W + jets Study at CDF Run II

Tests of enhanced leading order QCD in W boson plus jets events from 1.96 TeV $p\bar{p}$ collisions

We have studied the W + $\geq$ n jets process in Tevatron Run II experiment. This is the first results for the CDF Run II experiment. The data used corresponds to an integrated luminosity of 72 $pb^{-1}$ taken from Mar.2002 through Jan.2003. The lowest order QCD predictions have been tested with a new prescription of the parton-jet matching, which allows to construct the enhanced LO phase space. We found a good agreement between data and theory in all kinematics distributions. Number of events for each inclusive samples up to 3 jets are compared with Monte Carlo calculations. The comparison with Run I results is also presented.

These results will be presented at HEP2003 conference. For the moment, we do not present all details about the estimation of the cross section measurements until Lepton/Photon 2003.

Data set

The data used in this analysis were taken with the HIGH_PT_ELECTRON18 trigger from Mar.2002 to Jan.2003 (Run\# 141544 $\sim$ 156487) corresponding to an integrated luminosity of 72.0 $pb^{-1}$. Data were processed on CdfSoft2 Offline version 4.8.4 and, before filling the ntuples, the high level objects were remade by TopNtuple using CdfSoft2 Offline version 4.9.1hpt1. To ensure a good quality data we required each run to satisfy the set of minimal conditions.

W->enu selection cuts

For the event selection, we slightly modified the standard cuts used for the 2003 winter conferences. To better reject the background in the multijet samples we used an higher missing $E_{T}$ cut, and, to keep a reasonable amount of events, we lowered the electron $E_{T}$ threshold which doesn't play a crucial role in the electron background rejection. This choice is justified by the fact that the corrections to the missing $E_{T}$ are not yet fully understood and we preferred to sacrifice some selection efficiency keeping an high purity.

Et > 20 GeV , MET > 30 GeV

We use 31,726 events of the W candidates.

Jet selection

The JetClu algorithm is used in this analysis with a full jet energy correction (lvl.7). The requirements on transverse energy and on $\eta$ coverages are :

Et > 15 GeV , | eta | < 2.4 , Rc = 0.4 .

The systematics of the jet energy correction is +- 10 \%. This value is conservatively large because we saw some discrepancy between the energy of jets and matched partons at low $E_{T}$ region in the multi-partonic process. Also, since we do not apply any background subtraction, that size of systematics also includes the background contribution. The merging/splitting criteria to the observed jets is taken as the Jet Separation basis $R_{sep}^{95\%}$.

Comparison with data and MC

The W + 0 jet process is a HERWIG built-in process. The multi-jet processes are produced by GR@PPA event generator \cite{grappa} for 1,2, and 3 jets process and Alpgen event generator \cite{alpgen} for 4 jets process. The calculation results of GR@PPA and Alpgen are good agreement within 1 \%. Those generated events were pass though HERWIG showering program, and then passed though the full detector simulation. Two energy scales of M_{W}^{2} and ave.P_{T}^{2} are taken in the ME calculations, where the renormalization scale and factorization scale are fixed to the same value. For Alpgen, the energy scale of ave.P_{T}^{2} was not available. Also, we would emphasize that a new systematics of the parton-jet matching is included in the MC predictions.

Jet Et distribution

From the upper-most side, the distributions are the highest $E_{T}$ jet in W + $\geq$ 1 jet events, the second highest $E_{T}$ jet in W + $\geq$ 2 jet events, and so forth. The solid and dashed lines are the LO QCD predictions produced by GR@PPA and Alpgen with the energy scale of $M_{W}^{2}$ and $^{2}$, respectively. The shade band among the data point is estimated by the fluctuation of the 10\% systematics in the jet energy corrections. The MC prediction is good agreement with the data.

Angular and mass distributions

The invariant mass and the separation angle between two jets is a sensitive variable to the collinear/infrared singularity. Some differences may be an indicator to the higher order pertubative calculation. The plots shows the dijet mass distribution and the jet separation angle between the highest $E_{T}$ jet and the second highest $E_{T}$ jet in the W + $\geq$ 2 jets events and the W + $\geq$ 3 jets events, respectively.

Jet multiplicity

Using the cross section of the MC, we can compare the number of jets distribution with the data. The lower and upper band on the LO QCD predictions correspond to the energy scale of Mw^{2}$ and ave.Pt^{2}, respectively. All the acceptance or detection efficiencies are already included into the number of detected events because the MC events are also passed though the detector simulation. On this plot, we did not consider any background contributions. However, those background contaminations are almost negligible in the W + 0,1,2,3 jets events. Indeed, those fraction are $\sim$1.3\%, $\sim$4.4\%, $\sim$4.7\%, and $\sim$10.1\% in the W + 0,1,2,3 jets events, respectively.

The relative size of the jet multiplicity on the data is well reproduced by the LO calculations.

Ratio of the jet multiplicity

From the top, the ratio of theory to data, the ratio of n jets events to n-1 jets events, and the ratio to the ratio of n jets events to n-1 jets events,

R_{n}/(n-1) = \frac{\sigma_{n}}{\sigma_{n-1}} ,

are presented. Taking the ratio of the physics variable is to cancel out the uncertainties from the absolute source like the luminosity. The identification efficiency or acceptance etc. may also cancel somehow out. Remarkable feature is that the MC predictions are showing the almost constant behavior on each ratio plot. That means that our analysis method and MC prediction well describe the data. This flat behavior is crucial for the measurement of the strong coupling constant $\alpha_{s}$.

Comparison with Run I measurement

It is practical to compare with the Run I measurement. The fraction of the Run II data is slightly larger than the Run I results. This is not obvious feature.

Summary

We have studied the W + $\geq$ n jets process in Tevatron Run II experiment. Data was used for the winter conference with the luminosity of 72 $pb^{-1}$ during the period of Mar.2002 to Jan.2003. This is the first results for the CDF Run II experiment. The lowest order QCD perturbation have been tested with a new prescription of the parton-jet matching. This requirement is to construct the enhanced LO phase space. All the distributions are good agreements with the data and theory. Jet multiplicity is also compared with the data up to 3 jets events. Non-background condition is assumed. But those background effects are almost negligible in the less than 3 jets events. The constant (flat) behavior can be seen in the various ratio plots. This is very important feature to certify our rightness of the MC generation and analysis scheme, which will be crucial for the measurement of the strong coupling constant. In the comparison with Run I results, Run II results were slightly larger than Run I results.