title: Effective Field Theories from Soft Limits of Scattering Amplitudes.
abstract: We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
authors.affiliation: Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Clifford
authors.initials: C
authors.lastname: Cheung
authors.affiliation: Institute of Particle and Nuclear Physics, Charles University in Prague, Prague, Czech Republic.
authors.forename: Karol
authors.initials: K
authors.lastname: Kampf
authors.affiliation: Institute of Particle and Nuclear Physics, Charles University in Prague, Prague, Czech Republic.
authors.forename: Jiri
authors.initials: J
authors.lastname: Novotny
authors.affiliation: Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Jaroslav
authors.initials: J
authors.lastname: Trnka