The $U$ boson, interpolating between a generalized dark photon or dark $Z$, an axial boson and an axionlike particle

Abstract

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 $F={\gamma }_{Y}Y+{\gamma }_{B}B+{\gamma }_{L_i}{L}_i+{\gamma }_A{F}_A+{\gamma }_{F^{\prime }}{F}^{\prime }+{\gamma }_d{F}_d$, $F_d$ acting in a dark sector and $F^{\prime }$ 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 $SU(4{)}_{\mathrm{es}}$ 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 $\eta$.

arXiv comment25 pages

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