Résumé
We study the phenomenology of a new minimally extended supersymmetric standard model (nMSSM) where a gauge singlet superfield is added to the MSSR I spectrum. The superpotential of this model contains no dimensionful parameters, thus solving the mu. problem of the MSSM. A global discrete R symmetry, forbidding the cubic singlet self-interaction, imposed on the complete theory, guarantees its stability with respect to generated higher-order tadpoles of the singlet and solves both the domain wall and Peccei-Quinn axion problems. We give the free parameters of the model and display some general constraints on them. Particular attention is devoted to the neutralino sector when a (quasipure) singlino appears to be always the LSP of the model, leading to additional cascades, involving the NLSP --> LSP transition, compared with the MSSM. We then present the upper bounds on the masses of the lightest and next-to-lightest-when the lightest is an invisible singlet-CP-even Higgs bosons, including the full one-loop and dominant two-loop corrections. These bounds are found to be much higher than the equivalent ones in the MSSM. Finally, we discuss some phenomenological implications for the Higgs sector of the nMSSM in Higgs boson production at future hadron colliders.