at three loops in QCD with three mass scales
• Learning Feynman integrals from differential equations with neural networks
• The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO
• Electroweak double-box integrals for Moller scattering
• Photon pair production in gluon fusion: Top quark effects at NLO with threshold matching
• The spectrum of Feynman-integral geometries at two loops
• Virtual corrections to $gg\to ZH$ via a transverse momentum expansion
• A Feynman integral depending on two elliptic curves
• Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay