  Many theories beyond the Standard Model involve an extra U(1) gauge group.
The resulting gauge boson U, in general mixed with the Z and the photon, may be
massless or very light, and very weakly coupled. It may be viewed as a
generalized dark photon interacting with matter through a linear combination
(\epsilon_Q Q + \epsilon_B B+\epsilon_L L) e, involving B-L in a grand-unified
theory, presumably through B-L-.61 Q, inducing effectively a very small
repulsive force between neutrons.
  This new force, if long-ranged, may manifest through apparent violations of
the Equivalence Principle. They are approximately proportional to
\epsilon_B+\epsilon_L/2, times a combination involving mostly \epsilon_L. New
forces coupled to B-L or L should lead to nearly opposite values of the
E\"otv\"os parameter \delta, and to almost the same limits for \epsilon_{B-L}
or \epsilon_L, as long as no indication for \delta \neq 0 is found.
  We derive new limits from the first results of the MICROSCOPE experiment
testing the Equivalence Principle in space. A long-range force coupled to
(\epsilon_Q Q + \epsilon_{B-L} (B-L)) e or (\epsilon_Q Q + \epsilon_L L) e
should verify |\epsilon_{B-L}| or |\epsilon_L| < .8 10^{-24}, and a force
coupled to (\epsilon_Q Q + \epsilon_B B) e, |\epsilon_B| < 5 10^{-24}.
  We also discuss, within supersymmetric theories, how such extremely small
gauge couplings g", typically \simle 10^{-24}, may be related to a
correspondingly large \xi"D" term associated with a huge initial vacuum energy
density, \propto 1/g"^2. The corresponding hierarchy between energy scales, by
a factor \propto 1/\sqrt g" \simge 10^{12}, involves a very large scale ~
10^{16} GeV, that may be associated with inflation, or supersymmetry breaking
with a very heavy gravitino, leading to possible values of {\delta} within the
experimentally accessible range.
