Non-linear MSSM

Using the formalism of constrained superfields, we derive the most general effective action of a light goldstino coupled to the minimal supersymmetric standard model (MSSM) and study its phenomenological consequences. The goldstino-induced couplings become important when the (hidden sector) scale of spontaneous supersymmetry breaking, $\sqrt f$, is relatively low, of the order of few TeV. In particular, we compute the Higgs potential and show that the (tree level) mass of the lightest Higgs scalar can be increased to the LEP bound for $\sqrt f\sim 2$ TeV to 7 TeV. Moreover, the effective quartic Higgs coupling is increased due to additional tree-level contributions proportional to the ratio of visible to hidden sector supersymmetry breaking scales. This increase can alleviate the amount of fine tuning of the electroweak scale that exists in the MSSM. Among the new goldstino couplings, beyond those in MSSM, the most important ones generate an invisible decay of the Higgs boson into a goldstino and neutralino (if m_h>m_{χ_1^0}), with a partial decay rate that can be comparable to the SM channel h^0-> γγ. A similar decay of Z boson is possible if m_Z>m_{χ_1^0} and brings a lower bound on $\sqrt f$ that must be of about 700 GeV. Additional decay modes of the Higgs or Z bosons into a pair of light goldstinos, while possible, are suppressed by an extra 1/f factor and have no significant impact on the model.