Constraining extra neutral gauge bosons with atomic parity violation measurements

The discovery of a new neutral gauge boson $Z^{\prime }$ could provide the first concrete evidence of physics beyond the standard model. We explore how future parity violation experiments, especially atomic parity violation experiments, can be used to constrain $Z^{\prime }$ bosons. We use the recent measurement of the ${}^{133}\mathrm{Cs}$ nuclear weak charge to estimate lower bounds on the mass of $Z^{\prime }$ bosons for a number of representative models and to put constraints on the couplings of a newly discovered $Z^{\prime }$ boson. We also consider how these constraints might be improved by future atomic parity violation experiments that will measure nuclear weak charges of multiple isotopes. We show how measurements of a single isotope and combining measurements into ratios and differences can be used to constrain the couplings of a $Z^{\prime }$ and discriminate between models. We include in our results the constraints that can be obtained from the experiments Qweak and P2 that measure the proton weak charge. We find that current and future parity violation experiments could potentially play an important role in unravelling new physics if a $Z^{\prime }$ were discovered.

Figure 1

Allowed 68% C.L. regions for the couplings $\tilde{d}$ and $\tilde{u}$ for a 2.5 TeV $Z^{\prime }$. It is assumed that all measurements are in agreement with the SM. In (a) the blue (dark grey) band corresponds to the region allowed by the ${}^{133}\mathrm{Cs}$ weak charge measurement with 0.48% precision; the green (light grey) band corresponds to the allowed regions expected from the Qweak measurement of $Q_W^p$ with 4.1% precision; and the red (medium grey) oval is the region allowed by a combined fit of $Q_W({}^{133}\mathrm{Cs})$ and $Q_W^p$. In (b) the blue (dark grey) region is the region that would be constrained by the P2 measurement of $Q_W^p$ with 2.1% precision; the green (light grey) band is the region allowed by the ${\mathcal{R}}_{\mathrm{Fr}}(121,122)$ measurement with 0.1% precision; and the orange (medium grey) oval is the region allowed by a combined fit using the SoLID results, $Q_W^p$ from P2 and Qweak, ${\mathcal{R}}_{\mathrm{Fr}}(121,122)$, and $Q_W({}^{133}\mathrm{Cs})$. In (c) the blue (dark grey) band is the region that would be constrained by a ${}^{208}\mathrm{Fr}$ weak charge measured to the precision of 0.1%; the green (medium grey) band is the region that would be constrained by a $D_{\mathrm{Fr}}$ measured to 0.1%; and the yellow (lightest grey) oval is the region that would constrained from a combined fit to $Q_W({}^{208}\mathrm{Fr})$, $D_{\mathrm{Fr}}$, and the other five measurements. (d) collects the combined fits from (a), (b), and (c) to show how successive measurements can improve the constraints on $Z^{\prime }$ couplings.