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$\mathcal{O}$(1) GeV dark matter in SUSY and a very light pseudoscalar at the LHC

We analyze the prospects of the detection of a $\mathcal{O}(1)$ GeV neutralino dark matter, $\widetildeχ^0_{1}$, in the Next-to-Minimal Supersymmetric Standard Model at the 14 TeV LHC. We perform dedicated scans of the relevant parameter space of the model and find a large number of points where the thermal relic abundance due to such a dark matter is consistent with the PLANCK measurement. We note that this dark matter is highly singlino-dominated and is always accompanied by a pseudoscalar, $A_1$, with a mass around twice its own, which is responsible for its resonant annihilation. For two benchmark points from our scan, we then carry out a detector-level signal-to-background analysis of the pair production of a heavier higgsino neutralino and a chargino. The higgsino thus produced decays into the dark matter and either the $Z$ boson or the $A_1$. For the $Z$-associated production of $\widetildeχ^0_{1}$, we investigate the scope of the trilepton search channel. For the $A_1$-associated production mode, in order to identify the two collimated muons coming from the decay of the $A_1$, we employ an unconventional method of clustering them together into one jet-like object. Using this method, for certain parameter space configurations, a much larger sensitivity can be obtained at the 14 TeV LHC for the $A_1\widetildeχ^0_{1}$ channel compared to the $Z\widetildeχ^0_{1}$ channel, with an integrated luminosity of 300 fb$^{-1}$.