A Novel Scenario in the Semi-constrained NMSSM

In this work, we develop a novel efficient scan method, combining the Heuristically Search (HS) and the Generative Adversarial Network (GAN), where the HS can shift marginal samples to perfect samples, and the GAN can generate a huge amount of recommended samples from noise in a short time. With this efficient method, we find a new scenario in the semi-constrained Next-to Minimal Supersymmetric Standard Model (scNMSSM), or NMSSM with non-universal Higgs masses. In this scenario, (i) Both muon g-2 and right relic density can be satisfied, along with the high mass bound of gluino, etc. As far as we know, that had not been realized in the scNMSSM before this work. (ii) With the right relic density, the lightest neutralinos are singlino-dominated, and can be as light as 0-12 GeV. (iii) The future direct detections XENONnT and LUX-ZEPLIN (LZ-7 2T) can give strong constraints to this scenario. (iv) The current indirect constraints to Higgs invisible decay $h_2\to \tilde{\chi}^0_1 \tilde{\chi}^0_1$ are weak, but the direct detection of Higgs invisible decay at the future HL-LHC may cover half of the samples, and that of the CEPC may cover most. (v) The branching ratio of Higgs exotic decay $h_2\to h_1h_1, a_1a_1$ can be over 20 percent, while their contributions to the invisible decay $h_2\to4\chi_1^0$ are very small.