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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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PolyLogTools - Polylogs for the masses
/ Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC)
We review recent developments in the study of multiple polylogarithms, including the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an algorithm for finding fibration bases. We document how these algorithms are implemented in the Mathematica package PolyLogTools and show how it can be used to study the coproduct structure of polylogarithmic expressions and how to compute iterated parametric integrals over polylogarithmic expressions that show up in Feynman integal computations at low loop orders..
arXiv:1904.07279; CP3-19-17; CERN-TH-2019-045; SLAC-PUB-17423.-
2019-08-23 - 55 p.
- Published in : JHEP 1908 (2019) 135
Article from SCOAP3: scoap3-fulltext - PDF; scoap - PDF; Fulltext: PDF;
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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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Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
/ Broedel, Johannes (Humboldt U., Berlin, Inst. Math. ; Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Tancredi, Lorenzo (CERN)
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. [...]
arXiv:1712.07089; CERN-TH-2017-273; CP3-17-57; HU-EP-17-29; HU-Mathematik-2017-09; SLAC-PUB-17194; CERN-TH-2017-273.-
2018-05-15 - 54 p.
- Published in : JHEP 05 (2018) 093
Article from SCOAP3: scoap3-fulltext - PDF; scoap - 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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From positive geometries to a coaction on hypergeometric functions
/ Abreu, Samuel (Louvain U., CP3) ; Britto, Ruth (Trinity Coll., Dublin ; Hamilton Math. Inst., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Matthew, James (U. Edinburgh, Higgs Ctr. Theor. Phys.)
It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use intersection numbers and twisted homology theory to define a coaction on certain hypergeometric functions. [...]
arXiv:1910.08358; CERN-TH-2019-168.-
2020-02-20 - 45 p.
- Published in : JHEP 2002 (2020) 122
Article from SCOAP3: 5ec5b198a3165fc4cc32fea91e2ebad0 - PDFPDFA; scoap3-fulltext - PDF; Fulltext: PDF; External link: Article from SCOAP3
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