BCJ numerators from reduced Pfaffian

A bstract By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensi...

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Vydáno v:The journal of high energy physics Ročník 2017; číslo 4; s. 1 - 28
Hlavní autoři: Du, Yi-Jian, Teng, Fei
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017
Springer Nature B.V
SpringerOpen
Témata:
Classical and Quantum Gravitation
Color
Elementary Particles
Field theory
Gauge Symmetry
Graph theory
High energy physics
Nonlinearity
Particle physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
Rule based
Scattering Amplitudes
String Theory
Trees
Gauge Symmetry
Scattering Amplitudes
ISSN:1029-8479, 1029-8479
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Shrnutí:A bstract By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the ( n − 2)! DDM form BCJ numerators contains exactly ( n − 1)! terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most ( n − 2)! − ( n − 3)!, less than those of several previous constructions.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2017)033