Loop counting matters in SMEFT

Abstract

We show that, in addition to the counting of canonical dimensions, a counting of loop orders is necessary to fully specify the power counting of Standard Model Effective Field Theory (SMEFT). Using concrete examples, we demonstrate that considering the canonical dimensions of operators alone may lead to inconsistent results. The counting of both, canonical dimensions and loop orders, establishes a clear hierarchy of the terms in SMEFT. In practice, this serves to identify, and focus on, the potentially dominating effects in any given high-energy process in a meaningful way. Additionally, this will lead to a consistent limitation of free parameters in SMEFT applications.

27 pages, 2 figures; references and minor comments added, version published in SciPost

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• Complete two-loop Yukawa-induced running of the Higgs-gluon coupling in SMEFT
• Two loops, four tops and two ${\gamma }_5$ schemes: a renormalization story
• Exploring Higgs EFT in $t\bar{t}hh$ at High Luminosity LHC