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This study introduces new soft theorems for Goldstone-boson amplitudes, extending the Adler zero concept for theories with specific symmetries. These theorems generalize amplitude predictions and aid in reconstructing tree-level amplitudes.

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Area of Science:

  • High Energy Physics
  • Theoretical Physics
  • Quantum Field Theory

Background:

  • The Adler zero predicts vanishing scattering amplitudes in the soft limit for certain theories.
  • This prediction relies on assumptions about cubic vertices and field transformations.
  • Nonlinear realizations of shift symmetry can violate these assumptions.

Purpose of the Study:

  • To derive new soft theorems for Goldstone-boson amplitudes.
  • To generalize the Adler zero statement for theories that do not meet standard assumptions.
  • To provide a tool for reconstructing tree-level amplitudes.

Main Methods:

  • Derivation of new soft theorems for amplitudes with nonvanishing soft limits.
  • Analysis of theories with nonlinear shift symmetry.
  • Application to the SU(N)/SU(N-1) sigma model.

Main Results:

  • A generalized soft theorem is derived, involving linear combinations of lower-point amplitudes.
  • The new theorem accommodates theories with cubic vertices and linear field transformation terms.
  • The SU(N)/SU(N-1) sigma model serves as an explicit example.

Conclusions:

  • The derived soft theorems offer a broader framework for understanding Goldstone-boson amplitudes.
  • These theorems are crucial for modified soft recursion relations.
  • The findings facilitate the reconstruction of all tree-level amplitudes in relevant theories.