Simplest and Most Predictive Model of Muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math> and Thermal Dark Matter
Ian Holst, Dan Hooper, Gordan Krnjaic
Abstract
The long-standing $4.2\ensuremath{\sigma}$ muon $g\ensuremath{-}2$ anomaly may be the result of a new particle species which could also couple to dark matter and mediate its annihilations in the early Universe. In models where both muons and dark matter carry equal charges under a $U(1{)}_{{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}}$ gauge symmetry, the corresponding ${Z}^{\ensuremath{'}}$ can both resolve the observed $g\ensuremath{-}2$ anomaly and yield an acceptable dark matter relic abundance, relying on annihilations which take place through the ${Z}^{\ensuremath{'}}$ resonance. Once the value of $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ and the dark matter abundance are each fixed, there is very little remaining freedom in this model, making it highly predictive. We provide a comprehensive analysis of this scenario, identifying a viable range of dark matter masses between approximately 10 and 100 MeV, which falls entirely within the projected sensitivity of several accelerator-based experiments, including NA62, $\mathrm{NA}64\ensuremath{\mu}$, ${M}^{3}$, and DUNE. Furthermore, portions of this mass range predict contributions to $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$ which could ameliorate the tension between early and late time measurements of the Hubble constant, and which could be tested by stage 4 CMB experiments.