We consider the fully constrained version of the next-to-minimal supersymmetric extension of the standard model (cNMSSM) in which a singlet Higgs superfield is added to the two doublets that are present in the minimal extension (MSSM). Assuming unive
rsal boundary conditions at a high scale for the soft supersymmetry-breaking gaugino, sfermion and Higgs mass parameters as well as for the trilinear interactions, we find that the model is more constrained than the celebrated minimal supergravity model. The phenomenologically viable region in the parameter space of the cNMSSM corresponds to a small value for the universal scalar mass m_0: in this case, one single input parameter is sufficient to describe the phenomenology of the model once the available constraints from collider data and cosmology are imposed. We present the particle spectrum of this very predictive model and discuss how it can be distinguished from the MSSM.
In this paper we study $mu-e$ conversion in nuclei within the context of the Constrained Minimal Supersymmetric Standard Model, enlarged by three right handed neutrinos and their supersymmetric partners, and where the neutrino masses are generated vi
a a seesaw mechanism. Two different scenarios with either universal or non-universal soft supersymmetry breaking Higgs masses at the gauge coupling unification scale are considered. In the first part we present a complete one-loop computation of the conversion rate for this process that includes the photon-, $Z$-boson, and Higgs-boson penguins, as well as box diagrams, and compare their size in the two considered scenarios. Then, in these two scenarios we analyse the relevance of the various parameters on the conversion rates, particularly emphasising the role played by the heavy neutrino masses, $tan beta$, and especially $theta_{13}$. In the case of hierachical heavy neutrinos, an extremely high sensitivity of the rates to $theta_{13}$ is indeed found. The last part of this work is devoted to the study of the interesting loss of correlation between the $mu-e$ conversion and $mu to e gamma$ rates that occurs in the non-universal scenario. In the case of large $tan beta$ and light $H^0$ Higgs boson an enhanced ratio of the $mu-e$ to $mu to e gamma$ rates, with respect to the universal case is found, and this could be tested with the future experimental sensitivities.
We address the constraints on the SUSY seesaw parameters arising from Lepton Flavour Violation observables. Working in the Constrained Minimal Supersymmetric Standard Model extended by three right-handed (s)neutrinos, we study the predictions for the
branching ratios of $l_j to l_i gamma$ and $l_j to 3 l_i$ channels. We impose compatibility with neutrino data, electric dipole moment bounds, and further require a successful baryon asymmetry of the Universe (via thermal leptogenesis). We emphasise the interesting interplay between $theta_{13}$ and the LFV muon decays, pointing out the hints on the SUSY seesaw parameters that can arise from measurements of $theta_{13}$ and LFV branching ratios. This is a brief summary of the work of Ref. cite{Antusch:2006vw}.
