  We explore extensions of the double copy to massive theories and find a new
cubic theory with a local double copy. We consider the nonlinear sigma model
and the special galileon theory, massless versions of which are known to be
related through the double copy. We show that by performing a Kaluza-Klein
reduction of these theories from five dimensions down to four, a double copy
relation exists between the resulting massive four-dimensional scalar field
theories. This requires the vanishing contribution of new galileon terms
arising in high dimensions. We further explore if other interactions that do
not arise from a dimensional reduction of the nonlinear sigma model could be
double copied and find a new cubic interaction which satisfies the BCJ
relations up to 5-point amplitudes.
