Probing the "$\mu$ from $\nu$" supersymmetric standard model with displaced multileptons from the decay of a Higgs boson at the LHC

The “$\mu$ from $\nu$” supersymmetric standard model ($\mu \nu$SSM) cures the $\mu$-problem and concurrently reproduces measured neutrino data by using a set of usual right-handed neutrino superfields. Recently, the LHC has revealed the first scalar boson which naturally makes it tempting to test $\mu \nu$SSM in the light of this new discovery. We show that this new scalar while decaying to a pair of unstable long-lived neutralinos, can lead to a distinct signal with non-prompt multileptons. With concomitant collider analysis we show that this signal provides an unmistakable signature of the model, pronounced with light neutralinos. Evidence of this signal is well envisaged with sophisticated displaced vertex analysis, which deserves experimental attention.