Efficiency estimation

The W boson is identified by the presence of a well isolated and high energy electron plus a large amount of transverse missing energy in the event. The electrons are also required to be central (i.e. inside the fiducial volume of the COT) where the most precise measurements are made, and, on these electrons, quality cuts are applied to ensure low background contamination. To make a W boson candidate sample, events are finally required to pass two more global cuts: (a) the event should not be flagged as a $Z^0\to e^+ e^-$ decay, and (b) to keep electrons away from any hard hadronic activity, the electron should be separated in space from the closest reconstructed jet such that $\Delta R = \sqrt{\Delta \eta^2 + \Delta\phi^2}\ge 0.52$.

The above requirements necessarily reduce the number of events available for analysis to a small fraction of all the W events produced. Therefore the yield of selected events has to be corrected by the efficiency of all the cuts applied as well as trigger and Z vertex acceptances. For the efficiencies calculations, as in the data selection, jets are clustered with JETCLU using a cone radius of 0.4. Jets are corrected, using the official jet correction package up to the partons energy, and then are selected according to the following cuts:

$$E_{T} \; > \; 15 \; GeV\, ;\qquad \vert \eta_{det} \vert \; < \; 2.4 \;$$

Since some W selection cuts are biased against events with jets, the total efficiency is measured for each W + n jets sample independently.

$$\varepsilon_{tot} = \varepsilon_{geo} \cdot \varepsilon_{kin... ...Delta R_{ej}} \cdot \varepsilon_{trig}\cdot \varepsilon_{Zvtx}$$

Table 4: Summary of W + jets efficiencies. (.ps)

Eff.	W+$\ge 0$ jet	W+$\ge 1$ jet	W+$\ge 2$ jet	W+$\ge 3$ jet	W+$\ge 4$ jet
$\varepsilon_{kin\&Geo}$	0.224$\pm$0.003	0.238$\pm$0.003	0.250$\pm$0.003	0.264$\pm$0.005	0.276$\pm$0.006
$\varepsilon_{Zveto}$	1.000$\pm$0.001	0.995$\pm$0.001	0.991$\pm$0.002	0.986$\pm$0.003	0.986$\pm$0.007
$\varepsilon_{\Delta R_{ej}}$	0.948$\pm$0.010	0.917$\pm$0.009	0.887$\pm$0.011	0.856$\pm$0.009	0.819$\pm$0.012
$\epsilon _n$	0.210$\pm$0.012	0.215$\pm$0.010	0.217$\pm$0.014	0.221$\pm$0.018	0.223$\pm$0.022
$\varepsilon_{ID}$	0.831$\pm$0.005
$\varepsilon_{conv}$	0.967$\pm$0.004
$\varepsilon_{trig}$	0.965$\pm$0.001
$\varepsilon_{Zvtx}$	0.951$\pm$0.003

Table 5: Total efficiency results. The errors are separated into two categories: errors independent on the jet multiplicity (second column), errors jet multiplicity dependent (third column). (.ps)

Sample	$\varepsilon_{tot}$	Common $\delta\varepsilon_{tot}/\varepsilon_{tot}$	$\delta\varepsilon_{tot}/\varepsilon_{tot}$
W+$\ge 0$ jets	0.1573		$\pm$ 0.007(stat) $\pm$ 0.0015(syst)
W+$\ge 1$ jets	0.1612		$\pm$ 0.011(stat) $\pm$ 0.0010(syst)
W+$\ge 2$ jets	0.1629	$\pm$ 0.0076(stat) $\pm$ 0.043(syst)	$\pm$ 0.015(stat) $\pm$ 0.0020(syst)
W+$\ge 3$ jets	0.1651		$\pm$ 0.014(stat) $\pm$ 0.0020(syst)
W+$\ge 4$ jets	0.1652		$\pm$ 0.021(stat) $\pm$ 0.0020(syst)

Figure 4: The plot shows the jet dependent W identification efficiency as a function of the jet multiplicity. All the efficiencies are normalized to the $W+\ge 0$ jet efficiency (right scale). The magenta dots represent the overall W identification efficiency. The total efficiency errors are also reported in the plot.