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

Theoretical high energy, astroparticle and gravitational physics

28 Citations (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.

Original language	English
Journal	Nuclear Physics B
Volume	913
Pages (from-to)	964-986
Number of pages	23
ISSN	0550-3213
DOIs	https://doi.org/10.1016/j.nuclphysb.2016.10.012
Publication status	Published - 1 Dec 2016

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title = "Analytic representations of Yang–Mills amplitudes",

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 M{\"o}bius-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.",

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doi = "10.1016/j.nuclphysb.2016.10.012",

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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

SN - 0550-3213

VL - 913

SP - 964

EP - 986

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -

Analytic representations of Yang–Mills amplitudes

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