Light spin-$\frac{1}{2}$ or spin-0 dark matter particles

We recall and precise how light spin-0 particles could be acceptable dark matter candidates, and extend this analysis to spin-$\frac{1}{2}$ particles. We evaluate the (rather large) annihilation cross sections required, and show how they may be induced by a new light neutral spin-1 boson U. If this one is vectorially coupled to matter particles, the (spin-$\frac{1}{2}$ or spin-0) dark matter annihilation cross section into $e^{+}{e}^{-}$ automatically includes a $v_{\mathrm{dm}}^2$ suppression factor at threshold, as desirable to avoid an excessive production of $\gamma$ rays from residual dark matter annihilations. We also relate dark matter annihilations with production cross sections in $e^{+}{e}^{-}$ scatterings. Annihilation cross sections of spin-$\frac{1}{2}$ and spin-0 dark matter particles are given by exactly the same expressions. Just as for spin-0, light spin-$\frac{1}{2}$ dark matter particles annihilating into $e^{+}{e}^{-}$ could be responsible for the bright 511 keV $\gamma$ ray line observed by INTEGRAL from the galactic bulge.