Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
(2018) Physical Review D, Particles, Fields, Gravitation and Cosmology — Vol. 97, p. 116009 (2018)
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- Abstract
- We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves.These elliptic multiple polylogarithms are closely related to similar functions defined in pure math-ematics and string theory. We then focus on the equal-mass and non-equal-mass sunrise integrals,and we develop a formalism that enables us to compute these Feynman integrals in terms of ouriterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identifya set of integral kernels, whose precise form is determined by the branch points of the integral inquestion. These kernels allow us to express all iterated integrals on an elliptic curve in terms ofthem. The flexibility of our approach leads us to expect that it will be applicable to a large varietyof integrals in high-energy physics.
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Citations
Duhr, C., & et al. (2018). Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral. Physical Review D, Particles, Fields, Gravitation and Cosmology, 97, 116009. https://doi.org/10.1103/PhysRevD.97.116009 (Original work published 2018)