New Soft Theorems for Goldstone-Boson Amplitudes

Kampf, Karol; Novotny, Jiri; Shifman, Mikhail; Trnka, Jaroslav

doi:10.1103/PhysRevLett.124.111601

Title: New Soft Theorems for Goldstone-Boson Amplitudes

Abstract

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($$\textit{N}$$)/SU($$\textit{N}$$ – 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.

Authors:

;

; Shifman, Mikhail; Trnka, Jaroslav

Publication Date:: 2020-03-18

Research Org.:: Univ. of California, Davis, CA (United States); Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Czech Science Foundation (GACR)

OSTI Identifier:: 1605321

Alternate Identifier(s):: OSTI ID: 1802009; OSTI ID: 1834295

Grant/Contract Number:: SC0009999; SC0011842

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 124 Journal Issue: 11; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Physics; Quantum field theory; Scattering amplitudes; Sigma models

Citation Formats


                    Kampf, Karol, Novotny, Jiri, Shifman, Mikhail, and Trnka, Jaroslav. New Soft Theorems for Goldstone-Boson Amplitudes.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevLett.124.111601.

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                    Kampf, Karol, Novotny, Jiri, Shifman, Mikhail, & Trnka, Jaroslav. New Soft Theorems for Goldstone-Boson Amplitudes.  United States.  https://doi.org/10.1103/PhysRevLett.124.111601

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                    Kampf, Karol, Novotny, Jiri, Shifman, Mikhail, and Trnka, Jaroslav. Wed .  
"New Soft Theorems for Goldstone-Boson Amplitudes".  United States.  https://doi.org/10.1103/PhysRevLett.124.111601.

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@article{osti_1605321,

  title        = {New Soft Theorems for Goldstone-Boson Amplitudes},

  author       = {Kampf, Karol and Novotny, Jiri and Shifman, Mikhail and Trnka, Jaroslav},

  abstractNote = {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($\textit{N}$)/SU($\textit{N}$ – 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.},

  doi          = {10.1103/PhysRevLett.124.111601},

  journal      = {Physical Review Letters},

  number       = 11,

  volume       = 124,

  place        = {United States},

  year         = {2020},

  month        = {3}

}

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Title: New Soft Theorems for Goldstone-Boson Amplitudes

Abstract

Citation Formats

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Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models journal, August 1979

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New recursion relations for tree amplitudes of gluons journal, May 2005

Simple recursion relations for general field theories journal, June 2015

On-Shell Recursion Relations for Effective Field Theories journal, January 2016

Scattering of Massless Particles in Arbitrary Dimensions journal, October 2014

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM journal, July 2015

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Uniqueness from gauge invariance and the Adler zero journal, September 2019

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A renormalization-group study of helimagnets in D = 2 + ϵ dimensions journal, November 1993

Exact factorized S-matrix of the chiral field in two dimensions journal, July 1984

Soft bootstrap and effective field theories journal, November 2019

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A periodic table of effective field theories journal, February 2017

Scattering Amplitudes from Soft Theorems and Infrared Behavior journal, February 2019

Algebraic Aspects of Pionic Duality Diagrams journal, March 1970

New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order journal, April 2016

UV considerations on scattering amplitudes in a web of theories journal, December 2019

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Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance journal, June 2018

On the theory of nonabelian goldstone bosons in two dimensions; exact solution of the SU(N) ⊗ SU(N) nonlinear σ model journal, June 1984

Extensions of theories from soft limits journal, June 2016

Exact solution of the O(3) nonlinear σ-model journal, March 1985

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Unifying relations for scattering amplitudes journal, February 2018

Theory of nonabelian goldstone bosons in two dimensions journal, November 1983

Sigma models on fiber bundles with a Grassmannian base space journal, February 2020

Effective Field Theories from Soft Limits of Scattering Amplitudes journal, June 2015

Soft bootstrap and supersymmetry journal, January 2019

On-shell constructibility of tree amplitudes in general field theories journal, April 2011

Soft dilatons and scale renormalization in dual theories journal, August 1975

Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory journal, May 2005

Nonuniversality in helical and canted-spin systems journal, June 1990

Tree-level amplitudes in the nonlinear sigma model journal, May 2013

Exploring soft constraints on effective actions
journal, October 2016

Recursion relations from soft theorems
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Vector Effective Field Theories from Soft Limits
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Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
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Renormalization of dual models
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New recursion relations for tree amplitudes of gluons
journal, May 2005

Simple recursion relations for general field theories
journal, June 2015

On-Shell Recursion Relations for Effective Field Theories
journal, January 2016

Scattering of Massless Particles in Arbitrary Dimensions
journal, October 2014

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
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Higher-order tree-level amplitudes in the nonlinear sigma model
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Uniqueness from gauge invariance and the Adler zero
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Modular forms and SL(2, ℤ)-covariance of type IIB superstring theory
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A renormalization-group study of helimagnets in D = 2 + ϵ dimensions
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Exact factorized S-matrix of the chiral field in two dimensions
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Soft bootstrap and effective field theories
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Scattering Amplitudes from Soft Theorems and Infrared Behavior
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Algebraic Aspects of Pionic Duality Diagrams
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New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order
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Sigma models on fiber bundles with a Grassmannian base space
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Effective Field Theories from Soft Limits of Scattering Amplitudes
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Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory
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Nonuniversality in helical and canted-spin systems
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