  According to recent measurements, dark matter magnetic dipole moment is
strongly constrained. In the composite Higgs models the magnetic dipole moment
of the Dirac dark matter fermion and its mass can be suppressed by the
approximate U(1) symmetry. We consider E_6 inspired composite Higgs model
(E_6CHM) with U(1) symmetry violating operators, which give rise to dark
matter's mass and coupling constant to Higgs boson. The dependence of the
spin-independent dark matter-nucleon scattering cross section on the E_6CHM
parameters is explored. We argue that there are regions of the parameter space
which are still safe from all current constraints and may lead to spectacular
LHC signatures.
