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Title: Analysis of general power counting rules in effective field theory

We derive the general counting rules for a quantum effective field theory (EFT) in d dimensions. The rules are valid for strongly and weakly coupled theories, and they predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of the cross sections is controlled by the Λ power counting of EFT, not by chiral counting, even for chiral perturbation theory (χPT). The relation between Λ and f is generalized to d dimensions. We show that the naive dimensional analysis 4π counting is related to ℏ counting. The EFT counting rules are applied to χPT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.
Authors:
 [1] ;  [2] ;  [2] ;  [1]
  1. Autonomous Univ. of Madrid (Spain). Inst. of Theoretical Physics
  2. Univ. of California, San Diego, CA (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Publication Date:
Grant/Contract Number:
SC0009919; 340282; 340281; SEV-2012-0249; PITN-GA-2011-289442; H2020-MSCA-ITN-2015-674896; H2020- MSCA-RISE-2015-690575; FPA2012-31880
Type:
Accepted Manuscript
Journal Name:
European Physical Journal. C, Particles and Fields
Additional Journal Information:
Journal Volume: 76; Journal Issue: 9; Journal ID: ISSN 1434-6044
Publisher:
Springer
Research Org:
Univ. of California, San Diego, CA (United States); Autonomous Univ. of Madrid (Spain); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Simons Foundation (United States); Ministry of Economy and Competitiveness (MINECO) (Spain); European Union (EU); Interministerial Commission of Science and Technology (CICYT) (Spain)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
OSTI Identifier:
1437365

Gavela, Belen, Jenkins, Elizabeth E., Manohar, Aneesh V., and Merlo, Luca. Analysis of general power counting rules in effective field theory. United States: N. p., Web. doi:10.1140/epjc/s10052-016-4332-1.
Gavela, Belen, Jenkins, Elizabeth E., Manohar, Aneesh V., & Merlo, Luca. Analysis of general power counting rules in effective field theory. United States. doi:10.1140/epjc/s10052-016-4332-1.
Gavela, Belen, Jenkins, Elizabeth E., Manohar, Aneesh V., and Merlo, Luca. 2016. "Analysis of general power counting rules in effective field theory". United States. doi:10.1140/epjc/s10052-016-4332-1. https://www.osti.gov/servlets/purl/1437365.
@article{osti_1437365,
title = {Analysis of general power counting rules in effective field theory},
author = {Gavela, Belen and Jenkins, Elizabeth E. and Manohar, Aneesh V. and Merlo, Luca},
abstractNote = {We derive the general counting rules for a quantum effective field theory (EFT) in d dimensions. The rules are valid for strongly and weakly coupled theories, and they predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of the cross sections is controlled by the Λ power counting of EFT, not by chiral counting, even for chiral perturbation theory (χPT). The relation between Λ and f is generalized to d dimensions. We show that the naive dimensional analysis 4π counting is related to ℏ counting. The EFT counting rules are applied to χPT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.},
doi = {10.1140/epjc/s10052-016-4332-1},
journal = {European Physical Journal. C, Particles and Fields},
number = 9,
volume = 76,
place = {United States},
year = {2016},
month = {9}
}