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, lowenergy weak interactions, Standard Model EFT and the nontrivial case of Higgs EFT.
 Authors:

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^{[1]}
 Autonomous Univ. of Madrid (Spain). Inst. of Theoretical Physics
 Univ. of California, San Diego, CA (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
 Publication Date:
 Grant/Contract Number:
 SC0009919; 340282; 340281; SEV20120249; PITNGA2011289442; H2020MSCAITN2015674896; H2020 MSCARISE2015690575; FPA201231880
 Type:
 Accepted Manuscript
 Journal Name:
 European Physical Journal. C, Particles and Fields
 Additional Journal Information:
 Journal Volume: 76; Journal Issue: 9; Journal ID: ISSN 14346044
 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) (SC25); 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/s1005201643321.
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/s1005201643321.
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/s1005201643321. 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, lowenergy weak interactions, Standard Model EFT and the nontrivial case of Higgs EFT.},
doi = {10.1140/epjc/s1005201643321},
journal = {European Physical Journal. C, Particles and Fields},
number = 9,
volume = 76,
place = {United States},
year = {2016},
month = {9}
}