The Dispirited Case of Gauged $U(1)_{B-L}$ Dark Matter
  We explore the constraints and phenomenology of possibly the simplest
scenario that could account at the same time for the active neutrino masses and
the dark matter in the Universe within a gauged $U(1)_{B-L}$ symmetry, namely
right-handed neutrino dark matter. We find that null searches from lepton and
hadron colliders require dark matter with a mass below 900 GeV to annihilate
through a resonance. Additionally, the very strong constraints from high-energy
dilepton searches fully exclude the model for $ 150 \, \text{GeV} < m_{Z'} < 3
\, \text{TeV}$. We further explore the phenomenology in the high mass region
(i.e. masses $\gtrsim \mathcal{O}(1) \, \text{TeV}$) and highlight theoretical
arguments, related to the appearance of a Landau pole or an instability of the
scalar potential, disfavoring large portions of this parameter space.
Collectively, these considerations illustrate that a minimal extension of the
Standard Model via a local $U(1)_{B-L}$ symmetry with a viable thermal dark
matter candidate is difficult to achieve without fine-tuning. We conclude by
discussing possible extensions of the model that relieve tension with collider
constraints by reducing the gauge coupling required to produce the correct
relic abundance.
