Lepton flavour violating signature in supersymmetric $U(1)^\prime$ seesaw models at the LHC

We consider a $U(1)'$ supersymmetric seesaw model in which a right-handed sneutrino is a thermal dark matter candidate whose relic density can be in the right range due to its coupling to relatively light $\tilde{Z'}$, the superpartner of the extra gauge boson $Z'$. Such light $\tilde Z'$ can be produced at the LHC through cascade decays of colored superparticles, in particular, stops and sbottoms, and then decay to a right-handed neutrino and a sneutrino dark matter, which leads to lepton flavor violating signals of same/opposite-sign dileptons (or multileptons) accompanied by large missing energy. Taking some benchmark points, we analyze the opposite- and same-sign dilepton signatures and the corresponding flavour difference i.e., ($2e-2μ$). It is shown that $5σ$ signal significance can be reached for some benchmark points with very early data of $\sim 2$ fb$^{-1}$ integrated luminosity. In addition, $3\ell$ and $4\ell$ signatures also look promising to check the consistency in the model prediction, and it is possible to reconstruct the $\tilde{Z'}$ mass from $jj\ell$ invariant mass distribution.

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