Exploring the Higgs sector of a most natural NMSSM and its prediction on Higgs pair production at the LHC

As a most natural realization of the Next-to Minimal Supersymmetry Standard Model (NMSSM), lambda-SUSY is parameterized by a large lambda around one and a low tan beta below 10. In this work, we first scan the parameter space of lambda-SUSY by considering various experimental constraints, including the limitation from the Higgs data updated by the ATLAS and CMS collaborations in the slimmer of 2014, then we study the properties of the Higgs bosons. We get two characteristic features of lambda-SUSY in experimentally allowed parameter space. One is the triple self coupling of the SM-like Higgs boson may get enhanced by a factor over 10 in comparison with its SM prediction. The other is the pair production of the SM-like Higgs boson at the LHC may be two orders larger than its SM prediction. All these features seems to be unachievable in the Minimal Supersymmetric Standard Model and in the NMSSM with a low lambda. Moreover, we also find that naturalness plays an important role in selecting the parameter space of lambda-SUSY, and that the Higgs X-2 obtained with the latest data is usually significantly smaller than before due to the more consistency of the two collaboration measurmnents.