  The possible existence of a new gauge boson U, light and very weakly coupled,
allows for Light Dark Matter particles, which could also be at the origin of
the 511 keV line from the galactic bulge. Independently of dark matter, and
taking into account possible Z-U mixing effects, we show that, even under
favorable circumstances (no axial couplings leading to an axionlike behavior or
extra parity-violation effects, very small coupling to neutrinos), and using
reasonable assumptions (no cancellation effect in g(mu)-2, lepton
universality), the U coupling to electrons can be at most as large as ~ 1.5
10^-3 (for m(U) < m(mu)), and is likely to be smaller (e.g. <~ 3 10^-6 m(U)
(MeV), if the U couplings to neutrinos and electrons are similar). This
restricts significantly the detectability of a light U in e+e- --> gamma U, in
particular. U exchanges can still provide annihilation cross sections of LDM
particles of the appropriate size, even if this may require that light dark
matter be relatively strongly self-interacting.
