The ZZ kinetic mixing in the light of the recent direct and indirect dark matter searches

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 $U’(1)$.