Light dark matter in a gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ model

As experimental null results increase the pressure on heavy weakly interacting massive particles (WIMPs) as an explanation of thermal dark matter (DM), it seems timely to explore previously overlooked regions of the WIMP parameter space. In this work we extend the minimal gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ model studied in [M. Bauer, P. Foldenauer, and J. Jaeckel, J. High Energy Phys. 07 (2018) 094.] by a light (MeV-scale) vectorlike fermion $\chi$. Taking into account constraints from cosmology, direct and indirect detection we find that the standard benchmark of $M_V=3m_{\chi }$ for DM coupled to a vector mediator is firmly ruled out for unit DM charges. However, exploring the near-resonance region $M_V\gtrsim 2m_{\chi }$ we find that this model can simultaneously explain the DM relic abundance $\mathrm{\Omega }{h}^2=0.12$ and the $(g-2{)}_{\mu }$ anomaly. Allowing for small charge hierarchies of $\lesssim \mathcal{O}(10)$, we identify a second window of parameter space in the few-GeV region, where $\chi$ can account for the full DM relic density.

Figure 1

Current (left panels) and future (right panels) constraints on the combined parameter space of a $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge boson and vectorlike fermion of charge $Q_{\chi }=1$ for $m_{\chi }/M_{A^{\prime }}=0.33$ (upper panels) and $m_{\chi }/M_{A^{\prime }}=0.45$ (lower panels).

Figure 2

Same as lower left panel of Fig. 1, but with $Q_{\chi }=3$.