Study of di-boson production with the CMS detector at LHC

The relatively high cross sections and the clean signatures of multi-lepton final states make the pp → Z°Z° → e + e - e + e - and pp → WZ° → 3l(l = e, μ) processes accessible in early CMS data. The CMS potential for the observation and study of these processes is assessed using fully simulated signal and background Monte Carlo samples. The main systematic effects relevant for cross section measurements with 1 fb -1 and 10 fb -1 of data are addressed. We demonstrate that multiple gauge-boson production in pp collisions at LHC energies can be observed in the early phase of the experiment, with an integrated luminosity of 1 fb -1 or less.


Introduction
The study of multiple gauge-boson production at the ¢ ¡ ¤ £ scale constitutes a unique opportunity to test the Standard Model of electroweak interactions at the highest possible energies. ¤ ¥ production in collisions proceeds mainly through ¥ -channel quark annihilation, as shown in Fig. 1a. This process is sensitive to the ¤ triple gauge-boson coupling and allows to test the non-Abelian nature of the gauge symmetry of the Standard Model. No neutral triple-gauge-boson coupling exists in the Standard Model and the ¥ -channel contribution to the ¦ ¦ ¢ ¤ ¥ ¤ ¥ production is strongly suppressed: the ¡ ¢ ¤ ¥ § ¤ ¦ ¥ production proceeds through the § -channel process depicted on The multi-lepton final states of multiple gauge-boson production are an important background in the search for New Physics, in particular Supersymmetry. A sound understanding of their production process is therefore needed in the first phase of LHC data-taking before any discovery can be claimed. In particular, ¤ ¥ ¤ ¥ production is an irreducible background to the most-coveted discovery at the LHC: the Standard Model Higgs boson. Its early measurement is therefore important. , respectively [1]) and the multi-lepton final states of interest have clean signatures. Competing background processes include the production of single ¤ ¥ bosons together with one or two leptons, possibly from heavy-quark jets, and the production of top-quark pairs where both bosons in the final state decay leptonically.
The signal and background samples used in this analysis are discussed in Section 2. Section 3 describes the analysis, with particular emphasis on lepton selection, in Section 3.1. The event selections are presented in Section 3.2, the expected event yields in Section 3.3 and the main sources of systematic uncertainties in Section 4. The results expected for the first measurements of the ¡ ¢ ¤ ¥ ¤ ¥ and ¢ ¤ ¥ cross sections with 5 fb 9 8 and 5 6 fb 9 8 of integrated luminosity are presented in Section 5. Finally, Section 6 outlines the conclusion that di-boson production can be observed in early LHC data, with the first inverse femtobarn of luminosity or less.

Signal and background modeling 2.1 Signal
Several Monte Carlo generators model the ¢ ¤ ¥ § ¤ ¦ ¥ and ¢ ¤ ¥ processes at leading-order (LO): PYTHIA [2], HERWIG [3], DKS [4], MCFM-LO [5] and Baur-Rainwater [6]. They were compared and found to predict consistent cross sections and kinematic distributions. Most programs deal with finite-width gauge bosons and include the ¤ ¥ 0 ) 2 1 interference, with a lower cut on the mass of the virtual photon typically at 5 3 ¡ £ 2 4 5 7 6 . The studies described in this note are based on samples generated with PYTHIA: 3 .
Generated events were passed through the full GEANT simulation of the CMS detector. Underlying events and pile-up corresponding to the low-luminosity phase of the LHC are included in the simulation.  processes. Similarly, Figure 4 illustrates the contribution of off-shell bosons to the ¤ ¥ channel: the peak at the mass corresponds to the case of an on-shell boson produced in the ¥ -channel and decaying into an off-shell and a virtual photon. Figure 5 shows the differential cross section of the ¤ ¥ channel as a function of the lepton transverse momentum, ¨ . Only on-mass shell bosons are considered in Fig 5. This study concentrates only on final states with two on-shell gauge bosons. In the following, a lepton pair from an on-shell ¤ ¥ boson is defined as a lepton pair which, at generator level, originates from a common particle and has a mass between 70 and 110 ¡ of the simulated samples, respectively.
where the lepton phase-space cuts defined above are applied as well as the definition of on-shell bosons.  The cross section quoted above does not include contributions at the next-to-next-to-leading order nor those from the gluon-fusion box [4], ¡ ¢ ¤ ¥ § ¤ ¦ ¥ . These contributions could increase the signal cross section by as much as 20%.
The NLO ¤ ¥ cross sections are calculated with the MCFM program to be: not including the leptonic branching fractions for the gauge bosons. Figure 7 illustrates the dynamic difference between the NLO and LO cross sections. They result into an average & -factor of 1.92.  is due to a divergence in the NLO calculations. same ¢ -jet, even though this last case usually results in low-mass lepton pairs. Again, additional high-leptons can originate from heavy-flavor hadron decays in ¢ -quark jets.

Backgrounds
processes have large production cross sections and are potential sources of background. However, as discussed in Section 3.3.2, these processes are strongly suppressed by the event selection and are not detailed in the following. Four-lepton production through final-state radiation in ¥ -channel ¤ ¥ -boson production is also neglected since is expected to be highly suppressed by the selection cuts.
Despite their relatively-low cross-section, the ¤ ¥ ¤ ¥ and ¤ ¥ ) 1 processes are also potential backgrounds for the ¤ ¥ analysis. The ¤ ¥ ) 1 process is also a background in the ¤ ¥ ¤ ¦ ¥ analysis.
Other sources of background are due to the presence of one or more fake leptons. The ¤ ¥ and ¤ ¥ ¤ ¥ analyses aim to strongly suppress this background to cope with the large cross section of the dominant background processes. To better tune the analyses, the § § The background samples used in the analysis are summarized in Table 2. All generated events were passed through the full GEANT simulation of the CMS detector. Underlying events and pile-up corresponding to the low-luminosity phase of the LHC are included in the simulation.   is applied on the mass of the electron pair, effectively suppressing virtual-photon contribution.
. The ¤ ¥ boson or the virtual photon are forced to decay into¨ ¡ and at least four electrons must be present in the final state, within the acceptance cuts . The additional electron pair must satisfy The & -factors and the product of the NLO cross sections, of the branching ratio ratios into leptons and of the kinematical factors associated to pre-selections at the generator level are presented in Table 3    ) associated to the generator-level pre-selection, and equivalent integrated luminosity, for each of the samples used in this analysis.

Trigger and event reconstruction
The analyses discussed in this note are based on the selection of three or more charged leptons with the techniques discussed in the following both at the trigger level and the reconstruction level. Leptons originating from b-quarks as well as events containing additional hard jets are a background to suppress. Their identification is also discussed in the following.  Table 5 together with their total.

Trigger
The level-one and HLT efficiencies for events retained by the complete ¤ ¥ § ¤ ¦ ¥ and ¤ ¥ event selections discussed below are 100%.

Electron identification
Electron candidates are defined from clusters in the electromagnetic calorimeter associated to charged tracks. In order to reduce the small fraction of mis-matching, we require that the electron candidates satisfy 6 , where is the cluster energy and ¡ the track momentum, as shown in Figure 8. . This figure is mostly due to the tracking geometrical acceptance and to the track-matching efficiency. This is illustrated in Figure 9 where the efficiency decreases as a function of @ , as the amount of material in the tracker system increases, corresponding to a higher Bremsstrahlung probability. The drop in efficiency around 9@ 2 9 ' 5 D' corresponds to the transition between the barrel and end-cap region of the electromagnetic calorimeter. An efficiency of 0.7% is observed for fake electrons, i.e. electron candidates which do not correspond to a generated electron.
The following isolation cuts are defined to reject electron candidates originating from heavy quark semileptonic decays: , the ratio of energy deposited in the hadronic calorimeter to that deposited in the electromagnetic, in the region defined by the hadronic trigger tower behind the super-cluster crystal with highest energy; is the cluster energy and the sum runs over all tracks reconstructed with at least five hits in the tracker and with transverse momentum around the electron direction; is the number of tracks reconstructed with at least five hits in the tracker and with transverse momentum

Muon identification
Muon candidates are reconstructed from information in the muon chambers and the tracker. Leptons from the decay of ¢ quarks in the background processes are produced in a higher-multiplicity environment and two isolation

Identification of semileptonic b-decays
The significance of the lepton impact-parameter in the plane transverse to the beam, S £ ¡ , discriminates against leptons from heavy-quark decays in all Standard Model background processes. This variable is defined as the ratio between the measured impact parameter and its uncertainty. Figure 12 shows distribution of the S £ ¢ for muons from the ¤ ¥ signal and from the background samples. We require S £ ¢ A for all three leptons in the ¤ ¥ candidate selection. Figure 13 shows the reconstruction efficiency for muons with all selection criteria to be applied.

Jet reconstruction
The § § reconstructed for the signal and the different background processes is plotted in Figure 14.  , respectively. These thresholds are inspired by the differential cross sections presented in Figure 3. These cuts suppress the contribution from the ¤ ¥ ) corresponding to the virtual photon. Figure 16 shows the distribution of the difference between the reconstructed and generated¨# masses for the ¤ ¥ candidates,   . Figure 17 shows the distribution of the difference between the reconstructed and generated muon-pair masses for the ¤ ¥ candidates,    Figure 19: Mass distribution of the¨¨ pairs for selected events of the ¤ ¥ ¢ ¢ background, normalized to 5 7 6 fb 9 8 of data, with two entries per event. The dashed histogram represents the distribution after all cuts, while the solid histogram shows the effect of relaxing the cuts on the electron ¨ .

¤ ¥ sample
The number of events expected in 1 fb 9 8 of integrated luminosity and the selection efficiencies for the ¤ ¥ signal and the various background samples are presented in Tables 8 and 9, which also illustrate the sequential effect of each selection cut. The § § $ ! " 7 3 and ¤ ¥ ¢ ¢ final states are the most pernicious backgrounds, given their large cross section. They are usually associated with one or more hard jets. These backgrounds are reduced by removing events with at least one jet, as discussed in Section 3.1.5. In addition to the background sources listed in Tables 8 and 9, also the ¡ ¢ ¢ ¢ and the ¢ ¤ ¥ ¤ § ¦ § ¥ were considered. The former might mimic a ¤ ¥ boson with a lepton coming from the -boson decay and a lepton from heavy quark decays, or both lepton from heavy quark decays. As the mass of the this lepton pair tends to be small, no events survive the process may be a potential source of background in presence of fake leptons from the jets. No events from a dedicated Pythia Monte Carlo survived the selection. However, given the large cross section of this process, this study is extended. A limit of 1 event per fb @ 8 is derived by combining the probability for a fake lepton to be retained by the selection cuts, 5 D ¥ 5 7 6 ' , and the selection efficiency for the ¤ ¥ ¢ ¢ process.

Systematics
Several sources of systematic uncertainty will affect the calculation of the significance of the first observation of the ¤ ¥ and ¤ ¥ ¤ ¥ signals at the LHC and the measurement of their cross sections. They are listed in the following.
Luminosity. The knowledge of the integrated luminosity affects the measurement of the cross section of the ¤ ¥ and ¤ ¥ § ¤ ¦ ¥ signals, but not the calculation of the significance of their first observation. Systematic uncertainties of 10% and 5% are assigned for the luminosity measurement of the first 1 fb @ 8 and 10 fb @ 8 , respectively.
Trigger efficiency. The uncertainty on the efficiency of the level-one and HLT triggers, presented in Tables 4  and 5, is assumed to be 1%.
Background subtraction. The level of background retained by the ¤ ¥ and ¤ ¥ ¤ ¥ selections will be estimated from a study of the side bands of the mass distribution. At the same time, the signal yield will be derived from a maximum-likelihood fit to the mass distribution. This procedure will be sensitive to the shape of the main background components, mostly of the ¤ ¥ £ ¢ ¢ background which exhibits a peak behaviour in the di-lepton mass. The § § background does not have such a peak. These shapes will be derived from Monte Carlo simulations and checked on data. The high purity of the selections makes them rather insensitive to this source of systematic uncertainty, evaluated at 0.6%. contribution peaks around ¡ in the¨ mass spectrum, we conservatively assign a 1.2% systematic uncertainty on the estimation of this contribution. This is a conservative limit since the ¤ ¥ ) 1 component could be included in a global maximum-likelihood fit to estimate the signal yield.

Electron identification:
The control of the electron identification-efficiency is a potential source of systematic uncertainty due to possible discrepancies between data and Monte Carlo simulations. These effects will be extensively studied with high statistics control samples such as ¤ ¥ ¢ ¡ decays from the inclusive production of ¤ ¥ bosons which has a large cross section of 15 ¡ % . A statistical precision on the control of electron efficiency of better than 1% is expected with less than 1 fb @ 8 of data [11]. Taking into account a tracking efficiency uncertainty of 1% per track, we assign an uncertainty of 2% per identified electron for the first fb @ 8 of integrated luminosity, expected to decrease to 1.5% with 10 fb 9 8 .

Muon identification:
The muon identification-efficiency will be measured from data by using ¤ ¥ ¢ 1 9 1 control sample, with a procedure similar to the one outlined above for electrons. Given the similar statistical power of this method for the two channels, the same systematic uncertainty for muon identification is assigned as for electron identification.
Jet energy scale resolution: The efficiency of the jet veto cut depends on the energy scale uncertainty. The effect of this uncertainty, taken as 10% for jets with Ï ! 6 3 ¡ £ , is assessed by varying accordingly the threshold of the jet veto and observing the corresponding changes in the event yield. PDF and QCD scale uncertainty: The estimation of the signal significance is affected by the uncertainty on the number of expected events, due to the limited knowledge of signal cross section. This source of uncertainty does not affect the measurement of the signal cross sections. For the ¤ ¥ ¤ ¥ process, a a 6.4% uncertainty is assigned to the QCD scale and the PDF parameterization [12]. For the ¤ ¥ process, different PDF parametrizations and QCD scales are used to compute the production cross section with the MC@NLO Monte Carlo generator [13]. A 3.7% difference is observed in the cross section, which propagates to the signal yield. The kinematics of the event, and therefore the selection efficiencies, also depend on the PDF. This effect however is assumed to be small for the signal, and is neglected as a source of systematics.
The sources of systematic uncertainties and their effects on the estimation of the cross section and signal significance of the ¢ ¤ ¥ ¤ ¥ process are summarised in Tables 10 and 11, respectively, for integrated luminosities of 5 fb @ 8 and 5 6 fb @ 8 . Table 12 lists the corresponding systematic uncertainties for the ¢ ¤ ¥ process in 5 fb 9 8 of integrated luminosity. These are calculated weighting the four different final states according to their yield. All sources of systematic uncertainties are considered as uncorrelated.

Results
The expected event yield is computed as: for the different data samples are presented in Table 3. The event yields for the signal and the background sources in the ¤ ¥ § ¤ ¦ ¥ and ¤ ¥ selections are summarized in Tables 13  and 14, respectively.
An estimator based on the likelihood ratio is used to assess the significance of the signal observation. Figures 20 and 21 show the expected signal significance as a function of integrated luminosity for the ¤ ¥ ¤ ¥ and ¤ ¥ analyses, respectively. The dashed line corresponds the a signal efficiency taking into account a worsening by 2% per lepton of the identification efficiency. The dotted line accounts for the systematic uncertainties listed in Tables 11 and 12. A five-sigma significance for the ¤ ¥ § ¤ ¦ ¥ observation is expected for about one inverse femtobarn on integrated luminosity, while ¤ ¥ production will be observed at five sigma with just 150 inverse picobarn.        The NLO cross section of the ¡ ¢ ¤ ¥ ¤ ¥ ¢ ¡ process, within the four-electron acceptance of the CMS detector, is calculated to be 18.7 fb. The present analysis selects 38% of this signal with a yield of 7.1 signal events for 0.4 background events per inverse femtobarn of LHC integrated luminosity. The ¤ ¥ selection results in a yield of 97 signal for 21 background events per inverse femtobarn.
For the first 1 fb 9 8 of integrated luminosity, the total systematic uncertainties on the ¤ ¥ ¤ ¥ and ¤ ¥ cross section determinations are 12.9% and 17.4%, respectively. Both the ¤ ¥ § ¤ ¦ ¥ and ¤ ¥ final states can be selected with high purity and a significance of 4.8 and 12.8, which include systematic effects, is expected in the first 1 fb @ 8 of integrated luminosity. The ¤ ¥ channel can be observed with a significance of 5, including systematic uncertainties on detector effects and theoretical predictions, in an integrated luminosity of 150 pb @ 8 .
The relatively large signal yield and low level of background for the the ¤ ¥ § ¤ ¦ ¥ ¢ ¡ 4 ¡ and ¤ ¥ ¢ channels makes them particularly attractive for the study of anomalous triple gauge boson couplings, even with as low as 10 fb @ 8 of data.
In case of a very massive Higgs boson, extracting a Higgs boson to ¤ ¥ ¤ ¥ signal, and determining its spin-parity, will require a detailed understanding of the ¤ ¥ boson polarization and of spin correlations in the ¢ ¤ ¥ ¤ ¥ process. This study can start with relatively modest integrated luminosity.
In perspective, this study of multiple gauge-boson production and couplings at the LHC will be extended to include the ) [14] and ¤ ¥ ) [15] channels, as well as the other flavours of ¤ ¥ § ¤ ¦ ¥ fully-leptonic decays.