Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons

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 bi-adjoint 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 Yang-Mills+$\ddot{I}{•}^3$ theory, involving both gluons and gauged cubic bi-adjoint 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.

26 pages + appendices, 4 figures; typos fixed in v3