2016/01/31 by M. B. Gavela, Belén Gavela, E. E. Jenkins +5 · 1 citation
Mathematics · Physics and Astronomy · #Counting problem #Discrete mathematics #Effective field theory #Higgs boson #High-Energy Particle Collisions Research #Lambda #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Quantum mechanics #Statistical physics #hep-ph
paper · pdf · doi:10.1140/epjc/s10052-016-4332-1
published as Eur. Phys. J. C (2016) 76:485 · V2: more details and examples added; version published in journal. 17 pages, 4 figures, 2 tables
openalex created_date 2016/06/24 · openalex publication_date 2016/09/01 · arxiv created 2016/09/09 · arxiv updated 2016/09/12 · openalex updated_date 2026/08/06
Abstract We derive the general counting rules for a quantum effective field theory (EFT) in \mathsf d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> power counting of EFT, not by chiral counting, even for chiral perturbation theory ( χ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> PT). The relation between Λ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> and f is generalized to \mathsf d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>d</mml:mi> </mml:math> dimensions. We show that the naive dimensional analysis 4π <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> counting is related to ℏ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ħ</mml:mi> </mml:math> counting. The EFT counting rules are applied to χ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.