The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
By Luise Adams, Christian Bogner, Stefan Weinzierl. 2015
163 citations recorded by the source corpus.
We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O(e0)-part and the O(e1)-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the O(e1)-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/cce9bb716af2e5687c39b32b65ddf07229960f29
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In Astronomy and Astrophysics
- L. Tancredi
- Claude Duhr
- Falko Dulat
- Johannes Broedel
- Ettore Remiddi
- Costas G. Papadopoulos
- Hjalte Frellesvig
- A. Primo
In Nuclear and High Energy Physics
- Claude Duhr
- Falko Dulat
- L. Tancredi
- Hjalte Frellesvig
- Johannes Broedel
- Costas G. Papadopoulos
- Gudrun Heinrich
- Ettore Remiddi
Citations in the corpus
- Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism (2017, background): “Our paper is not the first to consider elliptic generalisations of MPLs [14, 17, 19, 20, 24, 31, 45, 49, 50] or iterated integrals over integration kernels that involve square roots of polynomials of degree greater than two [51].”
- Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016, methodology): “…in our knowledge of the mathematical structures that appear in multiloop Feynman integrals, thanks to the combined use of various computational techniques, such as to the method of differential equations [1–3], the introduction of a class of special functions (dubbed originally harmonic…”
- Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, unknown): “05 46”
- Cuts of Feynman Integrals in Baikov representation (2017, background): “when for instance enough internal masses are introduced, MI are not anymore expressible in terms of GPs, and in fact a new class of functions involving elliptic integrals is needed [60, 61, 62, 63, 64].”