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 Brout-Englert-Higgs (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 $\lesssim 2\times {10}^{-7}{m}_U(\mathrm{MeV})$, 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 $g^{\prime \prime }/4\simeq 2\times {10}^{-6}{m}_U(\mathrm{MeV})r/\sin 2\beta$. 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 grand unification scale, with $Q_U$ depending on $Q$, $B-L$, $F_A$, and $T_{3A}$ through three parameters ${\gamma }_Y$, ${\gamma }_A$, and $\eta$.

中文翻译：

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Uboson插值在广义暗光子或darkZ，轴向玻色子和类似轴突的粒子之间

浅色玻色子 $ü$ 从额外 $ü（\mathrm{1个}）$ 在耦合到的广义暗光子之间插值 $问$， $乙$， 和 ${\mathrm{大号}}_{\mathrm{一世}}$ （或者 $乙-\mathrm{大号}$），再加上可能的暗物质， $ž$ 耦合到 $ž$电流，并且轴向耦合至夸克和轻子。我们找出对应的$ü（\mathrm{1个}{）}_F$ 对称，具有 $F={\gamma }_{ÿ}ÿ+{\gamma }_{乙}乙+{\gamma }_{{\mathrm{大号}}_{\mathrm{一世}}}{\mathrm{大号}}_{\mathrm{一世}}+{\gamma }_{\mathrm{一种}}{F}_{\mathrm{一种}}+{\gamma }_{F^{\prime }}{F}^{\prime }+{\gamma }_d{F}_d$， $F_d$ 在黑暗领域行动 $F^{\prime }$可能的半惰性Brout-Englert-Higgs（BEH）双峰与夸克和轻子不耦合。这$ü$ 当前是从 $ü（\mathrm{1个}{）}_F$ 和 $ž$电流，并通过旋转0 BEH场确定混合。费用${问}_{ü}$ 手性夸克和轻子是 $问$， $乙$， ${\mathrm{大号}}_{\mathrm{一世}}$， 和 ${Ť}_{3\mathrm{大号}}$ 与轴向 $F_{\mathrm{一种}}$。它在两个BEH双峰存在的情况下，通常涉及等矢量和等量轴向项。纵向$ü$轴向联轴器具有增强的相互作用，并且表现得像轴突状颗粒。其轴向联轴器$G_{\mathrm{一种}}$，通常仅限于 $\lesssim \mathrm{2个}\times {10}^{-7}{米}_{ü}（\mathrm{电动汽车}）$，导致有效的伪标量 $G_P=G_{\mathrm{一种}}\times \mathrm{2个}{米}_{q，升}/{米}_{ü}={\mathrm{2个}}^{\mathrm{1个}/4}{G}_F^{\mathrm{1个}/\mathrm{2个}}{米}_{q，升}{\mathrm{一种}}_{\pm }$。 ${\mathrm{一种}}_{\pm }$ 与隐身参数成正比 $\mathrm{[R}=\cos {\theta }_{\mathrm{一种}}$ 由单线态vev诱发，可能很大，并允许 $ü$互动非常弱。这允许非常小的轨距耦合，用两个双峰和一个单峰表示为$G^{\prime \prime }/4\simeq \mathrm{2个}\times {10}^{-6}{米}_{ü}（\mathrm{电动汽车}）\mathrm{[R}/罪\mathrm{2个}\beta$。我们讨论了介子衰变，中微子相互作用，原子物理奇偶性违背，自然抑制的现象学意义${\pi }^0\to \gamma ü$ 衰减等。 $ü$ 玻色子符合大统一框架，与 $\mathrm{小号}ü（4{）}_{\mathrm{es}}$ 在整体统一尺度上打破了强电对称性，${问}_{ü}$ 根据 $问$， $乙-\mathrm{大号}$， $F_{\mathrm{一种}}$， 和 ${Ť}_{3\mathrm{一种}}$ 通过三个参数 ${\gamma }_{ÿ}$， ${\gamma }_{\mathrm{一种}}$， 和 $\eta$。