One-loop matching in the SMEFT extended with a sterile neutrino

We are grateful to Jose Santiago for helpful discussions. MC is supported by the Spanish MINECO under the Juan de la Cierva programme.We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective eld theory of the Standard Model extended with right-handed neutrinos (SMEFT). Our aim is twofold. First, to contextualise new collider signatures in models with sterile neutrinos so far studied only using the bottom-up approach. And second and more important, to provide a thorough example of one-loop matching in the diagrammatic approach, of which other matching techniques and automatic tools can bene t for cross-checks. As byproducts of this work, we provide for the rst time: (i) a complete off-shell basis for the vSMEFT and explicit relations between operators linked by equations of motion; (ii) a complete basis for the low-energy e ective eld theory (vLEFT) and the tree-level matching onto the vSMEFT; (iii) partial one-loop anomalous dimensions in the vLEFT. This way, our work comprises a new step forward towards the systematisation of one-loop computations in effective eld theories, especially if the SM neutrinos are Dirac.Spanish MINECO under the Juan de la Cierva programm