Right-handed sneutrino dark matter in $\mathbf{U(1)'}$ seesaw models and its signatures at the LHC

We suggest a real right-handed sneutrino, $\tilde N_1$, as a good dark matter candidate in a supersymmetric $Z'$ model realizing the seesaw mechanism. When the extra gaugino, $\tilde Z'$, is lighter than $Z'$, the thermal freeze-out of the dark matter annihilation to right-handed neutrinos, $ \tilde{N}_1 \tilde{N}_1 \to NN$, through the $t$-channel $\tilde Z'$ exchange is shown to produce the right dark matter density. It is essential to include the decay and inverse decay of $N$ in this process, otherwise $N$ decouples too early and thus dark matter is overproduced. At the LHC, the search for the seesaw mechanism can be made by observing the signatures of $pp \to \tilde Z' \tilde Z' \to NN + \ptmiss$ as $\tilde Z'$ can be copiously produced from the cascade decays of gluinos/squarks, which is complementary to the search of $pp\to Z' \to NN$. This may also open up a promising new channel of finding the Higgs boson from the displaced $N$ decay.