New Soft Theorems for Goldstone-Boson Amplitudes.

In this Letter we discuss new soft theorems for the Goldstone-boson amplitudes with nonvanishing soft limits. The standard argument is that the nonlinearly realized shift symmetry leads to the vanishing of scattering amplitudes in the soft limit, known as the Adler zero. This statement involves certain assumptions of the absence of cubic vertices and the absence of linear terms in the transformations of fields. For theories which fail to satisfy these conditions, we derive a new soft theorem which involves certain linear combinations of lower point amplitudes, generalizing the Adler zero statement. We provide an explicit example of the SU(N)/SU(N-1) sigma model which was also recently studied in the context of U(1) fibrated models. The soft theorem can be then used as an input into the modified soft recursion relations for the reconstruction of all tree-level amplitudes.

Precise Determination of the Branching Ratio of the Neutral-Pion Dalitz Decay.

We provide a new value for the ratio R=Γ(π^{0}→e^{+}e^{-}γ(γ))/Γ(π^{0}→γγ)=11.978(6)×10^{-3}, which is by 2 orders of magnitude more precise than the current Particle Data Group average. It is obtained using the complete set of the next-to-leading-order radiative corrections in the QED sector, and incorporates up-to-date values of the π^{0}-transition-form-factor slope. The ratio R translates into the branching ratios of the two main π^{0} decay modes: B(π^{0}→γγ)=98.8131(6)% and B(π^{0}→e^{+}e^{-}γ(γ))=1.1836(6)%.

Vector Effective Field Theories from Soft Limits.

We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions. These soft properties imply new recursion relations for on-shell scattering amplitudes in BI theory and suggest the existence of a wider class of vector effective field theories.

On-Shell Recursion Relations for Effective Field Theories.

We 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.

Effective Field Theories from Soft Limits of Scattering Amplitudes.

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.