Double copy for massive scalar field theories

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