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)(mu) naturally combines with the weak neutral current J(Zsm)(mu), both parity-violating, into a vectorial current J(U)(mu) combination of the B, L and electromagnetic currents with a possible dark-matter current. U-mu maybe expressed equivalently as cos xi C-mu + sin xi Z(sm)(mu) ( mixing with the Z) or (1/cos chi) C-mu + tan chi A(mu) (mixing with the photon), with (C) over cap coupled to B, L and dark matter. The U boson may be viewed as a generalized dark photon, coupled toSMparticles through Q(U) = Q+lambda B-B+lambda(i) L-i, with strength g '' cos xi cos(2)theta = e tan chi 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(gut)(U) = Q - 2 (B-L) at the GUT scale for SM particles, invariant under the SU(4) electrostrong symmetry group, with a non-vanishing epsilon = tan chi already present at the GUT scale, leading to Q(U) similar or equal to 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 showup through apparent violations of the equivalence principle.