  A light boson $U$ from an extra $U(1)$ interpolates between a generalized
dark photon coupled to $Q,\ B$ and $L_i$ (or $B-L$), plus possibly dark matter,
a dark $Z$ coupled to the $Z$ current, and one axially coupled to quarks and
leptons. We identify the corresponding $U(1)_F$ symmetries, with $F= \gamma_Y
Y+\gamma_B B+\gamma_{L_i}L_i+\gamma_A F_A+\gamma_{F'}F'\!+\gamma_d F_d$, $F_d$
acting in a dark sector and $F'$ on possible semi-inert BEH doublets uncoupled
to quarks and leptons. The $U$ current is obtained from the $U(1)_F $ and $Z$
currents, with a mixing determined by the spin-0 BEH fields. The charge $Q_U$
of chiral quarks and leptons is a combination of $Q,\ B,\ L_i$ and $T_{3L}$
with the axial $F_A$. It involves in general isovector and isoscalar axial
terms, in the presence of two BEH doublets. A longitudinal $U$ with axial
couplings has enhanced interactions, and behaves much as an axionlike particle.
Its axial couplings $g_A$, usually restricted to $< 2\times 10^{-7} m_U$(MeV),
lead to effective pseudoscalar ones $g_P= g_A\times 2m_{q,l}\,/m_U=2^{1/4}\,
G_F^{1/2}\, m_{q,l} \ A_\pm $. $\,A_\pm$ is proportional to an invisibility
parameter $r=\cos\theta_A$ induced by a singlet v.e.v., possibly large and
allowing the $U$ to be very weakly interacting. This allows for a very small
gauge coupling, expressed with two doublets and a singlet as $g"\!/4\simeq
2\times 10^{-6} m_U$(MeV) $ r/\sin 2\beta$. We discuss phenomenological
implications for meson decays, neutrino interactions, atomic-physics parity
violation, naturally suppressed $\pi^0\to\gamma U$ decays, etc.. The $U$ boson
fits within the grand-unification framework, in symbiosis with a $SU(4)_{\rm es
}$ electrostrong symmetry broken at the GUT scale, with $Q_U$ depending on $Q,\
B-L,\ F_A$ and $T_{3A}$ through three parameters $\gamma_Y,\ \gamma_A$ and
$\eta$.
