Amplitude relations in non-linear sigma model

A bstract In this paper, we investigate tree-level scattering amplitude relations in U( N ) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [ 23 , 24 ], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization...

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Published in:	The journal of high energy physics Vol. 2014; no. 1; pp. 1 - 27
Main Authors:	Chen, Gang, Du, Yi-Jian
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 2014 Springer Nature B.V
Subjects:	Amplitudes Classical and Quantum Gravitation Color Elementary Particles Formations High energy physics Nonlinearity Parametrization Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Relativity Theory Scattering amplitude String Theory Trees Yang-Mills theory Scattering Amplitudes Sigma Models
ISSN:	1029-8479, 1029-8479
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Abstract	A bstract In this paper, we investigate tree-level scattering amplitude relations in U( N ) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [ 23 , 24 ], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m -point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.
AbstractList	A bstract In this paper, we investigate tree-level scattering amplitude relations in U( N ) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [ 23 , 24 ], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m -point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation. In this paper, we investigate tree-level scattering amplitude relations in U(N) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [ 23 , 24 ], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation. In this paper, we investigate tree-level scattering amplitude relations in U( N ) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m -point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.
ArticleNumber	61
Author	Du, Yi-Jian Chen, Gang
Author_xml	– sequence: 1 givenname: Gang surname: Chen fullname: Chen, Gang organization: Department of Physics, Nanjing University – sequence: 2 givenname: Yi-Jian surname: Du fullname: Du, Yi-Jian email: yjdu@fudan.edu.cn organization: Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Department of Physics and Astronomy, University of Utah
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Snippet	A bstract In this paper, we investigate tree-level scattering amplitude relations in U( N ) non-linear sigma model. We use Cayley parametrization. As was shown... In this paper, we investigate tree-level scattering amplitude relations in U( N ) non-linear sigma model. We use Cayley parametrization. As was shown in the... In this paper, we investigate tree-level scattering amplitude relations in U(N) non-linear sigma model. We use Cayley parametrization. As was shown in the...
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SubjectTerms	Amplitudes Classical and Quantum Gravitation Color Elementary Particles Formations High energy physics Nonlinearity Parametrization Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Relativity Theory Scattering amplitude String Theory Trees Yang-Mills theory
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Title	Amplitude relations in non-linear sigma model
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