"Dark" Z implications for Parity Violation, Rare Meson Decays, and Higgs Physics

TL;DR

The paper analyzes mass mixing between the SM $Z$ and a light hidden-sector gauge boson $Z_d$ in a $U(1)_d$ theory, extending beyond kinetic mixing to parity-violating and Higgs-portal phenomena. It shows how $Z$-$Z_d$ mixing induces new low-energy parity violation, constrains the mixing parameters through atomic parity violation and polarized scattering, and impacts rare flavor decays and Higgs decays via the channel $H\to Z Z_d$, with a longitudinal enhancement that can yield observable signals. A simple Type-I two-Higgs-doublet model is presented as a concrete realization of the framework, linking the mixing to Higgs-sector vevs and providing explicit couplings and decay widths. The study highlights complementary probes from low-energy precision experiments and high-energy collider Higgs measurements, outlining a path to test a dark-sector gauge boson across a broad $m_{Z_d}$ range.

Abstract

General consequences of mass mixing between the ordinary Z boson and a relatively light Z_d boson, the "dark" Z, arising from a U(1)_d gauge symmetry, associated with a hidden sector such as dark matter, are examined. New effects beyond kinetic mixing are emphasized. Z-Z_d mixing introduces a new source of low energy parity violation well explored by possible future atomic parity violation and planned polarized electron scattering experiments. Rare K (B) meson decays into pi (K) l^+ l^- (l = e, mu) and pi (K) nu anti-nu are found to already place tight constraints on the size of Z-Z_d mixing. Those sensitivities can be further improved with future dedicated searches at K and B factories as well as binned studies of existing data. Z-Z_d mixing can also lead to the Higgs decay H -> Z Z_d, followed by Z -> l_1^+ l_1^- and Z_d -> l_2^+ l_2^- or "missing energy", providing a potential hidden sector discovery channel at the LHC. An illustrative realization of these effects in a 2 Higgs doublet model is presented.

Figures (3)

• Figure 1: Examples of diagrams contributing to $b \to s Z_d$. Similar diagrams give rise to $s \to d Z_d$.
• Figure 2: $Z_d$ lifetime with $Z_d$ mass for $\delta^2 = 10^{-4}$ with $\varepsilon = 0$ (solid blue curve) and $\varepsilon = 2 \times 10^{-3}$ (dashed blue curve) cases. We take $\rho$, $\phi$, $J/\psi$, $\Upsilon$ masses as the representative threshold for decays to mesons.
• Figure 3: Differential decay rate $H \to Z Z^* \to Z \ell^+ \ell^- \to 4 \ell$ vs $\ell^+ \ell^-$ invariant mass with $m_H = 125 ~{\rm GeV}$ in the SM (in blue). For the illustration, $H \to Z Z_d \to Z \ell^+ \ell^-$ with $m_{Z_d} = 5 ~{\rm GeV}$ and $\delta^2 {\rm BR} (Z_d \to \ell^+ \ell^-) = 10^{-5}$ (which would need $N_\text{Higgs} \simeq 10^6$ for $3 \sigma$ evidence) is also shown (spike at the $5 ~{\rm GeV}$ bin in red). Bin size is selected to be $2 ~{\rm GeV}$.