Meromorphic modular forms and the three-loop equal-mass banana integral
From MaRDI portal
Publication:2087333
DOI10.1007/JHEP02(2022)184MaRDI QIDQ2087333
Nils Matthes, Johannes Broedel, Claude Duhr
Publication date: 27 October 2022
Published in: Journal of High Energy Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.15251
Related Items
The ice cone family and iterated integrals for Calabi-Yau varieties, An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals, Constraints on sequential discontinuities from the geometry of on-shell spaces, Loop-by-loop differential equations for dual (elliptic) Feynman integrals, Bananas of equal mass: any loop, any order in the dimensional regularisation parameter, The three-loop equal-mass banana integral in \(\varepsilon\)-factorised form with meromorphic modular forms, Bananas: multi-edge graphs and their Feynman integrals, Duals of Feynman integrals. II: Generalized unitarity, A Feynman integral depending on two elliptic curves
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
- On genera of curves from high-loop generalized unitarity cuts
- Star integrals, convolutions and simplices
- A \(K3\) in \(\phi^{4}\)
- The elliptic dilogarithm for the sunset graph
- On the maximal cut of Feynman integrals and the solution of their differential equations
- CHAPLIN -- complex harmonic polylogarithms in Fortran
- Elliptic Feynman integrals and pure functions
- Baikov-Lee representations of cut Feynman integrals
- Numerical evaluation of multiple polylogarithms
- Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor-planar case
- Analytic treatment of the two loop equal mass sunrise graph
- Two-loop sunset diagrams with three massive lines
- Multiple polylogarithms, cyclotomy and modular complexes
- Numerical evaluation of two-dimensional harmonic polylogarithms
- On the reduction of generalized polylogarithms to \(\mathrm{Li}_n\) and \(\mathrm{Li}_{2,2}\) and on the evaluation thereof
- Feynman integrals and iterated integrals of modular forms
- On the algebraic structure of iterated integrals of quasimodular forms
- Cuts of Feynman integrals in Baikov representation
- Maximal cuts in arbitrary dimension
- Local mirror symmetry and the sunset Feynman integral
- Local integrals for planar scattering amplitudes
- The \(\varepsilon\)-form of the differential equations for Feynman integrals in the elliptic case
- On Rademacher's conjecture: congruence subgroups of genus zero of the modular group.
- Quasimodular forms: an introduction
- Inclusive heavy flavor hadroproduction in NLO QCD: the exact analytic result
- Cuts and isogenies
- Analytic structure of all loop banana integrals
- Three-loop contributions to the \(\rho\) parameter and iterated integrals of modular forms
- Algorithms and tools for iterated Eisenstein integrals
- Modular transformations of elliptic Feynman integrals
- Feynman integrals and iterated integrals on moduli spaces of curves of genus zero
- A second-order differential equation for the two-loop sunrise graph with arbitrary masses
- Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
- Modular forms in quantum field theory
- The two loop crossed ladder vertex diagram with two massive exchanges
- Root lattices and pencils of varieties
- Elliptic multiple zeta values and one-loop superstring amplitudes
- Invarianten linearer Differentialgleichungen
- Numerical implementation of harmonic polylogarithms to weight w = 8
- NEW METHOD OF MASSIVE N-POINT FEYNMAN DIAGRAMS CALCULATION
- A Feynman integral via higher normal functions
- The iterated structure of the all-order result for the two-loop sunrise integral
- Mathematical Aspects of Scattering Amplitudes
- Harmonic sums and polylogarithms generated by cyclotomic polynomials
- The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
- The kite integral to all orders in terms of elliptic polylogarithms
- Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics
- Elliptic Modular Forms and Their Applications
- Relations between elliptic multiple zeta values and a special derivation algebra
- Fourth order spectral functions for the electron propagator
- Hecke operators for weakly holomorphic modular forms and supersingular congruences
- Iterated path integrals
- Volumes of hyperbolic manifolds and mixed Tate motives
- HARMONIC POLYLOGARITHMS
- Iterated elliptic and hypergeometric integrals for Feynman diagrams
- TRANSFORMATION FORMULAS FOR GENERALIZED DEDEKIND ETA FUNCTIONS
- Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
- Iterated primitives of meromorphic quasimodular forms for 𝑆𝐿₂(ℤ)
- The two-loop sunrise graph with arbitrary masses
- Iterated integrals of modular forms and noncommutative modular symbols
- The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
- On the simple cubic lattice Green function
- SAGE
- Differential equations for two-loop four-point functions.
- Numerical evaluation of harmonic polylogarithms
- \texttt{handyG} -- rapid numerical evaluation of generalised polylogarithms in Fortran
- Numerical evaluation of iterated integrals related to elliptic Feynman integrals
