Precise determination of $Z\text{−}{Z}^{\prime }$ mixing at the CERN LHC

We discuss the expected sensitivity to $Z^{\prime }$ boson effects in the $W^{\pm }$ boson pair production process at the Large Hadron Collider (LHC). The results of a model-dependent analysis of $Z^{\prime }$ boson effects are presented as constraints on the $Z\text{−}{Z}^{\prime }$ mixing angle $\varphi$ and $Z^{\prime }$ boson mass. The process $pp\to W^{+}{W}^{-}+X$ allows us to place stringent constraints on the $Z\text{−}{Z}^{\prime }$ mixing angle. Specifically, we find that the present LHC bounds on the mixing angle are of the order a few times ${10}^{-3}$, which is of the same order as those derived from the electroweak data. These results were derived from analysis of $W$-pair production at $\sqrt{s}=8\mathrm{TeV}$ and integrated luminosity of $20{\mathrm{fb}}^{-1}$. Further improvement on the constraining of this mixing can be achieved from the analysis of data on $WW\to l\nu l^{\prime }{\nu }^{\prime }$ ($l,l^{\prime }=e$ or $\mu$) and $WW\to l\nu jj$ final states collected at the LHC with nominal energy and luminosity, 14 TeV and $100{\mathrm{fb}}^{-1}$, and should be $\varphi \sim {10}^{-4}–{10}^{-3}$.

Figure 1

Feynman diagrams of the $q\overline{q}(q^{\prime }{\overline{q}}^{\prime })\to W^{+}{W}^{-}$ process within the framework of the extended gauge models.

Figure 2

Invariant mass distribution of $W^{\pm }$ pairs in $pp\to W^{+}{W}^{-}+X$ in the SM (solid curve) and for the $Z_{\mathrm{SSM}}^{\prime }$ model ($M_{Z^{\prime }}=3.5\mathrm{TeV}$) with $Z\text{−}{Z}^{\prime }$ mixing angle of $\varphi ={10}^{-3}$ (dashed line) and $\varphi =0.7\times {10}^{-3}$ (dash-dotted line) at the LHC with $\sqrt{s}=14\mathrm{TeV}$.

Figure 3

Reach (at 95% C.L.) on $Z\text{−}{Z}^{\prime }$ mixing and $M_2$ mass for $Z_{\mathrm{SSM}}^{\prime }$ obtained from the inclusive process $pp\to WW\to l\nu l^{\prime }{\nu }^{\prime }$ ($l,l^{\prime }=e$ or $\mu$) at the LHC (solid lines). The allowed domain in $\varphi$ and $M_2$ is the hatched one. Current limits on $M_2$ for $Z_{\mathrm{SSM}}^{\prime }$ derived from the Drell–Yan ($l^{+}{l}^{-}$) process at the LHC (8 TeV) (horizontal solid line) as well as “typical” mass limits expected at the LHC (14 TeV) (horizontal dotted line) are shown. Limits on the $Z\text{−}{Z}^{\prime }$ mixing angle from electroweak precision data are displayed, and those expected from $W^{\pm }$ pair production at the ILC with polarized beams.

Figure 4

Same as in Fig. 3 but for $Z_{\chi }^{\prime }$.

Figure 5

Same as in Fig. 3 but for $Z_{\psi }^{\prime }$.

Figure 6

Reach (at 95% C.L.) on $Z\text{−}{Z}^{\prime }$ mixing and $M_2$ mass for $Z_{\mathrm{SSM}}^{\prime }$ obtained from the inclusive process $pp\to WW\to l\nu l^{\prime }{\nu }^{\prime }$ at the LHC with $\sqrt{s}=8\mathrm{TeV}$ and ${\mathcal{L}}_{\text{int}}=20{\mathrm{fb}}^{-1}$ (dashed curves) and $\sqrt{s}=14\mathrm{TeV}$ and ${\mathcal{L}}_{\text{int}}=100{\mathrm{fb}}^{-1}$ (solid curves). Also shown are current limits on $M_2$ derived from the Drell-Yan process at the LHC (8 TeV) denoted by the label $l^{+}{l}^{-}$ and constraints from electroweak precision data. Note that the scale is different from that of Figs. 3, 4, 5.

Figure 7

Same as in Fig. 3 but obtained from the process $pp\to WW\to l\nu jj+X$ at the LHC with $\sqrt{s}=14\mathrm{TeV}$ and ${\mathcal{L}}_{\text{int}}=100{\mathrm{fb}}^{-1}$. The dashed red line shows the predicted relation between $\varphi$ and $M_2$, given by Eq. (6) for the model of Ref. [50]. Note that the scale is different from those of Figs. 3, 4, 5, 6.