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Search for WW and WZ resonances decaying to electron, missing ET, and two jets in ppbar collisions at sqrt(s) = 1.96 TeV

Using data from 2.9/fb of integrated luminosity collected with the CDF II detector at the Tevatron, we search for resonances decaying into a pair of on-shell gauge bosons, WW or WZ, where one W decays into an electron and a neutrino, and the other boson decays into two jets. We observed no statistically significant excess above the expected standard model background, and we set cross section limits at 95% confidence level on G*(Randall-Sundrum graviton), Z', and W' bosons. By comparing these limits to theoretical cross sections, mass exclusion regions for the three particles are derived. The mass exclusion regions for Z' and W' are further evaluated as a function of their gauge coupling strength.

Using data from 2.9 fb −1 of integrated luminosity collected with the CDF II detector at the Tevatron, we search for resonances decaying into a pair of on-shell gauge bosons, W W or W Z, where one W decays into an electron and a neutrino, and the other boson decays into two jets. We observed no statistically significant excess above the expected standard model background, and we set cross section limits at 95% confidence level on G * (Randall-Sundrum graviton), Z ′ , and W ′ bosons. By comparing these limits to theoretical cross sections, mass exclusion regions for the three particles are derived. The mass exclusion regions for Z ′ and W ′ are further evaluated as a function of their gauge coupling strength. Some models of new physics beyond the standard model predict particles that decay into pairs of on-shell bosons, for example Z ′ , W ′ [1], or the Randall-Sundrum graviton G * [2]. Searches for these particles in different decay channels have been reported elsewhere [3][4][5][6][7]. Most of them used final states consisting of only leptons or photons. In this Letter we search for these particles in the form of diboson resonances where one boson is a W decaying into an electron and a neutrino, and the other is a W or Z which decays into two jets. This search has the advantage of detecting two types of diboson resonances, W W and W Z, with the same final-state topology. The hadronic decay mode of the W or Z to two jets has a higher branching fraction compared to the leptonic mode; however, the background from jets also increases. Thus we implement a selection based on transverse energy (E T ) [8] of the detected objects in the final state to reduce standard model backgrounds and enhance sensitivity.
The diboson decay modes of Z ′ and W ′ directly probe the gauge coupling strength between the new and the standard model gauge bosons. The coupling strength strongly influences the decay branching ratios and the natural widths of the new gauge bosons. In an extended gauge model theory [1] the standard model coupling strength, g ·cos θ w , is replaced by ξ ·g ·cos θ w , where ξ = C · (M W /M V ) 2 ; C is a parameter that sets the coupling strength; and M V is the mass of the new gauge boson, Z ′ or W ′ . We set cross section limits on Z ′ and W ′ as a function of mass and of ξ. Our results extend the sensitivity beyond the CDF Run I W ′ results [9] with almost 30 times the integrated luminosity, and, for the first time, set Z ′ limits as a function of mass and gauge coupling strength. For G * , the coupling constant k/M P l dictates the branching ratio and natural width [2], where k and M P l are respectively the curvature of the extra dimension and the reduced Planck mass scale. This is also the first search for the G * in the W W decay mode.
This analysis is based on data corresponding to an integrated luminosity of 2.9 fb −1 collected using the CDF II detector between March 2002 and February 2008. The detector is approximately forward-backward and azimuthally symmetric. The detector elements relevant to this analysis are the tracking system and the calorimeters. The tracking system consists of an eight-layer silicon tracker [10] surrounded by a 96-layer open-cell drift chamber (COT) [11]. The fiducial coverage of the COT is |η| < 1.0 [8], and the silicon detector extends the coverage to |η| < 2.0. The integrated tracking system is contained within a superconducting solenoid, providing a 1.4 T magnetic field. Surrounding the tracking system are the electromagnetic (EM) and hadronic calorimeters [12], divided into "central" (|η| < 1.1) and "plug" (1.1 < |η| < 3.6) regions. The calorimeters are made of lead (EM) and iron (hadronic) absorbers sandwiched between plastic scintillators that provide measurements of shower energies. At approximately the shower maximum, the EM calorimeters contain fine-grained detectors [13] for measuring shower positions and profiles.
As we are looking for events with an electron, a neutrino, and two jets, we start with data that were collected with an online selection requirement of a central electron with |η| < 1 and E T > 18 GeV. From this dataset we select events that have an isolated electron [14] with E T > 30 GeV, a neutrino identified by the requirement that the missing E T ( E T ) > 30 GeV, two or three jets with |η| < 2.5 and E T > 30 GeV, and an overall H T > 150 GeV, where H T is the scalar sum of the electron E T , the E T , and the E T of all jets [15].
To form a W W or W Z hypothesis for the selected events, the electron and E T are first combined to form a W candidate. Because the longitudinal component of the neutrino momentum (E ν z ) is not available, the invariant mass of the electron and E T is artificially set to the W mass. With this assumption, the conservation of energy and momentum results in a quadratic equation for E ν z . If the discriminant of the quadratic equation is negative, the combination is discarded. If it is positive, there are two solutions and both are kept. In addition, two jets are combined to form a second W candidate or a Z candidate. In the case of a W candidate, we require the two-jet invariant mass (M jj ) to fall between 65 and 95 GeV/c 2 , corresponding to ±1.5σ of the expected reconstructed W resolution. In the case of a Z candidate, this window is between 75 and 105 GeV/c 2 . For a three-jet event, there are three two-jet invariant mass combinations. In this case only the pair with the invariant mass closest to either the W or the Z mass is kept in order to reduce the combinatorial background. The reconstructed W or Z candidates are then combined to form the final W W or W Z invariant mass.
Twelve standard model processes are considered as background for this analysis: W (→ e ± ν)+jets, QCD jets, tt, W W , Z(→ e + e − )+jets, W (→ τ ± ν)+jets, single top, W Z, W γ, Z → τ + τ − , γγ, and ZZ. The dominating background is W +jets whose contribution is estimated by Monte Carlo simulation using the alpgen [16] event generator, interfaced to pythia [17] for parton showering and followed by the geant 3 [18] based CDF II detector simulation. With the exception of the QCD jet background, the rest of the background processes are all estimated by Monte Carlo simulation using the pythia event generator. The cross sections used for the simulated background processes are obtained from NLO calculations.
The QCD jet background comes from events with three or more jets where one of the jets is misidentified as an electron. With this misidentified electron, the event may pass through subsequent event selection criteria and the reconstruction processes. The contribution of the QCD jet background is estimated using a dataset that has an online selection requirement of one jet with E T > 20 GeV. We first exclude events that have any identified electrons, then each jet in the central region is treated as an electron with a weight corresponding to the probability that a jet is misidentified as an electron. This probability is a function of jet E T and varies from 10 −4 at 30 GeV to 10 −3 above 100 GeV [6]. The misidentified electron is combined with the E T and then with two jets to form W W or W Z candidates as described earlier. The resulting QCD jet background is normalized to the data by matching the E T spectrum between data and expected background at their peaks around 10 GeV, where little signal is expected and the QCD jet background dominates. This normalization factor is used for the QCD jet contribution throughout the analysis. Figure 1 shows the resulting E T spectrum for events with two jets that would have passed the event selection criteria except for the E T > 30 GeV cut.
The systematic uncertainties taken into account in the background calculations are the following, listed by decreasing significance: jet energy scale (JES) uncertainty [19], theoretical cross section uncertainty [20], luminosity uncertainty [21], and jet misidentification rate uncertainty. The dominating systematic uncertainty is the JES uncertainty which amounts to ∼ 13% of the estimated background. The cross section and luminosity uncertainties are ∼ 6% each.
Signal detection efficiencies are also determined from simulated events using the pythia event generator. For a set of selected mass values ranging from 165 GeV/c 2 to 1000 GeV/c 2 , the three types of particles are simulated: G * with k/M P l = 0.1, Z ′ and W ′ with pythia default settings corresponding to the extended gauge model with a suppression factor ξ = (M W /M V ) 2 , i.e., C = 1. The reconstructed signals are Gaussian in shape, and the mass resolution is linearly proportional to the generated mass values, varying from 20 GeV/c 2 at 200 GeV/c 2 mass to 80 GeV/c 2 at 1000 GeV/c 2 mass. For calculating the efficiencies we choose an acceptance mass window corresponding to ±1.5 times the reconstructed signal resolution. This choice gives a good signal to background ratio. The same acceptance mass windows are also used to obtain the number of background events.
The systematic uncertainties taken into account for the signal acceptance, defined as the product of signal detection efficiency and integrated luminosity, in order of decreasing significance, are: jet energy scale (JES) uncertainty, luminosity uncertainty, initial state radiation (ISR) uncertainty, final state radiation (FSR) uncertainty, and parton distribution function (PDF) uncertainty. Similarly to the background uncertainties, the JES uncertainty dominates the systematic uncertainties and varies from 12% at 170 GeV/c 2 mass to 6% at 700 GeV/c 2 mass for G * , 13% (170 GeV/c 2 ) to 6% (1000 GeV/c 2 ) for Z ′ , and 9% (190 GeV/c 2 ) to 6% (1000 GeV/c 2 ) for W ′ . ISR, FSR and PDF uncertainties are of the order of 1 − 3% each and decrease with increasing diboson mass.
In order to improve sensitivity at higher mass, addi-tional sets of higher E T cuts for the constituent particles (observed in the detector as electron, E T from neutrino, and jets) are tried. Two series of the E T cut sets are implemented. The first series requires a higher E T on all four participating particles ranging from 40 GeV to 80 GeV in steps of 10 GeV. The second series requires a higher E T on only one daughter particle from each of the decaying bosons, i.e., a higher E T for either the electron or the neutrino, and the same higher E T for one of the two jets. The E T values in this series range from 40 GeV to 120 GeV in steps of 10 GeV. For each set of E T cuts the systematic uncertainties for the backgrounds and the acceptances are re-evaluated, but are found to be not very sensitive to the variations. To find the optimal set of E T cuts at each selected mass point, the expected cross section limits, which are based only on the background and the signal acceptance, are calculated for each set of cuts. We found that the first series of E T cuts gives the best expected limits for Z ′ and W ′ , while the second series is best for G * . The optimal E T cuts for each particle type are then selected from their own optimal series. The sets that give the best expected limits are chosen without reference to their impact on the data sample. Although the background processes respond differently to the two series of E T cuts, the best expected limits obtained from each series are very similar. Generally, as the mass increases the higher E T cuts yield better expected limits.
We use a Bayesian method [22] to calculate cross section limits. Inputs to the calculation are signal acceptance, estimated background, and observed data. The signal acceptance and background are assigned priors and modeled via a Monte Carlo method that allows correlation of uncertainties between acceptance and background. In our analysis, the JES and luminosity uncertainties in the acceptance and in the background are correlated. The expected limits are calculated by simulating observed data based on the expected background with Poisson fluctuations. Figure 2 shows typical invariant mass distributions reconstructed for each particle type for a mass of 600 GeV/c 2 using the optimal set of E T cuts in each case. The W W invariant mass distributions are shown for G * and Z ′ , and the W Z invariant mass distribution is shown for W ′ . The optimal set of E T cuts for G * at 600 GeV/c 2 is from the second series with E T > 120 GeV, while both Z ′ and W ′ favor the first series with E T > 60 GeV. The background compositions, as shown in Table I, are found to be more sensitive to the different sets of E T cuts than to the different decay types (W W or W Z). For Z ′ and W ′ , the QCD jet background has a much lower contribution owing to the stricter E T requirements.
Without a statistically significant excess above the expected background in the invariant mass plots, we calcu-  Fig. 2. The uncertainties include both statistical and systematic uncertainties. late the cross section limits at 95% confidence level (C.L.) for the observed data. Figure 3 shows the observed and the expected 95% C.L. cross section limits overlaid with theoretical cross sections. The theoretical cross sections for G * and Z ′ are calculated from pythia version 6.216, and a constant K-factor of 1.3 is applied to take into account the NLO correction [4][5][6]. The theoretical cross section for W ′ is derived from a NLO calculation [23]. The upper right inserts in Fig. 3 show ratios of the limits to the theoretical cross sections. Where the ratio is below one the mass region is excluded.   The results shown in Fig. 3 and Table II for Z ′ and W ′ are based on a gauge coupling mixing factor of ξ = C · (M W /M V ) 2 , with C = 1. Since signal acceptance is the only quantity that changes with ξ in the cross section limit calculation, at each mass point we reevaluate signal acceptances for different ξ values and calculate cross section limits as a function of ξ. Comparing the calculated and theoretical cross sections as a function of ξ, a ξ exclusion region is derived at each mass point. These Z ′ and W ′ exclusion regions are shown in Fig. 4. The branching ratio of Z ′ or W ′ to fermions decreases as ξ increases. This is opposite to the diboson decay modes where branching ratios increase as ξ increases. Most Z ′ or W ′ search results [6,7] report mass limits along the ξ = (M W /M V ) 2 line and we have also done so for comparison. However, the diboson decay modes and the fermionic decay modes are sensitive to different parts of the gauge coupling strength phase space, so searches for bosonic and fermionic decays of Z ′ and W ′ are complementary to each other. The W ′ result shown in Fig. 4 is significantly improved compared to the previous result from CDF Run I [9]. The Z ′ result shown is the first to set an exclusion region as a function of ξ and mass.
In conclusion, we have searched for new particles decaying into a pair of bosons in the electron, E T , and two jets final state. In data from an integrated luminosity of 2.9 fb −1 , no significant excess over the standard model prediction is observed. Cross section limits at 95% C.L. and mass exclusion regions have been obtained for a Randall-Sundrum graviton, Z ′ and W ′ bosons. The W ′ exclusion region in the ξ − M W ′ plane has been extended significantly compared to the previous measurement. We have also presented the Z ′ exclusion region in the ξ −M Z ′ plane for the first time. We set the most stringent mass limits on W ′ and Z ′ bosons.
We     Table II. Also shown in the W ′ plot is the CDF Run I result.