The diagrammatic coaction and the algebraic structure of cut Feynman integrals

Samuel Abreu; Ruth Britto; Claude Duhr; Einan Gardi

The diagrammatic coaction and the algebraic structure of cut Feynman integrals

Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi

School of Physics and Astronomy

Research output: Contribution to conference › Other

Abstract

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. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon.

Original language	English
Number of pages	10
Publication status	Published - 15 Mar 2018
Event	13th International Symposium on Radiative Corrections : (Applications of Quantum Field Theory to Phenomenology - Universitat Wien, St Gilgen, Austria Duration: 25 Sept 2017 → 29 Sept 2017

Conference

Conference	13th International Symposium on Radiative Corrections
Country/Territory	Austria
City	St Gilgen
Period	25/09/17 → 29/09/17

Keywords / Materials (for Non-textual outputs)

hep-th
hep-ph

Access to Document

1803.05894v1Licence: Creative Commons: Attribution (CC-BY)

Particle Theory at the Higgs Centre
Ball, R. (Principal Investigator), Boyle, P. (Co-investigator), Del Debbio, L. (Co-investigator), Gardi, E. (Co-investigator), Horsley, R. (Co-investigator), Kennedy, A. (Co-investigator), O'Connell, D. (Co-investigator), Smillie, J. (Co-investigator) & Zwicky, R. (Co-investigator)
STFC
1/10/17 → 30/09/21
Project: Research

Cite this

@conference{0714383ce8af4246b6955cad2dddf74f,

title = "The diagrammatic coaction and the algebraic structure of cut Feynman integrals",

abstract = " 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. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon. ",

keywords = "hep-th, hep-ph",

author = "Samuel Abreu and Ruth Britto and Claude Duhr and Einan Gardi",

note = "10 pages. Talk at RADCOR 2017, the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austria; 13th International Symposium on Radiative Corrections : (Applications of Quantum Field Theory to Phenomenology ; Conference date: 25-09-2017 Through 29-09-2017",

year = "2018",

month = mar,

day = "15",

language = "English",

}

TY - CONF

T1 - The diagrammatic coaction and the algebraic structure of cut Feynman integrals

AU - Abreu, Samuel

AU - Britto, Ruth

AU - Duhr, Claude

AU - Gardi, Einan

N1 - 10 pages. Talk at RADCOR 2017, the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austria

PY - 2018/3/15

Y1 - 2018/3/15

N2 - 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. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon.

AB - 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. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon.

KW - hep-th

KW - hep-ph

M3 - Other

T2 - 13th International Symposium on Radiative Corrections

Y2 - 25 September 2017 through 29 September 2017

ER -

The diagrammatic coaction and the algebraic structure of cut Feynman integrals

Abstract

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Projects

Particle Theory at the Higgs Centre

Cite this