# Heavy RH Majorana Neutrinos coupled via mixing¶

Jon Butterworth

A study of a model [74] with three Right-Handed heavy Majorana neutrinos which couple in to the SM only by mixing with the active neutrinos. The UFO files came from the Feynrules model library (see [70][107]).

There are in principle three heavy neutrinos in this model, but we follow [70] and set two to very high masses, effectively decoupling them. The key parameters of the model are then the mixing of the remaining heavy neutrino with the three SM neutrino flavour eigenstates. Again following [70], we set the mixing to the second and third generations to the upper limits allowed by ElectroWeak precision data [108]: $$|V_{\mu N}|^2 < 3.2 \times 10^{−3}, |V_{\tau N}|^2 < 6.2 \times 10^{−3}$$ at 90% C.L., and scan in the plane of neutrino mass $$M_{\nu H}$$ and the mixing with the first generation. This mixing is constrained by neutrinoless double-beta decay, and this constraint is indicated on the plot.

The sensitivities derived from multiple measured distributions are combined into heatmaps which delineate the sensitivity of the SM measurements to this model in the parameter space of $$V_{eN}$$and $$M_{\nu H}$$. In th contour plot, the line and blue shaded region indicate the region excluded by neutrinoless double beta decay, the pink region is disfavoured by LHC measurements at the 90% c.l..

Heatmap and contour for all available data (measurements from 7, 8 and 13 TeV runs in Rivet as of 1/5/2019)

There is only sensitivity at low masses, much lower than those considered in [70], where they focussed on future measurements and concentrated on the range $$300 < M_{\nu H} < 1000$$ GeV.

No significant dependence on the electron-neutrino mixing is observed: in fact all the values allowed here are so small that the electron contribution is negligible. The sensitivity that is present comes from the muonic channels, principally the dimuon measurements away from the Z pole, for example the figure below, from [56].

Note that these results currently do not include the photon-induced processes (considered in [70]), which generally contribute around 20% to the cross-section, with somewhat different final state kinematics.

The model files are available in the SM_HeavyN_NLO directory here .