  We expose a double-copy structure in the scattering amplitudes of the generic
Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
theories in four and five dimensions. The Maxwell-Einstein supergravity
amplitudes are obtained through the color/kinematics duality as a product of
two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory
and the other from the dimensional reduction of a bosonic higher-dimensional
pure Yang-Mills theory. We identify a specific symplectic frame in four
dimensions for which the on-shell fields and amplitudes from the double-copy
construction can be identified with the ones obtained from the supergravity
Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity
theories are obtained by gauging a compact subgroup of the isometry group of
their Maxwell-Einstein counterparts. For the generic Jordan family this process
is identified with the introduction of cubic scalar couplings on the bosonic
gauge-theory side, which through the double copy are responsible for the
non-abelian vector interactions in the supergravity theory. As a demonstration
of the power of this structure, we present explicit computations at tree-level
and one loop. The double-copy construction allows us to obtain compact
expressions for the supergravity superamplitudes which are naturally organized
as polynomials in the gauge coupling constant.
