We revisit an anomaly-free extension of the Standard Model viz. the gauged $L_{\mu }-L_{\tau }$ model in the Dirac framework, where the local $U(1{)}_{L_{\mu }-L_{\tau }}$ symmetry breaks and gives rise to a new gauge boson $Z^{\prime }$ and corresponding gauge coupling $g_{\mu \tau }$. Three additional heavy vectorlike fermions, three light right-handed neutrinos and two heavy singlet scalars are added to complete the model framework for Dirac neutrinos. Another singlet vectorlike fermion is added with a new gauge charge, which serves as a viable dark matter (DM) candidate, and the correct relic abundance is obtained via the resonance effect. The resonance effect triggers early kinetic decoupling of the DM candidate, which significantly influences the cosmological sector of this study. The parameter space is considered after satisfying the current bounds on $M_{Z^{\prime }}$ and the gauge coupling $g_{\mu \tau }$. The influence of dark radiations coming from the additional light degrees of freedoms are studied in connection with the dark matter. After imposing the relevant theoretical and experimental constraints, the viable parameter space is found to be significantly restricted while remaining accessible to ongoing and near-future experiments. The framework provides a consistent setting in which neutrino masses, dark matter, and cosmological observables can be studied simultaneously. In particular, we identify viable regions of the parameter space that satisfy the constraints from neutrino masses, dark matter relic abundance, and cosmological observables.

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• Extensions of gauge sector
• Particle astrophysics
• Particle dark matter
• Phenomenology