Abstract
In this paper, we investigate the color-kinematics duality in nonlinear sigma model (NLSM). We present explicit polynomial expressions for the kinematic numerators (BCJ numerators). The calculation is done separately in two parametrization schemes of the theory using Kawai-Lewellen-Tye relation inspired technique, both lead to polynomial numerators. We summarize the calculation in each case into a set of rules that generates BCJ numerators for all multilplicities. In Cayley parametrization we find the numerator is described by a particularly simple formula solely in terms of momentum kernel.
Highlights
Double-copy formula reproduces gravity amplitude [1, 7]
In this paper, we investigate the color-kinematics duality in nonlinear sigma model (NLSM)
The focus of this paper is on the nonlinear sigma model (NLSM), described by the chiral Lagrangian originally designed to capture the phenomenological behavior of the Golstone bosons corresponding to the G × G → G isospin symmetry breaking
Summary
We briefly review color-kinematics duality and amplitude relations in nonlinear sigma model necessary for the discussions in this paper. N) factorizes into products of a color-dressed scalar amplitude A(n, σ2,n−1, 1) and a color-ordered Yang-Mills amplitude A(1, ρ2,n−1, n) [53]. Both eq (2.1) and eq (2.2) treat the color scalar and the color-ordered Yang-Mills amplitudes . In viewing of the fact that the same algebraic properties are shared between color and kinematic structures, it is natural to expect that various BCJ-dual color decompositions describe Yang-Mills amplitude. In particular it can be decomposed using half ladder kinematic factors n1|σ(2,...,n−1)|n,. To the decomposition illustrated in [54], which we shall refer to as the dual Del Duca-Dixon-Maltoni (DDM) form in this paper
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