Abstract
We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.
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