Completing the one-loop $\nu$SMEFT Renormalization Group Evolution

In this work we consider the Standard Model Effective Field Theory extended with right-handed neutrinos, the $\nu$SMEFT, and calculate the full set of one-loop anomalous dimensions that are proportional to Yukawa couplings. These contributions are particularly relevant when symmetry-protected low scale seesaw models are embeded in the SMEFT, since large neutrino Yukawa couplings are expected. By combining our results with the already available gauge anomalous dimensions, we provide the complete set of one-loop renormalization group evolution equations for the dimension six $\nu$SMEFT. As a possible phenomenological implication of our results, we discuss the sensitivity of lepton flavor-violating observables to $\nu$SMEFT operators, focusing on the more sensitive $\mu\to e$ transitions.