Impact of LHC probes of SUSY and recent measurement of $(g-2)_{\mu}$ on $\mathbb{Z}_3$-NMSSM
It is well known that excessively heavy supersymmetric particles (sparticles) are disfavored to explain the $(g-2)_\mu$ anomaly, but some people overlook that moderately light sparticles are also disfavored by the LHC probes of supersymmetry. We take the Next-to-Minimal Supersymmetric Standard Model as an example to emphasize the latter point. It is found that, if the theory is required to explain the anomaly at $2\sigma$ level and meanwhile keep consistent with the LHC results, the following lower bounds may be set: $\tan \beta \gtrsim 20$, $|M_1| \gtrsim 275~{\rm GeV}$, $M_2 \gtrsim 300~{\rm GeV}$, $\mu \gtrsim 460~{\rm GeV}$, $m_{\tilde{\mu}_L} \gtrsim 310~{\rm GeV}$, and $m_{\tilde{\mu}_R} \gtrsim 350~{\rm GeV}$, where $M_1$ and $M_2$ denote gaugino masses, $\mu$ represents the Higgsino mass, and $m_{\tilde{\mu}_L}$ and $m_{\tilde{\mu}_R}$ are the mass of Smuons with $L$ and $R$ denoting their dominant chiral component. This observation has significant impacts on dark matter (DM) physics, e.g., the popular $Z$- and Higgs-funnel regions have been excluded, and the Bino-dominated neutralino DM has to co-annihilate with the Wino-dominated electroweakinos (in most cases) and/or Smuons (in few cases) to obtain the correct density. It is also inferred that these conclusions should apply to the Minimal Supersymmetric Standard Model since the underlying physics for the bounds are the same.