Abstract
We investigate the existence of double copy structure, or the lack thereof, in higher derivative operators for Nambu-Goldstone bosons. At the leading ${\cal O}(p^2)$, tree amplitudes of Nambu-Goldstone bosons in the adjoint representation can be (trivially) expressed as the double copy of itself and the cubic bi-adjoint scalar theory, through the Kawai-Lewellen-Tye bilinear kernel. At the next-to-leading ${\cal O}(p^4)$ there exist four operators in general, among which we identify one operator whose amplitudes exhibit the flavor-kinematics duality and can be written as the double copy of ${\cal O}(p^2)$ Nambu-Goldstone amplitudes and the Yang-Mills+$\phi^3$ theory, involving both gluons and gauged cubic bi-adjoint scalars. The specific operator turns out to coincide with the scalar ${\cal O}(p^4)$ operator in the so-called extended Dirac-Born-Infeld theory, for which the aforementioned double copy relation holds more generally.
Highlights
The nonlinear sigma model (NLSM) [1,2,3] is an effective field theory (EFT) of Nambu-Goldstone bosons (NGB’s) arising from spontaneously broken symmetries
In this paper we extend the results on color-kinematics duality beyond the four-point amplitudes, to higher multiplicity, and investigate whether it is possible to construct double copy relations for the NLSM at Oðp4Þ
The color-kinematics duality of scattering amplitudes was first discovered for YM theories, the n-point tree amplitudes of which can be written in the following form [17,42]: MYn M
Summary
The nonlinear sigma model (NLSM) [1,2,3] is an effective field theory (EFT) of Nambu-Goldstone bosons (NGB’s) arising from spontaneously broken symmetries. The NLSM is a key element of the color-kinematics duality and the ensuing Bern-CarrascoJohansson (BCJ) double copy [17], as well as the CachazoHe-Yuan (CHY) formalism for S-matrix [18,19,20,21]. In the space of consistent quantum theories, the NLSM can be related to YM through transmutation operators and dimensional reduction [23,24,25] or to a biadjoint scalar through soft limits [9,26,27,28] These fascinating aspects are somewhat hidden in the traditional Lagrangian formulation. In this paper we extend the results on color-kinematics duality beyond the four-point amplitudes, to higher multiplicity, and investigate whether it is possible to construct double copy relations for the NLSM at Oðp4Þ.
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