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 λ, its intensity is proportional to 1/(λ²F²), 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 quasi-massless spin-0 particle, having pseudoscalar couplings proportional to 1/F. Similarly, in supersymmetric theories, a very light spin-$\text{3}\text{2}$ gravitino might be detectable as a quasi-massless spin-$\text{1}\text{2}$ goldstino, despite the extreme smallness of Newton's gravitational constant G_N, provided that the supersymmetry-breaking scale is not too large.

Searches for such U bosons in ψ and ϒ 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.