The iterated structure of the all-order result for the two-loop sunrise integral

Abstract

We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation $\epsilon$. This is done by introducing a class of functions (generalisations of multiple polylogarithms to include the elliptic case) and by showing that all integrations can be carried out within this class of functions.

20 pages, v2: version to be published

References in corpus (8)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Feynman Diagrams and Differential Equations
• Resolution of singularities for multi-loop integrals
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The massless higher-loop two-point function
• Elliptic integral evaluations of Bessel moments
• BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

Cited by in corpus (59)

• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• 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
• The kite integral to all orders in terms of elliptic polylogarithms
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• Elliptic polylogarithms and Feynman parameter integrals
• An analytic solution for the equal-mass banana graph
• Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• Energy-energy correlations at next-to-next-to-leading order
• RationalizeRoots: Software Package for the Rationalization of Square Roots
• Elliptic Polylogarithms and Basic Hypergeometric Functions
• Bananas of equal mass: any loop, any order in the dimensional regularisation parameter
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Top-bottom interference effects in Higgs plus jet production at the LHC
• Algorithms and tools for iterated Eisenstein integrals
• Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• The electron self-energy in QED at two loops revisited
• The elliptic double box and symbology beyond polylogarithms
• The complete set of two-loop master integrals for Higgs + jet production in QCD
• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• Meromorphic modular forms and the three-loop equal-mass banana integral
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Three-loop contributions to the $\rho$ parameter and iterated integrals of modular forms
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
• On $\epsilon$-factorised bases and pure Feynman integrals
• Massive kite diagrams with elliptics
• $\epsilon$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^{+}{e}^{-}\to 2(Q\bar{Q})$
• Iterated integrals over letters induced by quadratic forms
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Schottky-Kronecker forms and hyperelliptic polylogarithms
• The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Cuts and Isogenies
• On series and integral representations of some NRQCD master integrals
• Master integrals for $\mathcal{O}(\alpha {\alpha }_s)$ corrections to $H\to Z{Z}^{\ast }$
• The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO
• Dispersion Approach in Two-Loop Calculations
• Discontinuities of banana integrals in dispersion relation representation
• Electroweak double-box integrals for Moller scattering
• Generalizations of polylogarithms for Feynman integrals
• Calculation of master integrals in terms of elliptic multiple polylogarithms
• Integral representation for three-loop banana graph
• The diagrammatic coaction beyond one loop
• A Feynman integral depending on two elliptic curves
• Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations