Intersections of twisted forms: New theories and double copies

Tree–level scattering amplitudes of particles have a geometrical description in terms intersection numbers pairs twisted differential forms on the moduli space Riemann spheres with punctures. We customize catalog containing both already known and new forms. By pairing elements from this list various theories can be furnished to compute their amplitudes. Some latter are familiar through CHY description, but others unknown. Likewise, certain pairings give rise novel double–copy constructions spin–two theories. This way we find double copy for many theories, including higher derivative gravity, (partial massless) bimetric gravity some more exotic Furthermore, present derivation amplitude relations theory.