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Following searches for photinos and very light gravitinos in invisible decays of psi and Upsilon, we discuss new limits on Light Dark Matter and U bosons, from psi and Upsilon decays, as well as rare decays of K+ and invisible decays of pi0, eta and eta' ... . The new limits involving the vector couplings of the U to quarks turn out, not surprisingly, to be much less restrictive than existing ones on axial couplings, from an axionlike behavior of a light U boson, tested in psi --> gamma U, Upsilon --> gamma U and K+ --> pi+ U decays (or as compared to the limit from parity-violation in atomic physics, in the presence of an axial coupling to the electron). Altogether the hypothesis of light U bosons, and light dark matter particles, remains compatible with particle physics constraints, while allowing for the appropriate annihilation cross sections required, both at freeze-out (for the relic abundance) and nowadays (if e+ from LDM annihilations are at the origin of the 511 keV line from the galactic bulge).