Effective Field Theories from Soft Limits of Scattering Amplitudes
Abstract
Here, we derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Furthemore, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
- Authors:
-
- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
- Charles Univ., Prague (Czech Republic). Inst. of Particle and Nuclear Physics
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1596701
- Alternate Identifier(s):
- OSTI ID: 1183796
- Grant/Contract Number:
- SC0011632; SC0010255
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 114; Journal Issue: 22; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, and Trnka, Jaroslav. Effective Field Theories from Soft Limits of Scattering Amplitudes. United States: N. p., 2015.
Web. doi:10.1103/PhysRevLett.114.221602.
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, & Trnka, Jaroslav. Effective Field Theories from Soft Limits of Scattering Amplitudes. United States. https://doi.org/10.1103/PhysRevLett.114.221602
Cheung, Clifford, Kampf, Karol, Novotny, Jiri, and Trnka, Jaroslav. Fri .
"Effective Field Theories from Soft Limits of Scattering Amplitudes". United States. https://doi.org/10.1103/PhysRevLett.114.221602. https://www.osti.gov/servlets/purl/1596701.
@article{osti_1596701,
title = {Effective Field Theories from Soft Limits of Scattering Amplitudes},
author = {Cheung, Clifford and Kampf, Karol and Novotny, Jiri and Trnka, Jaroslav},
abstractNote = {Here, we derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Furthemore, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.},
doi = {10.1103/PhysRevLett.114.221602},
journal = {Physical Review Letters},
number = 22,
volume = 114,
place = {United States},
year = {Fri Jun 05 00:00:00 EDT 2015},
month = {Fri Jun 05 00:00:00 EDT 2015}
}
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