  We discuss the possible existence of new long-range forces mediated by spin-1
or spin-0 particles. They would add their effects to those of gravity, and
could lead to apparent violations of the Equivalence Principle. Informations on
the (vector and axial) couplings of a new spin-1 U boson may be obtained from
spontaneously broken gauge invariance. The charge associated with the vector
coupling may be expressed as a linear combination of B and L. If the new force
has a finite range lambda, its intensity turns out to be proportional to
1/(lambda^2 F^2), F being the extra U(1) symmetry-breaking scale.
  Quite surprisingly, particle physics experiments can provide constraints on
such a force, even if the corresponding gauge coupling is extremely small (<<
10^-19 !). An "equivalence theorem" shows that a very light spin-1 U boson with
non-vanishing axial couplings does not in general decouple even when its gauge
coupling vanishes, but behaves as a quasimassless pseudoscalar. (This
equivalence theorem is similar to the one of supersymmetry/supergravity
theories, according to which a very light spin-3/2 gravitino might get
detectable as a quasi massless spin-1/2 goldstino, despite the extreme
smallness of Newton's gravitational constant G_N.) Searches for the radiative
production of such U bosons in psi and upsilon decays restrict the extra U(1)
symmetry-breaking scale F to be larger than the electroweak scale, providing
constraints on the intensity of the corresponding new force.
