high-energy theoretical physics

NLSM amplitudes from a quartic two-derivative theory

arXiv:2607.27345

summary

The paper presents a local scalar Lagrangian with a single quartic two-derivative interaction that exactly reproduces planar nonlinear sigma model (NLSM) amplitudes at all loop orders, simplifying the computation of high-multiplicity scattering processes.

Abstract

We revisit the well-known nonlinear sigma model (NLSM), an effective field theory describing the scattering of Goldstone bosons and characterized by an infinite tower of two-derivative interactions. We introduce a local scalar Lagrangian involving two scalar fields carrying opposite "polarities", whose interacting part consists of a single polynomial quartic two-derivative operator, and prove that it reproduces planar NLSM amplitudes at all loop orders. This quartic two-derivative formulation reveals a previously hidden simplicity of the NLSM: its Feynman rules involve only a single quartic interaction vertex, making the Adler zero and the leading double-soft factor manifest at all loop orders on generalized cuts and significantly improving the efficiency of high-multiplicity computations. We also suggest a possible analogous description of the NLSM + theory in terms of a finite tower of local interactions.

12 pages, 14 figures

Topics & keywords

#nonlinear sigma model#scattering amplitudes#effective field theory#quartic interaction#loop calculations#soft theoremsSU(N) Goldstone bosonstwo-derivative operatorplanar limitAdler zerodouble-soft factorFeynman rules
NLSM amplitudes from a quartic two-derivative theory · wovepaper