Impact of recent $(g-2)_{\mu}$ measurement on the light CP-even Higgs scenario in general Next-to-Minimal Supersymmetric Standard Model

The General Next-to-Minimal Supersymmetric Standard Model (GNMSSM) is an attractive theory that is free from the tadpole problem and the domain-wall problem of $Z_3$-NMSSM, and can form an economic secluded dark matter (DM) sector to naturally predict the DM experimental results. It also provides mechanisms to easily and significantly weaken the constraints from the LHC search for supersymmetric particles. These characteristics enable the theory to explain the recently measured muon anomalous magnetic moment, $(g-2)_\mu$, in a broad parameter space that is consistent with all experimental results and at same time keeps the electroweak symmetry breaking natural. This work focuses on a popular scenario of the GNMSSM in which the next-to-lightest CP-even Higgs boson corresponds to the scalar discovered at the Large Hadron Collider (LHC). Both analytic formulae and a sophisticated numerical study show that in order to predict the scenario without significant tunings of relevant parameters, the Higgsino mass $\mu_{tot} \lesssim 500~{\rm GeV}$ and $\tan \beta \lesssim 30$ are preferred. This character, if combined with the requirement to account for the $(g-2)_\mu$ anomaly, will entail some light sparticles and make the LHC constraints very tight. As a result, this scenario can explain the muon anomalous magnetic moment in very narrow corners of its parameter space.