Two-loop sunset diagrams with three massive lines

Abstract

In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit representations for the master integrals and an analytic result through O(epsilon) in d=4-2epsilon space-time dimensions for the case of equal masses, m = M.

11 pages

References in corpus (5)

• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Analytic treatment of the two loop equal mass sunrise graph
• The Quark Form Factor at Higher Orders
• Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics

Cited by in corpus (54)

• The elliptic dilogarithm for the sunset graph
• Feynman Diagrams and Differential Equations
• 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
• The $\epsilon$-form of the differential equations for Feynman integrals in the elliptic case
• 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
• The unequal mass sunrise integral expressed through iterated integrals on ${\overline{\mathcal{M}}}_{1,3}$
• Elliptic polylogarithms and Feynman parameter integrals
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• An analytic solution for the equal-mass banana graph
• Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
• Two-Loop Formfactors in Theories with Mass Gap and Z-Boson Production
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Hypergeometric representation of the two-loop equal mass sunrise diagram
• Algorithms and tools for iterated Eisenstein integrals
• The ice cone family and iterated integrals for Calabi-Yau varieties
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• Calculating four-loop tadpoles with one non-zero mass
• The complete set of two-loop master integrals for Higgs + jet production in QCD
• Meromorphic modular forms and the three-loop equal-mass banana integral
• Two-loop diagrams in non-relativistic QCD with elliptics
• Heavy-quark QCD vacuum polarisation function: analytical results at four loops
• The property of maximal transcendentality in the N=4 Supersymmetric Yang-Mills
• The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$
• Three-loop contributions to the $\rho$ parameter and iterated integrals of modular forms
• Counting master integrals: integration-by-parts procedure with effective mass
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Massive kite diagrams with elliptics
• The property of maximal transcendentality: calculation of master integrals
• The property of maximal transcendentality: calculation of Feynman integrals
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• On canonical differential equations for Calabi-Yau multi-scale Feynman integrals
• Non-planar elliptic vertex
• An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice
• On series and integral representations of some NRQCD master integrals
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• Heavy-quark pair production in polarized photon-photon collisions at next-to-leading order: Fully integrated total cross sections
• The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO
• Sunrise integral with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms
• Irrational constants in positronium decays
• Calculation of master integrals in terms of elliptic multiple polylogarithms
• Differential equations for Feynman integrals beyond multiple polylogarithms
• Sunrise integral in non-relativistic QCD with elliptics
• Integral representation for three-loop banana graph