Neutralinos and Sleptons at the LHC in Light of Muon $(g-2)_{\mu}$

We study the muon $(g-2)_{\mu}$ anomaly in light of neutralino dark matter and the LHC. We scan the MSSM parameters relevant to $(g-2)_{\mu}$ and focus on three distinct cases with different neutralino compositions. We find that the 2$\sigma$ range of $(g-2)_{\mu}$ requires the smuon ($\tilde{\mu}_1$) to be lighter than $\sim$ 500 (1000) GeV for $\tan \beta=10\,(50)$. Correspondingly the two lightest neutralinos, $\tilde{\chi}_{1}^0, \tilde{\chi}_{2}^0$, have to be lighter than $\sim$ 300 (650) GeV and 900 (1000) GeV respectively. We explore the prospects of searching the light smuon and neutralinos at the LHC, in conjunction with constraints arising from indirect dark matter (DM) detection experiments. The upcoming run of the LHC will be able to set $95\%$ CL exclusion limit on $M_{\tilde{\chi}_{2}^0}$ ($\sim 475 - 1300$ GeV) and $m_{\tilde{l}}$ ($\sim 670-775$ GeV) with $M_{\tilde{\chi}_{1}^0} \sim 100-250$ GeV at 3000 fb$^{-1}$ luminosity in multi-lepton + missing energy channel.