The Stueckelberg $Z'$ Extension with Kinetic Mixing and Milli-Charged Dark Matter From the Hidden Sector

TL;DR

This work extends the Standard Model with a Stueckelberg $Z'$ arising from a hidden $U(1)_X$ and includes kinetic mixing with $U(1)_Y$. The authors derive the full gauge-kinetic and mass-sector structure, identify the effective parameter $\bar{\epsilon}$ governing electroweak deviations in the no-hidden-matter limit, and show that hidden-sector content reintroduces dependence on both $\epsilon$ and $\delta$. They analyze milli-charged dark matter from the hidden sector, compute relic densities with thermal averaging, and demonstrate regions of parameter space compatible with WMAP-3 while allowing for narrow $Z'$ resonances observable via Drell-Yan dilepton signals at the Tevatron and LHC. The results indicate that kinetic mixing expands viable models and yields testable predictions for collider and cosmological data. Overall, the paper provides a consistent framework for a Stueckelberg $Z'$ with kinetic mixing that accommodates milli-charged dark matter and realistic collider phenomenology.

Abstract

An analysis is given of the Stueckelberg extension of the Standard Model with a hidden sector gauge group $U(1)_X$ where the mass growth for the extra gauge boson occurs via the Stueckelberg mechanism, and where the kinetic mixing in the $U(1)_X\times U(1)_Y$ sector is included. Such a kinetic mixing is generic in a broad class of supergravity and string models. We carry out a detailed global fit of the model with the precision LEP data on and off the $Z$ pole, with $χ^2$ within 1% of the $χ^2$ of the Standard Model fit. Further, it is shown that in the absence of matter in the hidden sector, there is a single effective parameter that controls the deviations from the Standard Model predictions, and the dependence on the kinetic mixing emerges only when matter in the hidden sector is included. An analysis is also given of milli-charged dark matter arising from the hidden sector, where it is shown that such dark matter from the Stueckelberg extension can satisfy WMAP-3 data while allowing for a sharp $Z'$ resonance which can be detected at the Tevatron and at the LHC via a dilepton signal generated by the Drell-Yan process.

Figures (9)

• Figure 1: An analysis of $\chi^2$ in StkSM model in the $\epsilon-\delta$ plane. The center white region is where $\chi^2$ of the StkSM model is within 1% of the SM fits. Along the line $\epsilon=\delta$ the $Z'$ decouples and the model gives the same $\chi^2$ fit to data as in the SM (see also Appendix A).
• Figure 2: The plots give an analysis of the LEPII constraint. The upper plot, which has a $Z'$ mass range of $.2 - 1$ TeV, shows the relevant LEPII contact interaction parameter $\Lambda^{\pm l}_{VV}$ as a function of $\chi^2$ for the 19 observable of Table(1), where a $\chi^2 \sim$ 25 is the SM fit as given in Table(1), and where the (yellow,red) shaded regions correspond to $\Lambda^{\pm l}_{VV}$ = (21.7, 17.1) TeV Leptwo. The lower plot for $\chi^2$ in the range (25-50) gives $\Lambda^{\pm l}_{VV}$ as a function of the $Z$ prime mass.
• Figure 3: An analysis of the relic density of milli-charged particles arising in the StSM $Z'$ model from the hidden sector for the case $\delta =0$, $M_{\chi} =$ 150 GeV, $\epsilon = (.01-.06)$ with .01 for the innermost curve and moving outward in steps of .01. The (yellow, grey) regions ($M_{Z'}<2M_{\chi}$, $M_{Z'}>2M_{\chi}$) correspond to a (narrow, broad) $Z'$ resonance, and the WMAP-3 relic density constraints are satisfied for both a broad $Z'$ resonance and a narrow $Z'$ resonance as exhibited by the 2$\sigma$ WMAP-3 red and black bands. The region of narrow $Z'$ resonance is constrained by the LEP and Tevatron data. The region in the $2\sigma$ WMAP-3 band can be probed via a dilepton signal as shown in Fig.(\ref{['relic4']}). The red band to the left is excluded by the CDF 95% C.L. CDF data while the black band is consistent or on the edge thereof, with all constraints which can produce an observable dilepton signal.
• Figure 4: An exhibition of the dilepton signal $\sigma \cdot Br(Z'\rightarrow l^+l^-)$ at the Tevatron consistent with the WMAP-3 relic density constraint as a function of $M_{Z'}$ when $2M_{\chi}=300$ GeV. The curves in ascending order are for values of $\bar{\epsilon}$ in the range $(0.01-0.06)$ in steps of 0.01. The dilepton signal has a dramatic fall as $M_{Z'}$ crosses the point $2M_{\chi}=300$ GeV where the $Z'$ decay into the hidden sector fermions is kinematically allowed, widening enormously the $Z'$ decay width. The green shaded regions are where the WMAP-3 relic density constraints are satisfied for the case when there is no kinetic mixing. Red and blue regions are for the case when kinetic mixing is included. The DØ data set Abazov:2005pi was collected in the search for narrow resonances (RS) and is a stronger constraint to apply on this model than the recent CDF CDF data which put constraints on the parameter space when the $Z'$ can decay only into matter in the visible sector.
• Figure 5: Same as Fig.(\ref{['relic4']}) except that only the mass region with a detectable dilepton signal at the Tevatron is exhibited but additional $\delta$ values are included in the analysis. The plots show that the region allowed by WMAP-3 constraints moves to the right for positive $\delta$ and to the left for negative $\delta$. This phenomenon is explained in Appendix D. The inclusion of kinetic mixing is seen to enlarge the parameter space where the relic density constraints are satisfied and where an observable dilepton signal at the Tevatron can occur.