Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

doi:10.1103/PhysRevD.97.116009

Title: Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

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 mathematics 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 our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.

Authors:: Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

Publication Date:: 2018-06-12

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland); Humboldt Univ. of Berlin (Germany)

Sponsoring Org.:: USDOE; European Research Council (ERC); German Research Foundation (DFG)

OSTI Identifier:: 1441235

Alternate Identifier(s):: OSTI ID: 1457782

Grant/Contract Number:: AC02-76SF00515; 637019

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; electroweak radiative corrections; perturbative QCD; quantum electrodynamics

Citation Formats


                    Broedel, Johannes, Duhr, Claude, Dulat, Falko, and Tancredi, Lorenzo. Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral.  United States: N. p., 2018. 
        Web.  doi:10.1103/PhysRevD.97.116009.

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                    Broedel, Johannes, Duhr, Claude, Dulat, Falko, & Tancredi, Lorenzo. Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral.  United States.  doi:https://doi.org/10.1103/PhysRevD.97.116009

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                    Broedel, Johannes, Duhr, Claude, Dulat, Falko, and Tancredi, Lorenzo. Tue .  
        "Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral".  United States.  doi:https://doi.org/10.1103/PhysRevD.97.116009.

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@article{osti_1441235,

  title        = {Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral},

  author       = {Broedel, Johannes and Duhr, Claude and Dulat, Falko and Tancredi, Lorenzo},

  abstractNote = {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 mathematics 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 our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.},

  doi          = {10.1103/PhysRevD.97.116009},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 97,

  place        = {United States},

  year         = {2018},

  month        = {6}

}

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DOI: https://doi.org/10.1103/PhysRevD.97.116009

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Title: Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

Abstract

Citation Formats

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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes journal, August 2012

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Simple one-dimensional integral representations for two-loop self-energies: the master diagram journal, July 1995

Harmonic sums and polylogarithms generated by cyclotomic polynomials journal, October 2011

The kite integral to all orders in terms of elliptic polylogarithms journal, December 2016

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Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to
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A non-planar two-loop three-point function beyond multiple polylogarithms
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The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
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The iterated structure of the all-order result for the two-loop sunrise integral
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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
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Connection between Feynman integrals having different values of the space-time dimension
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