A phenomenological study of heavy neutrinos and the seesaw mechanism

In this thesis, we review the motivations for proposing the existence of heavy neutrinos and the so-called seesaw mechanism. In particular, we show how this mechanism provides a natural explanation for the small masses of the Standard Model (SM) neutrinos. We study three specific realisations of the seesaw mechanism; two with heavy neutrinos that couple to SM bosons with the neutrinos being either Majorana or pseudo-Dirac fermions, and one version of the Left-Right Symmetric Model (LRSM) with heavy Majorana neutrinos. For each of the models we perform simulations of heavy neutrino production at the LHC, considering the three lepton and missing energy final state for the Majorana and pseudo-Dirac models and the two-lepton plus two jets (2l+2j) final state for the LRSM. For the Majorana and pseudo-Dirac models, we study neutrino masses $m_N$ in the range 200 GeV to 1200 GeV, while for the LRSM we look at models with $W_R$ boson masses $M_{W_R}$ from 3 TeV to 6 TeV, and neutrino masses that are between $M_{W_R}/2$ and $M_{W_R}$. We study the kinematics of the simulated events for the different masses, and for the three lepton final state we develop a method of identifying the lepton pair from the production and decay of the heavy neutrino that is up to $50\%$ more efficient than simply ordering the leptons by their transverse momenta $p_T$. For the 2l+2j final state, we find that the invariant mass of the four objects in the final state can be used to reconstruct $M_{W_R}$, and that the $p_T$ of the leptons can be used to estimate the mass difference between $W_R$ and the heavy neutrino. We then perform a sensitivity study for the ATLAS detector at the LHC for the three signal processes after the current Run 3 and the future HL-LHC. For the Majorana and pseudo-Dirac signals we find that they are very difficult to discover and impossible to exclude even after the entire HL-LHC run, due to the strict constraints on the mixing between the heavy neutrinos and the SM neutrinos. For the LRSM models, we find that we can improve on results from previous studies. For the case $M_{W_R}=3$ TeV we are able to put a $95\%$ CL expected upper limit on the relative right-handed coupling strength $\kappa_R$ of $\kappa_R\approx 0.2$ if no signal is seen after Run 3, and an upper limit of less than 0.1 after HL-LHC. We also find that models with masses as high as $M_{W_R}=5$ TeV and $m_N=4$ TeV can be discovered at $5\sigma$ during HL-LHC. If no signal is seen after HL-LHC, it will be possible to expand the current $95\%$ CL excluded region in the $\left(M_{W_R},m_N\right)$ parameter space up to at least (5 TeV, 4.5 TeV) and the $90\%$ CL excluded region will extend beyond (6 TeV, 4 TeV).