2013/09/03 by Elizabeth Jenkins, Elizabeth E. Jenkins, Aneesh V. Manohar +1 · 1 citation
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Combinatorics #Constant (computer programming) #Coupling (piping) #Coupling constant #Dimension (graph theory) #Field (mathematics) #Field theory (psychology) #Gauge (firearms) #Gauge theory #Mathematical physics #Mathematics #Operator (biology) #Order (exchange) #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Scattering #Scattering amplitude #hep-ph #hep-th
paper · pdf · doi:10.1016/j.physletb.2013.09.020
published as Phys.Lett. B726 (2013) 697 - 702 · 10 pages, 1 fig
arxiv created 2013/09/03 · openalex publication_date 2013/09/26 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an operator is defined in this paper, and the general NDA formula for perturbative order N is derived. The formula is used to explain why the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model effective field theory has entries with perturbative order ranging from 0 to 4. The results in this paper are valid for an arbitrary effective field theory, and they constrain the coupling constant dependence of anomalous dimensions and scattering amplitudes in a general effective field theory.