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So far the most sophisticated experiments have shown no trace of new physicsat the TeV scale. Consequently, new models with unexplored parameter regionsare necessary to explain current results, re-examine the existing data, andpropose new experiments. In this Letter, we present a modified version of the$\mu\nu$SSM supersymmetric model where a non-Universal extra U(1) gaugesymmetry is added in order to restore an effective R-parity that ensures protonstability. We show that anomalies equations cancel without having to add\emph{any} exotic matter, restricting the charges of the fields under the extrasymmetry to a discrete set of values. We find that it is the viability of themodel through anomalies cancellation what defines the conditions in whichfermions interact with dark matter candidates via the exchange of $Z'$ bosons.The strict condition of universality violation means that LHC constraints for a$Z'$ mass do not apply directly to our model, allowing for a yet undiscoveredrelatively light $Z$', as we discuss both in the phenomenological context andin its implications for possible flavour changing neutral currents. Moreover,we explore the possibility of isospin violating dark matter interactions; weobserve that this interaction depends, surprisingly, on the Higgs charges underthe new symmetry, both limiting the number of possible models and allowing toanalyse indirect dark matter searches in the light of well defined, particularscenarios.

Surprising phenomenology in the non-Universal U(1) gauge extended $\mu\nu$SSM