Search for new particles leading to $Z+\mathrm{\text{jets}}$ final states in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We present the results of a search for new particles that lead to a $Z$ boson plus jets in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using the Collider Detector at Fermilab (CDF II). A data sample with a luminosity of $1.06{\mathrm{fb}}^{-1}$ collected using $Z$ boson decays to $ee$ and $\mu \mu$ is used. We describe a completely data-based method to predict the dominant background from standard model $Z+\mathrm{\text{jet}}$ events. This method can be similarly applied to other analyses requiring background predictions in multijet environments, as shown when validating the method by predicting the background from $W+\mathrm{\text{jets}}$ in $t\overline{t}$ production. No significant excess above the background prediction is observed, and a limit is set using a fourth generation quark model to quantify the acceptance. Assuming $\mathrm{BR}(b^{\prime }\to bZ)=100\%$ and using a leading-order calculation of the $b^{\prime }$ cross section, $b^{\prime }$ quark masses below $268\mathrm{GeV}/c^2$ are excluded at 95% confidence level.

Figure 1

Distribution of $M_{\ell \ell }$ of $Z\to ee$ and $Z\to \mu \mu$ data (black points and errors) using the baseline $Z$ selection described in the text. Overlaid are standard model $Z\to ee$ and $Z\to \mu \mu$ Monte Carlo events, normalized to the number of events expected with the given luminosities using the expected cross section of 250 pb.

Figure 2

$E_T$ distribution of the third highest $E_T$ jet in standard model $Z\to \mu \mu$ Monte Carlo simulations. Events with $N_{\mathrm{jet}}^{30}\le 2$ have $E_T<30\mathrm{GeV}$; events with $N_{\mathrm{jet}}^{30}\ge 3$ have $E_T>30\mathrm{GeV}$.

Figure 3

$E_T$ distribution of the third highest $E_T$ jet in standard model $Z\to \mu \mu$ Monte Carlo events. The distribution is fit to Eq. (1) in the range $15<E_T<30\mathrm{GeV}$, and extrapolated to the $E_T>30\mathrm{GeV}$ region. In this and following figures, when comparing binned histograms to unbinned fits, we place the $x$-value of each bin at the average of the entries in that bin.

Figure 4

$E_T$ of the highest $E_T$ jet in standard model $Z\to \mu \mu$ Monte Carlo events. The distribution is fit to Eq. (1) in the region $20<E_T<80\mathrm{GeV}$ (dotted line), and again in the region $20<E_T<40\mathrm{GeV}$ (solid line).

Figure 5

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=1$ events (open squares) and in $N_{\mathrm{jet}}^{30}=2$ events (solid circles) in $Z\to \ell \ell$ data. Events with higher $N_{\mathrm{jet}}^{30}$ have harder $E_T$ spectra.

Figure 6

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=1$ events in standard model $Z\to \mu \mu$ Monte Carlo events. The distribution is fit to Eq. (1) in the range $E_T>30$.

Figure 7

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=2$ events in standard model $Z\to \mu \mu$ Monte Carlo events. The distribution is fit to Eq. (1) in the range $E_T>30$, with the parameter $p_2$ fixed to that obtained from Fig. 6.

Figure 8

The extrapolation of the exponential parameter $p_1$ vs $N_{\mathrm{jet}}^{30}$ in standard model $Z\to \mu \mu$ Monte Carlo events.

Figure 9

$N_{\mathrm{jet}}^{30}$ distribution in standard model $Z\to \mu \mu$ Monte Carlo events, fit to an exponential in the range $N_{\mathrm{jet}}^{30}\le 2$. This shape is used to estimate the relative fractions of events with 3, 4, 5, … jets.

Figure 10

The $E_T$ of a random jet vs the $E_T$ of the other, using jets with $N_{\mathrm{jet}}^{30}=2$ in $Z\to \ell \ell$ data.

Figure 11

The prediction for the $J_T^{30}$ distribution (blue, solid line) of standard model $Z$ Monte Carlo and its uncertainty (gray band), compared to the actual distribution (black points with errors).

Figure 12

$E_T$ distribution of the third highest $E_T$ jet in $“X”+\mathrm{\text{jet}}$ events selected with the jet triggers as described in the text. The distribution is fit to Eq. (1) in the $15<E_T<30\mathrm{GeV}$ region and extrapolated to the $E_T>30\mathrm{GeV}$ region.

Figure 13

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=1$ $“X”+\mathrm{\text{jet}}$ events, selected with the jet triggers as described in the text. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region.

Figure 14

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=2$ $“X”+\mathrm{\text{jet}}$ events selected with the jet triggers as described in the text. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region with the parameter $p_2$ fixed to that obtained from the fit in Fig. 13.

Figure 15

The extrapolation of the exponential parameter $p_1$ vs $N_{\mathrm{jet}}^{30}$ in $“X”+\mathrm{\text{jet}}$ events selected with the jet triggers as described in the text.

Figure 16

$N_{\mathrm{jet}}^{30}$ distribution in $“X”+\mathrm{\text{jet}}$ events selected with the jet triggers as described in the text. The distribution is fit to an exponential in the range $N_{\mathrm{jet}}^{30}\le 2$.

Figure 17

The prediction (blue, solid line) and uncertainty (gray band) for the $J_T^{30}$ distribution of $“X”+\mathrm{\text{jet}}$ events selected with the jet triggers as described in the text. The prediction is compared to the actual distribution (black points with errors). The observation agrees with the prediction.

Figure 18

Distribution of $M_X$ in $“X”+\mathrm{\text{jet}}$ events selected from the electron triggers as described in the text. The shaded regions are removed; that is, events with $M_X>70\mathrm{GeV}/c^2$ are selected, and the $81<M_X<101\mathrm{GeV}/c^2$ region is vetoed.

Figure 19

$E_T$ distribution of the third highest $E_T$ jet in $“X”+\mathrm{\text{jet}}$ events selected with the electron triggers as described in the text. The distribution is fit to Eq. (1) in the $15<E_T<30\mathrm{GeV}$ region and extrapolated to the $E_T>30\mathrm{GeV}$ region.

Figure 20

The prediction (blue, solid line) and uncertainty (gray band) for the $J_T^{30}$ distribution of $“X”+\mathrm{\text{jet}}$ events selected with the electron triggers as described in the text. The prediction is compared to the actual distribution (black points with errors). The observation agrees with the prediction, with a maximum fluctuation downward of $1.9\sigma$. The data are below the prediction for several points because the shape uncertainty is correlated between bins.

Figure 21

The $J_T^{30}$ distribution without the $N_{\mathrm{jet}}^{30}\ge 3$ requirement in the $Z+\mathrm{\text{jet}}$ data (black line), compared to $“X”+\mathrm{\text{jet}}$ data selected with the jet triggers (red, shaded histogram) and to $“X”+\mathrm{\text{jet}}$ data selected with the electron triggers (dotted blue line).

Figure 22

$E_T$ distribution of the third highest $E_T$ jet in $W+\mathrm{\text{jet}}$ events (black line and points). The distribution is fit to Eq. (1) in the $15<E_T<30\mathrm{GeV}$ region and extrapolated to the $E_T>30\mathrm{GeV}$ region. The dotted green line shows the contribution from $t\overline{t}$ at the measured cross section of 9 pb. There is very little contribution from $t\overline{t}$ within the fit region. The extrapolated distribution is inconsistent with the background-only hypothesis, but consistent with the background plus $t\overline{t}$ hypothesis.

Figure 23

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=1$ $W+\mathrm{\text{jet}}$ events. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region.

Figure 24

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=2$ $W+\mathrm{\text{jet}}$ events. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region with the parameter $p_2$ fixed to that obtained from the fit in Fig. 23.

Figure 25

The extrapolation of the exponential parameter $p_1$ vs $N_{\mathrm{jet}}^{30}$ in $W+\mathrm{\text{jet}}$ events.

Figure 26

$N_{\mathrm{jet}}^{30}$ distribution in $W+\mathrm{\text{jet}}$ events. The distribution is fit to an exponential in the range $N_{\mathrm{jet}}^{30}\le 2$.

Figure 27

The prediction (cyan, light shaded histogram) and uncertainty (dotted lines) for the $J_T^{30}$ distribution of $W+\mathrm{\text{jet}}$ events. The expectation from $t\overline{t}$ is added to the prediction. The data (points with errors) agree with the background plus $t\overline{t}$ hypothesis.

Figure 28

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=2$ $W+\mathrm{\text{jet}}$ events. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region without fixing the parameter $p_2$.

Figure 29

Prediction for the $J_T^{30}$ distribution in standard model $Z\to \mu \mu$ events, with and without the presence of a $200\mathrm{GeV}/c^2$ $b^{\prime }$ signal introduced. The difference between the two predictions is small compared to the excess of signal at large $J_T^{30}$.

Figure 30

$E_T$ distribution of the third highest $E_T$ jet in $Z\to ee$ and $Z\to \mu \mu$ events with $N_{\mathrm{jet}}^{30}\le 2$. The distribution is fit to Eq. (1) in the $15<E_T<30\mathrm{GeV}$ region and extrapolated to the $E_T>30\mathrm{GeV}$ region. Events with $N_{\mathrm{jet}}^{30}\ge 3$ (equivalent to $E_T>30\mathrm{GeV}$, the hatched region) are removed from the distribution.

Figure 31

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=1$ $Z\to ee$ and $Z\to \mu \mu$ events. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region.

Figure 32

$E_T$ distribution of jets in $N_{\mathrm{jet}}^{30}=2$ $Z\to ee$ and $Z\to \mu \mu$ events. The distribution is fit to Eq. (1) in the $E_T>30\mathrm{GeV}$ region with the parameter $p_2$ fixed to that obtained from the fit in Fig. 31.

Figure 33

The extrapolation of the exponential parameter $p_1$ vs $N_{\mathrm{jet}}^{30}$ in $Z\to ee$ and $Z\to \mu \mu$ events.

Figure 34

$N_{\mathrm{jet}}^{30}$ distribution in $Z\to ee$ and $Z\to \mu \mu$ events. The distribution is fit to an exponential in the range $N_{\mathrm{jet}}^{30}\le 2$.

Figure 35

The prediction (solid blue line) and uncertainty (gray band) for the $J_T^{30}$ distribution of $Z\to ee$ and $Z\to \mu \mu$ events.

Figure 36

$E_T$ distribution of the third highest $E_T$ jet in $Z\to ee$ and $Z\to \mu \mu$ events. The fit from Fig. 30 is overlaid. The fit extrapolation matches the distribution above 30 GeV well.

Figure 37

The $J_T^{30}$ prediction and uncertainty from Fig. 35 compared to the observed distribution (black points and errors) in $Z\to ee$ and $Z\to \mu \mu$ events with $N_{\mathrm{jet}}^{30}\ge 3$. The prediction agrees well with the data.

Figure 38

Cross section limit vs $b^{\prime }$ mass, set at a confidence level of 95%. In the acceptance calculation $\mathrm{BR}(b^{\prime }\to bZ)\equiv \beta =100\%$ was assumed. If $\beta <100\%$, the acceptance would scale by the factor $1-(1-\beta {)}^2$, since the $b^{\prime }$ is produced in pairs and only one of them is required to decay to a $Z$ with our selection. In addition, non-$Z$ decays could change the acceptance of the $N_{\mathrm{jet}}^{30}\ge 3$ cut.