  In this study, we apply LHC data to constrain the extension of the Standard
Model by an anomaly-free $U(1)_{L_\mu-L_\tau}$ gauge group; this model contains
a new gauge boson ($Z^\prime$) and a scalar dark matter particle ($\phi_{\rm
DM}$). We recast a large number of LHC analyses from ATLAS and CMS of
multi-lepton final states. We find that for $10$ GeV $< m_{Z^\prime} < 60$ GeV
the strongest constraint comes from a dedicated $Z^\prime$ search in the $4\mu$
final state by the CMS collaboration; for larger $Z^\prime$ masses, searches
for final states with three leptons plus missing $E_T$ are more sensitive.
Searches for final states with two leptons and missing $E_T$, which are
sensitive to $Z^\prime$ decays into dark matter particles, can only probe
regions of parameter space that are excluded by searches in the $3$ and $4$
lepton channels. The combination of LHC data excludes values of $Z^\prime$ mass
and coupling constant that can explain the deficit in $g_\mu-2$ for $4$ GeV
$\leq m_{Z^\prime} \leq 500$ GeV. However, for much of this range the LHC bound
is weaker than the bound that can be derived from searches for trident events
in neutrino-nucleus scattering.
