Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory

A bstract Tree-level color-ordered Yang-Mills (YM) amplitudes can be decomposed in terms of ( n − 2)! bi-scalar (BS) amplitudes, whose expansion coefficients form a basis of Bern-Carrasco-Johansson (BCJ) numerators. By the help of the recursive expansion of Einstein-Yang-Mills (EYM) amplitudes, the...

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Vydáno v:The journal of high energy physics Ročník 2022; číslo 1; s. 1 - 50
Hlavní autoři: Wu, Konglong, Du, Yi-Jian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2022
Springer Nature B.V
SpringerOpen
Témata:
Amplitudes
Antisymmetry
Classical and Quantum Gravitation
Decomposition
Elementary Particles
Functions (mathematics)
Gauge Symmetry
High energy physics
Mathematical analysis
Physics
Physics and Astronomy
Polynomials
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
String Theory
Thermal expansion
Vectors (mathematics)
Yang-Mills theory
Gauge Symmetry
Scattering Amplitudes
ISSN:1029-8479, 1029-8479
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Shrnutí:A bstract Tree-level color-ordered Yang-Mills (YM) amplitudes can be decomposed in terms of ( n − 2)! bi-scalar (BS) amplitudes, whose expansion coefficients form a basis of Bern-Carrasco-Johansson (BCJ) numerators. By the help of the recursive expansion of Einstein-Yang-Mills (EYM) amplitudes, the BCJ numerators are given by polynomial functions of Lorentz contractions which are conveniently described by graphic rule. In this work, we extend the expansion of YM amplitudes to off-shell level. We define different types of off-shell extended numerators that can be generated by graphs. By the use of these extended numerators, we propose a general decomposition formula of off-shell Berends-Giele currents in YM. This formula consists of three terms: (i). an effective current which is expanded as a combination of the Berends-Giele currents in BS theory (The expansion coefficients are one type of off-shell extended numerators) (ii). a term proportional to the total momentum of on-shell lines and (iii). a term expressed by the sum of lower point Berends-Giele currents in which some polarizations and momenta are replaced by vectors proportional to off-shell momenta appropriately. In the on-shell limit, the last two terms vanish while the decomposition of effective current precisely reproduces the decomposition of on-shell YM amplitudes with the expected coefficients (BCJ numerators in DDM basis). We further symmetrize these coefficients such that the Lie symmetries are satisfied. These symmetric BCJ numerators simultaneously satisfy the relabeling property of external lines and the algebraic properties (antisymmetry and Jacobi identity).
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2022)162