  To know the total width of the recently discovered Higgs boson particle, it
is important to measure the invisible decay width of the Higgs boson. However,
the signal for this measurement at the LHC, i.e., a charged lepton pair and
missing energy in the final state, cannot be definitely understood as the
product of the intermediate produced $Z$ and $H$ bosons due to the possible
interaction between dark matter and a $Z$ boson or quarks, which can be
described by representative effective operators. First, we consider the relic
abundance, the LUX direct detection experiment and the result of searching for
Higgs boson invisible decay at the LEP and LHC to find the allowed parameter
region for the effective operators. Then we investigate the transverse momentum
distribution of the missing energy and propose two observables that can be used
to distinguish the different underlying processes. Moreover, with these two
observables, we may be able to determine the masses of invisible particles.
