Note on symmetric BCJ numerator

Self Cite

148

Abstract:In this paper, we study from various perspectives the expansion of tree level single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered YangMills amplitudes. By applying the gauge invariance principle, a programable recursive construction is devised to expand EYM amplitude with arbitrary number of gravitons into EYM amplitudes with fewer gravitons. Based on this recursive technique we write down the complete expansion of any single trace EYM amplitude in the basis of color-order Yang-Mills amplitude. As a byproduct, an algorithm for constructing a polynomial form of the BCJ numerator for Yang-Mills amplitudes is also outlined in this paper. In addition, by applying BCFW recursion relation we show how to arrive at the same EYM amplitude expansion from the on-shell perspective. And we examine the EYM expansion using KLT relations and show how to evaluate the expansion coefficients efficiently.

Section: )mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Expansion of Einstein-Yang-Mills amplitude

Huang

et al. 2017

Self Cite

148

“…As pointed out in [127,128] one can always symmetrize Jacobi-satisfying numerators to arrive at a crossing symmetric function for the generically dressed half-ladder topology in a manner that preserves linear relations (like Jacobi). One can note that fully crossingsymmetric local numerators of [19] were arrived at by evaluating the Berends-Giele currents in the pion parameterization scheme.…”

Section: Jhep06(2017)093mentioning

confidence: 99%

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

Carrasco

Mafra

Schlotterer

2017

144

232

In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory -the collection of putative scalar effective field theories encoding all the α ′ -expansion of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of α ′ in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The amplitude relations due to Kleiss-Kuijf as well as Bern, Johansson and one of the current authors obeyed by Z-theory amplitudes thereby apply to all α ′ -corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kinematic numerators obey the duality between color and kinematics to all orders in α ′ .

“…An interesting application of our gauge invariance induced relation is the proof of equivalence between different approaches to NLSM amplitudes. Full color-dressed NLSM amplitudes can be spanned in terms of bi-scalar amplitudes via dual Del Duca-Dixon-Maltoni (DDM) [33] decomposition (The dual DDM decomposition for Yang-Mills amplitudes are given in [11,22,[34][35][36][37][38][39][40][41], for NLSM amplitudes are provided in [8,16,23,24]), in which the coefficients are half-ladder BCJ numerators with fixing the first and the last lines. Although the three distinct approaches: Feyman rules, Abelian Z theory and CHY formula provide different types of half-ladder BCJ numerators, they must produce the same NLSM amplitudes through the dual DDM decomposition.…”

Section: Introductionmentioning

confidence: 99%

Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes

Zhang

2018

Self Cite

In this paper, we derive generalized Bern-Carrasco-Johansson (BCJ) relations for color-ordered Yang-Mills amplitudes by imposing gauge invariance conditions and dimensional reduction appropriately on the new discovered graphic expansion of EinsteinYang-Mills amplitudes. These relations are also satisfied by color-ordered amplitudes in other theories such as bi-scalar theory and nonlinear sigma model (NLSM). As an application of the gauge invariance induced relations, we further prove that the three types of BCJ numerators in NLSM, which are derived from Feynman rules, Abelian Z-theory and Cachazo-He-Yuan (CHY) formula respectively, produce the same total amplitudes. In other words, the three distinct approaches to NLSM amplitudes are equivalent to each other.