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:
- Publication Date:
- 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.
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
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.
@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}
}
https://doi.org/10.1103/PhysRevLett.124.111601
Web of Science
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