Abstract
We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos (νSMEFT). 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 benefit for cross-checks. As byproducts of this work, we provide for the first time: (i) a complete off-shell basis for the νSMEFT and explicit relations between operators linked by equations of motion; (ii) a complete basis for the low-energy effective field theory (νLEFT) and the tree-level matching onto the νSMEFT; (iii) partial one-loop anomalous dimensions in the νLEFT. This way, our work comprises a new step forward towards the systematisation of one-loop computations in effective field theories, especially if the SM neutrinos are Dirac.
Highlights
We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos
As byproducts of this work, we provide for the first time: (i) a complete off-shell basis for the νSMEFT and explicit relations between operators linked by equations of motion; (ii) a complete basis for the low-energy effective field theory and the tree-level matching onto the νSMEFT; (iii) partial one-loop anomalous dimensions in the νLEFT
If N is Majorana, new Higgs decays not yet studied experimentally at the LHC can test this model better than other studies already performed at low-energy facilities; most importantly, searches for Z → ννγγ. This observation is relatively straightforward in the generic EFT, because constrained operators can be set to zero independently of those triggering the signal of interest, this is highly non-trivial in the EFT obtained in this model, in which all Wilson coefficients depend on solely four arbitrary couplings
Summary
We consider the SM extended with a light RH fermionic singlet N , as well as two heavy vector-like fermions XE ∼ (1, 2)1/2, XN ∼ (1, 1) and a heavy singly-charged scalar φ ∼ (1, 1)−1. The operators in grey can be removed from the action by suitable field redefinitions which, up to dimension-eight effects, can be implemented by using the equations of motion [51,52,53]. (The top Yukawa coupling is not negligible; its only impact would be the generation of four-fermion operators involving top quarks and N , for which there are no sensible searches.) As a consequence, the following. Let us note that, in light of these equations, effective operators involving N do not generate any purely SMEFT operators upon using the equations of motion
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