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$U(1)'$ extensions of the $μν$SSM

In the $μν$SSM, the presence of $R$-parity violating couplings involving right-handed (RH) neutrinos solves simultaneously the $μ$- and $ν$-problems. We explore extensions of the $μν$SSM adding a $U(1)'$ gauge group, which provides the RH neutrinos with a non-vanishing charge. In these models, dubbed U$μν$SSM, the anomaly cancellation conditions impose the presence of exotic quarks in the spectrum that are vector-like under the standard model (SM) gauge group: either three pairs $SU(2)$ quark singlets, or a pair of quark singlets together with a pair of quark doublets. Several extra singlets under the SM group can also be present, with the $U(1)'$ charges making distinctions among them, and therefore allowing different types of couplings. Some of these singlets dynamically generate Majorana masses for the RH neutrinos, and others can be candidates for dark matter. The useful characteristics of models with $U(1)'$s are also present in U$μν$SSM models: baryon-number-violating operators as well as explicit Majorana masses and $μ$ terms are forbidden, and the domain wall problem is avoided. The phenomenology of U$μν$SSM models is very rich. We analyze the experimental constraints on their parameter space, specially on the mass and mixing of the new $Z'$ boson. In addition to the exotic quarks, which can hadronize inside the detector or decay producing SM particles, the U$μν$SSM models can also have new signals such as decays of the $Z'$ to sparticle pairs like right sneutrinos, charginos or neutralinos. Besides, $Z'$ and Higgs mediated annihilations and interactions with the visible sector of WIMP dark matter particles, can also be present.