Local integrals for planar scattering amplitudes

A bstract Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry of the theory. This has made it possible to easily study the structure...

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Published in	The journal of high energy physics Vol. 2012; no. 6
Main Authors	Arkani-Hamed, N., Bourjaily, J., Cachazo, F., Trnka, J.
Format	Journal Article
Language	English
Published	Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2012 Springer Nature B.V
Subjects	Amplitudes Classical and Quantum Gravitation Elementary Particles High energy physics Integrals Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Relativity Theory Scattering Singularities String Theory Duality in Gauge Field Theories Scattering Amplitudes
Online Access	Get full text
ISSN	1029-8479 1029-8479
DOI	10.1007/JHEP06(2012)125

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Abstract	A bstract Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry of the theory. This has made it possible to easily study the structure of multi-loop amplitudes in the theory. In this paper we describe a remarkable fact revealed by these investigations: the integrand can be expressed in an amazingly simple and manifestly local form when represented in momentum-twistor space using a set of chiral integrals with unit leading singularities. As examples, we present very-concise expressions for all 2- and 3-loop MHV integrands, as well as all 2-loop NMHV integrands. We also describe a natural set of manifestly IR-finite integrals that can be used to express IR-safe objects such as the ratio function. Along the way we give a pedagogical introduction to the foundations of the subject. The new local forms of the integrand are closely connected to leading singularities — matching only a small subset of all leading singularities remarkably suffices to determine the full integrand. These results strongly suggest the existence of a theory for the integrand directly yielding these local expressions, allowing for a more direct understanding of the emergence of local spacetime physics.
AbstractList	A bstract Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry of the theory. This has made it possible to easily study the structure of multi-loop amplitudes in the theory. In this paper we describe a remarkable fact revealed by these investigations: the integrand can be expressed in an amazingly simple and manifestly local form when represented in momentum-twistor space using a set of chiral integrals with unit leading singularities. As examples, we present very-concise expressions for all 2- and 3-loop MHV integrands, as well as all 2-loop NMHV integrands. We also describe a natural set of manifestly IR-finite integrals that can be used to express IR-safe objects such as the ratio function. Along the way we give a pedagogical introduction to the foundations of the subject. The new local forms of the integrand are closely connected to leading singularities — matching only a small subset of all leading singularities remarkably suffices to determine the full integrand. These results strongly suggest the existence of a theory for the integrand directly yielding these local expressions, allowing for a more direct understanding of the emergence of local spacetime physics. Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry of the theory. This has made it possible to easily study the structure of multi-loop amplitudes in the theory. In this paper we describe a remarkable fact revealed by these investigations: the integrand can be expressed in an amazingly simple and manifestly local form when represented in momentum-twistor space using a set of chiral integrals with unit leading singularities. As examples, we present very-concise expressions for all 2- and 3-loop MHV integrands, as well as all 2-loop NMHV integrands. We also describe a natural set of manifestly IR-finite integrals that can be used to express IR-safe objects such as the ratio function. Along the way we give a pedagogical introduction to the foundations of the subject. The new local forms of the integrand are closely connected to leading singularities — matching only a small subset of all leading singularities remarkably suffices to determine the full integrand. These results strongly suggest the existence of a theory for the integrand directly yielding these local expressions, allowing for a more direct understanding of the emergence of local spacetime physics.
ArticleNumber	125
Author	Bourjaily, J. Cachazo, F. Arkani-Hamed, N. Trnka, J.
Author_xml	– sequence: 1 givenname: N. surname: Arkani-Hamed fullname: Arkani-Hamed, N. organization: School of Natural Sciences, Institute for Advanced Study – sequence: 2 givenname: J. surname: Bourjaily fullname: Bourjaily, J. email: bourjaily@fas.harvard.edu organization: School of Natural Sciences, Institute for Advanced Study, Department of Physics, Princeton University – sequence: 3 givenname: F. surname: Cachazo fullname: Cachazo, F. organization: Perimeter Institute for Theoretical Physics – sequence: 4 givenname: J. surname: Trnka fullname: Trnka, J. organization: School of Natural Sciences, Institute for Advanced Study, Department of Physics, Princeton University
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Snippet	A bstract Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in SYM has been described, generalizing the BCFW... Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in SYM has been described, generalizing the BCFW formula...
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SubjectTerms	Amplitudes Classical and Quantum Gravitation Elementary Particles High energy physics Integrals Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Relativity Theory Scattering Singularities String Theory
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Title	Local integrals for planar scattering amplitudes
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