Current experimental constraints on NMSSM with large lambda
  The next-to-minimal supersymmetric model (NMSSM) with a large lambda (the mixing parameter between the singlet and doublet Higgs fields) is well motivated since it can significantly push up the upper bound on the SM-like Higgs boson mass to solve the little hierarchy problem. In this work we examine the current experimental constraints on the NMSSM with a large lambda, which include the direct search for Higgs boson and sparticles at colliders, the indirect constraints from precision electroweak measurements, the cosmic dark matter relic density, the muon anomalous magnetic moment, as well as the stability of the Higgs potential. We find that, with the increase of lambda, parameters like tan-beta, M_A, mu and M_2 are becoming more stringently constrained. It turns out that the maximal reach of lambda is limited by the muon anomalous magnetic moment, and for smuon masses of 200 GeV (500 GeV) the parameter space with lambda > 1.5 (0.6) is excluded. 
Junjie Cao, Jin Min Yang