Equivalence Principle tests, Equivalence theorems and New long-range forces

We discuss the possible existence of new long-range forces mediated by spin-1 or spin-0 particles. By adding their effects to those of gravity, they could lead to apparent violations of the Equivalence Principle. While the vector part in the couplings of a new spin-1 U boson involves, in general, a combination of the B and L currents, there may also be, in addition, an axial part as well. If the new force has a finite range \lambda, its intensity is 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 new force, even if it is extremely weak, the corresponding gauge coupling being extremely small (<< 10^-19 !). An ``equivalence theorem'' shows that a very light spin-1 U boson does not in general decouple even when its gauge coupling vanishes, but behaves as a quasimassless spin-0 particle, having pseudoscalar couplings proportional to 1/F. Similarly, in supersymmetric theories, a very light spin-3/2 gravitino might be detectable as a quasi massless spin-1/2 goldstino, despite the extreme smallness of Newton's gravitational constant G_N, provided the supersymmetry-breaking scale is not too large. Searches for such U bosons in \psi and \Upsilon decays restrict F to be larger than the electroweak scale (the U actually becoming, as an axion, quasi ``invisible'' in particle physics for sufficiently large F). This provides strong constraints on the corresponding new force and its associated EP violations. We also discuss briefly new spin-dependent forces.