Analytic representations of Yang–Mills amplitudes

N. Emil J. Bjerrum-Bohr; Jacob Lewis Bourjaily; Poul Henrik Damgaard; Bo Feng

doi:10.1016/j.nuclphysb.2016.10.012

Analytic representations of Yang–Mills amplitudes

N. Emil J. Bjerrum-Bohr, Jacob Lewis Bourjaily, Poul Henrik Damgaard, Bo Feng

Teoretisk højenergi, astropartikel og gravitationel fysik

28 Citationer (Scopus)

72 Downloads (Pure)

Abstract

Scattering amplitudes in Yang–Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space—fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang–Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.

Originalsprog	Engelsk
Tidsskrift	Nuclear Physics B
Vol/bind	913
Sider (fra-til)	964-986
Antal sider	23
ISSN	0550-3213
DOI	https://doi.org/10.1016/j.nuclphysb.2016.10.012
Status	Udgivet - 1 dec. 2016

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10.1016/j.nuclphysb.2016.10.012Licens: CC BY

1-s2.0-S0550321316303145-mainForlagets udgivne version, 530 KBLicens: CC BY

Citationsformater

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T1 - Analytic representations of Yang–Mills amplitudes

AU - Bjerrum-Bohr, N. Emil J.

AU - Bourjaily, Jacob Lewis

AU - Damgaard, Poul Henrik

AU - Feng, Bo

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Scattering amplitudes in Yang–Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space—fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang–Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.

AB - Scattering amplitudes in Yang–Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space—fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang–Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.

U2 - 10.1016/j.nuclphysb.2016.10.012

DO - 10.1016/j.nuclphysb.2016.10.012

M3 - Journal article

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VL - 913

SP - 964

EP - 986

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

ER -

Analytic representations of Yang–Mills amplitudes

Abstract

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