Energy-enhanced expansion of the standard model effective field theory

We formalize energy-scaling arguments in the standard model effective field theory (SMEFT) to estimate the effects of operators up to dimension ten. Our approach relies on weakly coupled UV completions with no presumed large hierarchies between the Wilson coefficients. We introduce a classification based on the number of external legs and an energy-counting parameter. We establish a dual expansion in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>v</a:mi><a:mo>/</a:mo><a:mi mathvariant="normal">Λ</a:mi></a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>E</d:mi><d:mo>/</d:mo><d:mi mathvariant="normal">Λ</d:mi></d:math>. Extending to four-, five-, and six-particle vertices, our framework highlights energy-enhanced operators that dominate high-energy processes at the High Luminosity-Large Hadron Collider. This organization streamlines experimental analyses to only include operators with energetic impact in their analyses and enhances the discoverability of new physics within the SMEFT framework.