The light U boson as the mediator of a new force, coupled to a combination of Q,B,L and dark matter

A new light gauge boson U may have both vector and axial couplings. In a large class of theories, however, the new U (1) current J F μ naturally combines with the weak neutral current J Z sm μ , both parity-violating, into a vectorial current J U μ , combination of the B , L and electromagnetic currents with a possible dark-matter current. U μ may be expressed equivalently as cos ξ C μ + sin ξ Z sm μ (“mixing with the Z ”) or ( 1 / cos χ ) C ^ μ + tan χ A μ (“mixing with the photon”), with C ^ coupled to B , L and dark matter. The U boson may be viewed as a generalized dark photon, coupled to SM particles through Q U = Q + λ B B + λ i L i , with strength g ′ ′ cos ξ cos 2 θ = e tan χ . “Kinetic-mixing” terms, gauge invariant or not, simply correspond to a description in a non-orthogonal field basis (rather than to a new physical effect), with the dark photon in general also coupled to B and L . In a grand-unified theory Q U gut = Q - 2 ( B - L ) at the GUT scale for SM particles, invariant under the SU (4) electrostrong symmetry group, with a non-vanishing ϵ = tan χ already present at the GUT scale, leading to Q U ≃ Q - 1.64 ( B - L ) at low energy. This also applies, for a very light or massless U boson, to a new long-range force, which could show up through apparent violations of the equivalence principle.