Searching for left sneutrino LSP at the LHC

We analyze relevant signals expected at the LHC for a left sneutrino as the lightest supersymmetric particle (LSP). The discussion is carried out in the `$\mu$ from $\nu$' supersymmetric standard model ($\mu \nu$SSM), where the presence of $R$-parity breaking couplings involving right-handed neutrinos solves the $\mu$ problem and reproduces neutrino data. The sneutrinos are pair produced via a virtual $W$, $Z$ or $\gamma$ in the $s$ channel. From the prompt decay of a pair of left sneutrinos LSPs of any family, a significant diphoton signal plus missing transverse energy (MET) from neutrinos can be present in the mass range 118-132 GeV, with 13 TeV center-of-mass energy and an integrated luminosity of 100 fb$^{-1}$. In addition, in the case of a pair of tau left sneutrinos LSPs, given the large value of the tau Yukawa coupling diphoton plus leptons and/or multileptons can appear. We find that the number of expected events for the multilepton signal, together with properly adopted search strategies, is sufficient to give a significant evidence for a sneutrino of mass in the range 130-310 GeV, even with the integrated luminosity of 20 fb$^{-1}$. In the case of the signal producing diphoton plus leptons, an integrated luminosity of 100 fb$^{-1}$ is needed to give a significant evidence in the mass range 95-145 GeV. Finally, we discuss briefly the presence of displaced vertices and the associated range of masses.