Clifford CheungKarol KampfJiri NovotnyChia-Hsien ShenJaroslav Trnka2024-10-092024-10-092016-01-25https://scholars.lib.ntu.edu.tw/handle/123456789/721940We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible. © 2016 American Physical Society.[SDGs]SDG10journal article10.1103/physrevlett.116.041601