Analytic results for two-loop planar master integrals for Bhabha scattering

Abstract

We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equa- tions with canonical bases. We obtain results in terms of multiple polylogarithms for all the master integrals but one, for which we derive a compact result in terms of elliptic mul- tiple polylogarithms. As a byproduct, we also provide a compact analytic result in terms of elliptic multiple polylogarithms for an integral belonging to the first family of planar Bhabha integrals, whose computation in terms of polylogarithms was addressed previously in the literature.

arXiv comment28 pages, 3 figures

References in corpus (53)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Differential Equations for Feynman Graph Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Numerical evaluation of multiple polylogarithms
• Kira - A Feynman Integral Reduction Program
• Local Integrals for Planar Scattering Amplitudes
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Integral Reduction with Kira 2.0 and Finite Field Methods
• Multiple polylogarithms and mixed Tate motives
• From polygons and symbols to polylogarithmic functions
• FIESTA 4: optimized Feynman integral calculations with GPU support
• PolyLogTools - Polylogs for the masses
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Elliptic multiple zeta values and one-loop superstring amplitudes
• Soft triple-real radiation for Higgs production at N3LO
• The massless higher-loop two-point function
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• Expansion by regions: revealing potential and Glauber regions automatically
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• Geometric approach to asymptotic expansion of Feynman integrals
• Elliptic Feynman integrals and pure functions
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• 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
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• The Two-Loop Master Integrals for $q\bar{q}\to VV$
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Two-Loop Integrals for Planar Five-Point One-Mass Processes
• Master integrals for massive two-loop Bhabha scattering in QED
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• Analytic results for two-loop master integrals for Bhabha scattering I
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• RationalizeRoots: Software Package for the Rationalization of Square Roots
• The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
• Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case
• Numerical evaluation of iterated integrals related to elliptic Feynman integrals
• Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering
• BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• Two-Loop N_F=1 QED Bhabha Scattering Differential Cross Section
• Virtual Hadronic and Leptonic Contributions to Bhabha Scattering
• The planar four-point master integrals for massive two-loop Bhabha scattering
• Two-Loop Fermionic Corrections to Massive Bhabha Scattering
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• Bhabha scattering at NNLO with next-to-soft stabilisation
• A Numerical Routine for the Crossed Vertex Diagram with a Massive-Particle Loop
• Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering
• The H-graph with equal masses in terms of multiple polylogarithms
• Differential equations and massive two-loop Bhabha scattering: the B5l2m3 case
• Planar two-loop master integrals for massive Bhabha scattering: N_f=1 and N_f=2
• Harmonic polylogarithms for massive Bhabha scattering

Cited by in corpus (7)

• FIESTA5: numerical high-performance Feynman integral evaluation
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Symbology for elliptic multiple polylogarithms and the symbol prime
• An Infinite Family of Elliptic Ladder Integrals
• Master integrals for $\mathcal{O}(\alpha {\alpha }_s)$ corrections to $H\to Z{Z}^{\ast }$
• Two-loop tensor integral coefficients in OpenLoops