Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons

TL;DR

This paper explores the double copy structure in higher derivative operators of Nambu-Goldstone bosons, revealing specific operators where the double copy relation holds at different derivative orders, including connections to extended Dirac-Born-Infeld theory.

Contribution

It identifies operators in higher derivative Nambu-Goldstone boson theories that exhibit double copy structures and flavor-kinematics duality, extending the understanding of these relations beyond leading order.

Findings

At leading order, Nambu-Goldstone boson amplitudes are trivially double copied.

At next-to-leading order, one operator exhibits flavor-kinematics duality and double copy structure.

The identified operator coincides with a scalar operator in extended Dirac-Born-Infeld theory.

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.