Abstract: We provide a complete systematic classification of all two-loop realizations of the dimension four operator for Dirac neutrino masses. Our classification is multi-layered, starting first with a classification in terms of all possible distinct two loop topologies. Then we discuss the possible diagrams for each topology. Model-diagrams originating from each diagram are then considered. The criterion for genuineness is also defined and discussed at length. Finally, as examples, we construct two explicit models which also serve to highlight the intimate connection between the Dirac nature of neutrinos and the stability of dark matter.

Abstract: The framed Standard Model (FSM) predicts a 0(+) boson with mass around 20 MeV in the “hidden sector,” which mixes at tree level with the standard Higgs hW and hence acquires small couplings to quarks and leptons which can be calculated in the FSM apart from the mixing parameter rho Uh. The exchange of this mixed state U will contribute to g – 2 and to the Lamb shift. By adjusting rho Uh alone, it is found that the FSM can satisfy all present experimental bounds on the g – 2 and Lamb shift anomalies for μand e, and for the latter for both hydrogen and deuterium. The FSM predicts also a 1(-) boson in the “hidden sector” with a mass of 17 MeV, that is, right on top of the Atomki anomaly X. This mixes with the photon at 1-loop level and couples thereby like a dark photon to quarks and leptons. It is however a compound state and is thought likely to possess additional compound couplings to hadrons. By adjusting the mixing parameter and the X's compound coupling to nucleons, the FSM can reproduce the production rate of the X in beryllium decay as well as satisfy all the bounds on X listed so far in the literature. The above two results are consistent in that the U, being 0(+), does not contribute to the Atomki anomaly if parity and angular momentum are conserved, while X, though contributing to g – 2 and Lamb shift, has smaller couplings than U and can, at first instance, be neglected there. Thus, despite the tentative nature of the three anomalies in experiment on the one hand and of the FSM as theory on the other, the accommodation of the former in the latter has strengthened the credibility of both. Indeed, if this FSM interpretation were correct, it would change the whole aspect of the anomalies from just curiosities to windows into a vast hitherto hidden sector comprising at least in part the dark matter which makes up the bulk of our universe.

Abstract: If neutrinos are Dirac particles and, as suggested by the so far null LHC results, any new physics lies at energies well above the electroweak scale, the Standard Model effective field theory has to be extended with operators involving the right-handed neutrinos. In this paper, we study this effective field theory and set constraints on the different dimension-six interactions. To that aim, we use LHC searches for associated production of light (and tau) leptons with missing energy, monojet searches, as well as pion and tau decays. Our bounds are generally above the TeV for order one couplings. One particular exception is given by operators involving top quarks. These provide new signals in top decays not yet studied at colliders. Thus, we also design an LHC analysis to explore these signatures in the tt production. Our results are also valid if the right-handed neutrinos are Majorana and long-lived.