  We extend the double copy picture of scattering amplitudes to a class of
matrix elements (so-called form factors) that involve local gauge invariant
operators. Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen
and Tye (KLT) formalisms are considered and novel properties are observed. One
remarkable feature is that through the double-copy construction, certain
spurious poles hidden in the gauge form factors become physical propagators in
gravity. This mechanism also reveals new hidden relations for form factors
which can be understood as a generalization of the BCJ relations.
