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
Online Access:Get full text
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Summary: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.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2014)061