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We study the low scale predictions of supersymmetric standard model extendedby $U(1)_{B-L}\times U(1)_{R}$ symmetry, obtained from $SO(10)$ breaking via aleft-right supersymmetric model, imposing universal boundary conditions. Twosinglet Higgs fields are responsible for the radiative $U(1)_{B-L}\timesU(1)_{R}$ symmetry breaking, and a singlet fermion $S$ is introduced togenerate neutrino masses through inverse seesaw mechanism. The lightestneutralino or sneutrino emerge as dark matter candidates, with different lowscale implications. We find that the composition of the neutralino LSP changesconsiderably depending on the neutralino LSP mass, from roughly half $U(1)_R$bino, half MSSM bino, to singlet higgsino, or completely dominated by MSSMhiggsino. The sneutrino LSP is statistically much less likely, and when itoccurs it is a 50-50 mixture of right-handed sneutrino and the scalar $\tildeS$. Most of the solutions consistent with the relic density constraint survivethe XENON 1T exclusion curve for both LSP cases. We compare the two scenariosand investigate parameter space points and find consistency with the muonanomalous magnetic moment only at the edge of $2\sigma$ deviation from themeasured value. However, we find that the sneutrino LSP solutions could beruled out completely by strict reinforcement of the recent $Z^\prime $ massbounds. We finally discuss collider prospects for testing the model.

Exploring the supersymmetric U(1)$_{B-L} \times$ U(1)$_{R}$ model with dark matter, muon $g-2$ and $Z^\prime$ mass limits