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The diagrammatic coaction and the algebraic structure of cut Feynman integrals
/ Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (Edinburgh U.)
We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. [...]
arXiv:1803.05894; CERN-TH-2018-002; CP3-18-01; Edinburgh 2018/1; FR-PHENO-2018-001; EDINBURGH-2018-1.-
SISSA, 2018-03-15 - 10 p.
- Published in : PoS RADCOR (2018) 002
Fulltext: 1803.05894 - PDF; PoS(RADCOR2017)002 - PDF; External link: PoS server
In : 13th International Symposium on Radiative Corrections : Application of Quantum Field Theory to Phenomenology, St. Gilgen, Austria, 24 - 29 Sep 2017, pp.002
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2.
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Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
/ Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Trinity Coll., Dublin ; Hamilton Math. Inst., Dublin ; IPhT, Saclay ; Santa Barbara, KITP) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.)
We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). [...]
arXiv:1704.07931; CERN-TH-2017-092; CP3-17-11; EDINBURGH-2017-09; FR-PHENO-2017-010; TCDMATH-17-09.-
2017-12-15 - 74 p.
- Published in : JHEP 12 (2017) 090
Article from SCOAP3: scoap3-fulltext - PDF; scoap - PDF; Fulltext: PDF;
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3.
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Coaction for Feynman integrals and diagrams
/ Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Hamilton Math. Inst., Dublin ; Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Matthew, James (U. Edinburgh, Higgs Ctr. Theor. Phys.)
We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and graphical operations on Feynman diagrams. [...]
arXiv:1808.00069; CERN-TH-2018-165; CP3-18-46; FR-PHENO-2018-007.-
SISSA, 2018-07-31 - 10 p.
- Published in : PoS LL2018 (2018) 047
Fulltext: 1808.00069 - PDF; PoS(LL2018)047 - 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.047
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The diagrammatic coaction beyond one loop
/ Abreu, Samuel (CERN ; UCLA ; U. Edinburgh, Higgs Ctr. Theor. Phys.) ; 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.)
The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions. The coaction on the functions is constructed by pairing a basis of differential forms, corresponding to master integrals, with a basis of integration contours, corresponding to independent cut integrals. [...]
arXiv:2106.01280.-
2021-10-15 - 65 p.
- Published in : JHEP 2110 (2021) 131
Fulltext: document - PDF; 2106.01280 - PDF;
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Diagrammatic Coaction of Two-Loop Feynman Integrals
/ Abreu, Samuel (Louvain U., CP3) ; Britto, Ruth (Hamilton Math. Inst., Dublin ; Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys. ; Edinburgh U., Inst. Astron.) ; Matthew, James (U. Edinburgh, Higgs Ctr. Theor. Phys.)
It is known that one-loop Feynman integrals possess an algebraic structure encoding some of their analytic properties called the coaction, which can be written in terms of Feynman integrals and their cuts. This diagrammatic coaction, and the coaction on other classes of integrals such as hypergeometric functions, may be expressed using suitable bases of differential forms and integration contours. [...]
arXiv:1912.06561; CERN-TH-2019-218; CP3-19-59.-
2019 - 10 p.
- Published in : PoS RADCOR2019 (2019) 065
Fulltext: PoS(RADCOR2019)065 - PDF; 1912.06561 - PDF;
In : 14th International Symposium on Radiative Corrections : Application of Quantum Field Theory to Phenomenology, Avignon, France, 8 - 13 Sep 2019, pp.065
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7.
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The Diagrammatic Coaction
/ Gardi, Einan (Edinburgh U.) ; Abreu, Samuel (CERN ; Edinburgh U.) ; Britto, Ruth (Trinity Coll., Dublin) ; Duhr, Claude (Bonn U.) ; Matthew, James (Edinburgh U.)
The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. [...]
arXiv:2207.07843; CERN-TH-2022-122; BONN-TH-2022-18.-
2022-10-20 - 19 p.
- Published in : PoS LL2022 (2022) 015
Fulltext: 2207.07843 - PDF; document - PDF;
In : 16th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2022, Ettal, Germany, 25 - 30 Apr 2022, pp.015
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Cuts from residues: the one-loop case
/ Abreu, Samuel (Freiburg U.) ; Britto, Ruth (Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys. ; Edinburgh U.)
Using the multivariate residue calculus of Leray, we give a precise definition of the notion of a cut Feynman integral in dimensional regularization, as a residue evaluated on the variety where some of the propagators are put on shell. These are naturally associated to Landau singularities of the first type. [...]
arXiv:1702.03163; CERN-TH-2017-033; CP3-17-05; Edinburgh-2017-05; FR-PHENO-2017-001.-
2017-06-14 - 57 p.
- Published in : JHEP 06 (2017) 114
Article from SCOAP3: PDF; Fulltext: PDF;
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Generalized hypergeometric functions and intersection theory for Feynman integrals
/ Abreu, Samuel (Louvain U., CP3) ; Britto, Ruth (Hamilton Math. Inst., Dublin ; Trinity Coll., Dublin ; IPhT, Saclay) ; Duhr, Claude (CERN) ; Gardi, Einan (U. Edinburgh, Higgs Ctr. Theor. Phys.) ; Matthew, James (U. Edinburgh, Higgs Ctr. Theor. Phys.)
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection theory. [...]
arXiv:1912.03205; CERN-TH-2019-219; CP3-19-58.-
2019 - 10 p.
- Published in : PoS RADCOR2019 (2019) 067
Fulltext: PoS(RADCOR2019)067 - PDF; 1912.03205 - PDF;
In : 14th International Symposium on Radiative Corrections : Application of Quantum Field Theory to Phenomenology, Avignon, France, 8 - 13 Sep 2019, pp.067
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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: scoap3-fulltext - PDF; 5ec5b198a3165fc4cc32fea91e2ebad0 - PDFPDFA; Fulltext: PDF; External link: Article from SCOAP3
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