  Several constructions, of stringy origins or not, generate abelian gauge
extensions of the Standard Model (SM). Even if the particles of the SM are not
charged under this extra $U'(1)$, one cannot avoid the presence of a kinetic
mixing between $U'(1)$ and the hypercharge $U_Y(1)$. In this work, we
constraint drastically this kinetic mixing, taking into account the recent
experimental data from accelerator physics, direct detection and indirect
detection of dark matter. We show that the region respecting WMAP and
experimental constraints is now very narrowed along the pole line where
$M_{Z_D}\simeq 2 m_{DM}$, $Z_D$ being the gauge boson associated to the extra
$U'(1)$.
