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

Abstract

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.