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Matching a full theory onto an effective field theory (EFT) by integrating out heavy fields is often useful for connecting low-energy phenomenology to high-scale physics. I introduce a new formulation of one-loop matching in terms of "covariant diagrams," which, unlike conventional Feynman diagrams, preserve gauge covariance and thus simplify calculations. Starting from a set of simple rules, I will demonstrate the use of covariant diagrams with examples. I will also discuss an interesting universal structure of one-loop effective Lagrangians revealed by such calculations.
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