Tree-level Amplitudes in the Nonlinear Sigma Model
arXiv:1304.3048 · doi:10.1007/JHEP05(2013)032
Abstract
We study in detail the general structure and further properties of the tree-level amplitudes in the SU(N) nonlinear sigma model. We construct the flavor-ordered Feynman rules for various parameterizations of the SU(N) fields U(x), write down the Berends-Giele relations for the semi-on-shell currents and discuss their efficiency for the amplitude calculation in comparison with those of renormalizable theories. We also present an explicit form of the partial amplitudes up to ten external particles. It is well known that the standard BCFW recursive relations cannot be used for reconstruction of the the on-shell amplitudes of effective theories like the SU(N) nonlinear sigma model because of the inappropriate behavior of the deformed on-shell amplitudes at infinity. We discuss possible generalization of the BCFW approach introducing "BCFW formula with subtractions" and with help of Berends-Giele relations we prove particular scaling properties of the semi-on-shell amplitudes of the SU(N) nonlinear sigma model under specific shifts of the external momenta. These results allow us to define alternative deformation of the semi-on-shell amplitudes and derive BCFW-like recursion relations. These provide a systematic and effective tool for calculation of Goldstone bosons scattering amplitudes and it also shows the possible applicability of on-shell methods to effective field theories. We also use these BCFW-like relations for the investigation of the Adler zeroes and double soft limit of the semi-on-shell amplitudes.
57 pages, 14 figures
References in corpus (8)
- Gluon scattering amplitudes at strong coupling
- The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
- Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
- The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
- Precise Predictions for W + 4 Jet Production at the Large Hadron Collider
- On-shell constructibility of tree amplitudes in general field theories
- Boundary Contributions Using Fermion Pair Deformation
- Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
Cited by in corpus (66)
- Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
- On-Shell Recursion Relations for Effective Field Theories
- A Periodic Table of Effective Field Theories
- Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- Extensions of Theories from Soft Limits
- Non-abelian -theory: Berends-Giele recursion for the -expansion of disk integrals
- Soft Bootstrap and Supersymmetry
- Amplitude Relations in Non-linear Sigma Model
- Higher-spin massless S-matrices in four-dimensions
- Semi-abelian Z-theory: NLSM+phi^3 from the open string
- New Double Soft Emission Theorems
- Locality and Unitarity from Singularities and Gauge Invariance
- Covariant Color-Kinematics Duality
- On the kinematic algebra for BCJ numerators beyond the MHV sector
- Perturbiner Methods for Effective Field Theories and the Double Copy
- Scattering Amplitudes from Soft Theorems and Infrared Behavior
- Twofold Symmetries of the Pure Gravity Action
- Pions as Gluons in Higher Dimensions
- Geometric Soft Theorems
- Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions
- Amplitudes meet Cosmology: A (Scalar) Primer
- Tree-level amplitudes from the pure spinor superstring
- UV considerations on scattering amplitudes in a web of theories
- New Soft Theorems for Goldstone Boson Amplitudes
- Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Models
- Soft Bootstrap and Effective Field Theories
- Double-soft behavior of the dilaton of spontaneously broken conformal invariance
- New structures in scattering amplitudes: a review
- Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models
- The Infrared Structure of Nambu-Goldstone Bosons
- On single and double soft behaviors in NLSM
- Towards Color-Kinematics Duality in Generic Spacetimes
- Smoothly Splitting Amplitudes and Semi-Locality
- Uniqueness from gauge invariance and the Adler zero
- Anomalous Dimensions of Effective Theories from Partial Waves
- Radiation of scalar modes and the classical double copy
- Shift symmetries, soft limits, and the double copy beyond leading order
- Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
- Soft theorems from anomalous symmetries
- Effective Field Theories and Cosmological Scattering Equations
- Operator Counting and Soft Blocks in Chiral Perturbation Theory
- One-loop renormalization in Galileon effective field theory
- The B-field soft theorem and its unification with the graviton and dilaton
- No Particle Production in Two Dimensions: Recursion Relations and Multi-Regge Limit
- Universal Relations in Composite Higgs Models
- Soft limits of the wavefunction in exceptional scalar theories
- The Infrared Structure of Exceptional Scalar Theories
- Higher-order tree-level amplitudes in the nonlinear sigma model
- All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
- Amplitude/Operator Basis in Chiral Perturbation Theory
- Multi-spin soft bootstrap and scalar-vector Galileon
- The ChPT: top-down and bottom-up
- Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
- Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
- Hilbert series and higher-order Lagrangians for the model
- Soft Phonon Theorems
- New Factorization Relations for Non-Linear Sigma Model Amplitudes
- Leading order multi-soft behaviors of tree amplitudes in NLSM
- Scattering Equations and Factorization of Amplitudes II: Effective Field Theories
- Six-meson amplitude in QCD-like theories
- UV consistency conditions for CHY integrands
- Non-perturbative quantum Galileon in the exact renormalization group
- Soft-Theorems for Scalar Particles: The Dilatons Story
- Extended DBI and its generalizations from graded soft theorems
- Soft unification of exceptional effective field theories in de Sitter space
- Geometric duality between effective field theories I: scattering amplitudes