$Z^{\prime }$ gauge bosons at the Fermilab Tevatron

We study the discovery potential of the Tevatron for a $Z^{\prime }$ gauge boson. We introduce a parametrization of the $Z^{\prime }$ signal which provides a convenient bridge between collider searches and specific $Z^{\prime }$ models. The cross section for $p\overline{p}\to Z^{\prime }X\to {\ell }^{+}{\ell }^{-}X$ depends primarily on the $Z^{\prime }$ mass and the $Z^{\prime }$ decay branching fraction into leptons times the average square coupling to up and down quarks. If the quark and lepton masses are generated as in the standard model, then the $Z^{\prime }$ bosons accessible at the Tevatron must couple to fermions proportionally to a linear combination of baryon and lepton numbers in order to avoid the limits on $Z-Z^{\prime }$ mixing. More generally, we present several families of U(1) extensions of the standard model that include as special cases many of the $Z^{\prime }$ models discussed in the literature. Typically, the CDF and D0 experiments are expected to probe $Z^{\prime }$-fermion couplings down to 0.1 for $Z^{\prime }$ masses in the 500–800 GeV range, which in various models would substantially improve the limits set by the LEP experiments.

Figure 1

Lower bounds on $M_{Z^{\prime }}/g_z$ from the LEP-II search for $LL$, $RR$, $LR$ and $RL$ contact interactions, applied to the models of Table  as a function of the continuous parameter $x$. For $\mathrm{U}(1{)}_{B-xL}$, we have included the bound on vectorlike $e^{+}{e}^{-}\to {\ell }^{+}{\ell }^{-}$, as is appropriate for that model.

Figure 2

Excluded regions in the $c_d-c_u$ plane from the current 95% C.L. limit for $\sigma ·\mathrm{B}\mathrm{r}(Z^{\prime }\to l^{+}{l}^{-})$ given in 27, for different values of the $Z^{\prime }$ mass. The thick straight line corresponds to values of $c_u$ and $c_d$ in the $B-xL$ model, in which $c_u=c_d$. The area between the two thin straight lines is the region where the $q+xu$ model lies.

Figure 3

The ratio of the $\mathcal{O}({\alpha }_s)$ and $\mathcal{O}({\alpha }_s^2)$ corrections to the hadronic structure function over the Born contribution, assuming SM couplings for the $Z^{\prime }$. The full line corresponds to the $\mathcal{O}({\alpha }_s)$ corrections. The dashed and dotted lines, which, within the resolution of the figure, appear as a single line, correspond to the total $\mathcal{O}({\alpha }_s^2)$ contributions and to the $\mathcal{O}({\alpha }_s^2)$ corrections retaining only those terms that give contributions proportional to $c_u$ and $c_d$ to the cross section, respectively.

Figure 4

NLO and NNLO $k$-factors for SM-like couplings as a function of the invariant mass of the lepton pair. Also shown is an approximation, Eq. (3.11), for the NLO $k$-factor which only takes into account the soft corrections to the structure function in the deeply inelastic scattering scheme.

Figure 5

(a) Angular distribution, in the CM frame of the lepton pair, at LO in QCD for different models. The lines labeled no $u$ ($d$) coupling correspond to SM charges but neglecting the coupling of up (down) type quarks to the $Z^{\prime }$. (b) Ratio between the differential cross section (shown in panel a) in different models and the case of SM-like charges.

Figure 6

The Acceptance ($A$), computed from the LO cross section integrated over the azimuthal angle of the leptons in the laboratory frame in the region ${50}^{°}\le {\theta }_{\mathrm{l}\mathrm{a}\mathrm{b}}\le {130}^{°}$. We considered the cases of SM couplings, SM couplings without $u$-quark couplings and without $d$-quark couplings, respectively. To show the variation compared to a most extreme situation, we normalize to the corresponding LO acceptance of the $\mathrm{U}(1{)}_I$ model.

Figure 7

Projected bounds for the $B-xL$ (left upper panel) and $10+x\overline{5}$ (right upper panel) models and projected excluded regions in the $c_d-c_u$ plane (lower panel). In the two upper panels, the vertical marks show the current LEP bounds for the $Z^{\prime }$ mass obtained as described in Sec. 2c. In the $B-xL$ case, for $x=3$ this last bound is $M_{Z^{\prime }}\ge 1800\mathrm{G}\mathrm{e}\mathrm{V}$; for the $10+x\overline{5}$, the bound for $x=0$ is $M_{Z^{\prime }}\ge 119\mathrm{G}\mathrm{e}\mathrm{V}$, beyond the scope of the figure. The projected bounds at luminosities $\mathcal{L}=2{\mathrm{f}\mathrm{b}}^{-1},10{\mathrm{f}\mathrm{b}}^{-1}$ are obtained from Fig. 2 by scaling with a factor $1/\sqrt{\mathcal{L}}$. The lower panel also shows the regions in the $c_d-c_u$ plane corresponding to the $B-xL$ and $q+xu$ models, as in Fig. 2, showing the projected increase in reach with two ${\mathrm{f}\mathrm{b}}^{-1}$. The dots labeled $a$, $b$ and $c$ correspond to the $B-L$ model with $g_z=0.1$, $g_z=0.3$ and $g_z=0.5$, respectively.

Figure 8

The forward-backward asymmetry at LO for the $B-L$ and $U(1{)}_{d-xu}$ models with $M_{Z^{\prime }}=700\mathrm{G}\mathrm{e}\mathrm{V}$. In the case of $B-L$ we chose $g_z=0.1$. For the $\mathrm{U}(1{)}_{d-xu}$ models, we fixed $x=1$ and $g_z=0.5$ We also show the SM prediction and recent CDF data for this observable [36].

Figure 9

NLO differential cross sections for the production of electron-positron pairs as a function of the invariant mass of the pair, in the $\mathrm{U}(1{)}_{B+L}$ model. The solid curves correspond to the total cross sections for the signal, including interference terms, for the gauge coupling fixed to $g_z=0.05$ and $g_z=0.2$ respectively. Dashed lines are the same cross sections neglecting interference terms and the dotted lines correspond to the SM background.