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An analytic solution for the equal-mass banana graph
/ Broedel, Johannes (Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Marzucca, Robin (Louvain U., CP3) ; Penante, Brenda (CERN) ; Tancredi, Lorenzo (CERN)
We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses. The results are remarkably simple and all integrals are expressed as linear combinations of iterated integrals of modular forms of uniform weight for the same congruence subgroup as for the two-loop equal-mass sunrise graph. [...]
arXiv:1907.03787; CP3-19-34; CERN-TH-2019-105; HU-Mathematik-2019-04; HU-EP-19/20, SLAC-PUB-17453; HU-EP-19/20,
SLAC-PUB-17453.-
2019-09-16 - 36 p.
- Published in : JHEP 1909 (2019) 112
Article from SCOAP3: PDF; Fulltext: PDF;
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Elliptic polylogarithms and Feynman parameter integrals
/ Broedel, Johannes (Humboldt U., Berlin, Inst. Math.) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Penante, Brenda (CERN) ; Tancredi, Lorenzo (CERN)
In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. [...]
arXiv:1902.09971; CP3-19-07; CERN-TH-2019-016; HU-Mathematik-2019-01; HU-EP-19/03, SLAC-PUB-17406; HU-EP-19/03,
SLAC-PUB-17406.-
2019-05-21 - 37 p.
- Published in : JHEP 05 (2019) 120
Article from SCOAP3: PDF; Fulltext: PDF;
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3.
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Cuts and Feynman amplitudes beyond polylogarithms
/ Broedel, Johannes (Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Penante, Brenda (CERN) ; Primo, Amedeo (Zurich U.) ; Tancredi, Lorenzo (CERN)
In this contribution to the proceedings of Loops and Legs in Quantum Field Theory 2018, we discuss some recent developments in the calculation of multiloop Feynman integrals which evaluate to functions beyond multiple polylogarithms..
SISSA, 2018 - 9 p.
- Published in : PoS LL2018 (2018) 062
Fulltext: PDF; External link: PoS server
In : 14th DESY Workshop on Elementary Particle Physics : Loops and Legs in Quantum Field Theory 2018, St Goar, Germany, 29 Apr - 04 May 2018, pp.062
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Elliptic Feynman integrals and pure functions
/ Broedel, Johannes (Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Penante, Brenda (CERN) ; Tancredi, Lorenzo (CERN)
We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term. We investigate several non-trivial elliptic two-loop Feynman integrals with up to three external legs and express them in terms of our functions. [...]
arXiv:1809.10698; CP3-18-58; CERN-TH-2018-211; HU-Mathematik-2018-09; HU-EP-18/29; SLAC-PUB-17336.-
2019-01-03 - 47 p.
- Published in : JHEP 1901 (2019) 023
Article from SCOAP3: scoap3-fulltext - PDF; scoap - PDF; Fulltext: PDF;
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6.
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Elliptic polylogarithms and two-loop Feynman integrals
/ Broedel, Johannes (Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Penante, Brenda (CERN) ; Tancredi, Lorenzo (CERN)
We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are closely related to the elliptic multiple polylogarithms (eMPLs) studied in the mathematics literature. [...]
arXiv:1807.06238; CERN-TH-2018-163; CP3-18-45; HU-EP-18-22; HU-Mathematik-2018-08; SLAC-PUB-17302.-
SISSA, 2018-07-13 - 10 p.
- Published in : PoS LL2018 (2018) 005
Fulltext: 1807.06238 - PDF; arXiv:1807.06238 - PDF; PoS(LL2018)005 - PDF; External link: PoS server
In : 14th DESY Workshop on Elementary Particle Physics : Loops and Legs in Quantum Field Theory 2018, St Goar, Germany, 29 Apr - 04 May 2018, pp.005
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From modular forms to differential equations for Feynman integrals
/ Broedel, Johannes (Humboldt U., Berlin ; Humboldt U., Berlin, Inst. Math.) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Penante, Brenda (CERN) ; Tancredi, Lorenzo (CERN)
In these proceedings we discuss a representation for modular forms that is more suitable for their application to the calculation of Feynman integrals in the context of iterated integrals and the differential equation method. In particular, we show that for every modular form we can find a representation in terms of powers of complete elliptic integrals of the first kind multiplied by algebraic functions. [...]
arXiv:1807.00842; CERN-TH-2018-152.-
2019 - 25 p.
- Published in : 10.1007/978-3-030-04480-0_6
Fulltext: PDF;
In : KMPB Conference : Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Zeuthen, Germany, 23 - 26 Oct 2017, pp.107-131
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