Analysis of general power counting rules in effective field theory

Belen Gavela; Elizabeth E. Jenkins; Aneesh V. Manohar; Luca Merlo

doi:10.1140/epjc/s10052-016-4332-1

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2016) 76: 485
https://doi.org/10.1140/epjc/s10052-016-4332-1

Regular Article - Theoretical Physics

Analysis of general power counting rules in effective field theory

Belen Gavela¹, Elizabeth E. Jenkins²^,3, Aneesh V. Manohar²^,3 and Luca Merlo¹^*

¹ Instituto de Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain
² Department of Physics, University of California at San Diego, La Jolla, CA, 92093, USA
³ CERN TH Division, 1211, Geneva 23, Switzerland

^* e-mail: luca.merlo@uam.es

Received: 13 July 2016
Accepted: 12 August 2016
Published online: 2 September 2016

Abstract

We derive the general counting rules for a quantum effective field theory (EFT) in $\mathsf {d}$ 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 $\Lambda$ power counting of EFT, not by chiral counting, even for chiral perturbation theory ( $\chi$ PT). The relation between $\Lambda$ and f is generalized to $\mathsf {d}$ dimensions. We show that the naive dimensional analysis $4\pi$ counting is related to $\hbar$ counting. The EFT counting rules are applied to $\chi$ PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.