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Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions

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.

preprint2013arXivOpen access
Elizabeth E. JenkinsAneesh V. ManoharMichael Trott
hep-phhep-th
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Elizabeth E. JenkinsAneesh V. ManoharMichael Trott

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