Double copy in higher derivative operators of Nambu-Goldstone bosons
Ian Low, Laurentiu Rodina, Z.W. Yin
Abstract
We investigate the existence of double copy structure, or the lack thereof, in higher derivative operators for Nambu-Goldstone bosons. At the leading $\mathcal{O}({p}^{2})$, tree amplitudes of Nambu-Goldstone bosons in the adjoint representation can be (trivially) expressed as the double copy of itself and the cubic biadjoint scalar theory, through the Kawai-Lewellen-Tye bilinear kernel. At the next-to-leading $\mathcal{O}({p}^{4})$ 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 $\mathcal{O}({p}^{2})$ Nambu-Goldstone amplitudes and the $\mathrm{Yang}\text{\ensuremath{-}}\mathrm{Mills}+{\ensuremath{\phi}}^{3}$ theory, involving both gluons and gauged cubic biadjoint scalars. The specific operator turns out to coincide with the scalar $\mathcal{O}({p}^{4})$ operator in the so-called extended Dirac-Born-Infeld theory, for which the aforementioned double copy relation holds more generally.