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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:
ORCiD logo; ORCiD logo; ;
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevLett.124.111601

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