Effective Field Theories from Soft Limits

Understand

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 Galileons.
• 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.