Cross sections results

The $W\to e \nu + \ge$ n jet cross section is obtained through the following equation:

$$\sigma_n(W) = \frac{N_n - B_n}{\zeta \cdot\epsilon_n\cdot \mathcal{L}}.$$

Here the quantities with the subscript $n$ are dependent on the number of jets in the event, and were measured in the inclusive $W +$ n jets samples. In the previous expression $N_n$ represents the number of selected events, $B_n$ is the estimated background contamination, $\zeta$ contains the jet independent efficiency, $\epsilon _n$ accounts for those inefficiencies affected by the jet multiplicity and $\mathcal{L}$ is the luminosity of the data sample.

Table 6: W inclusive cross section (.ps)

$\sigma_{0}(W) = 2669 \pm 11(stat) \pm 79(syst) \pm 160(Lum)$ pb

Table 7: W candidates ($N_n$), total background ($B_n$), total W efficiency ($\epsilon _n$) and the cross section relative to the inclusive cross section ($f_n$).(.ps)

	$\ge 0$	$\ge 1$	$\ge 2$	$\ge 3$	$\ge 4$
$N_n$	54799	11615	2680	602	145
$B_n$	1869	951	349	138	55
$\epsilon _n$	0.210	0.215	0.217	0.221	0.223
$f_n$	1.000	0.197	0.423 $\times 10^{-1}$	0.835 $\times 10^{-2}$	0.1610 $\times 10^{-3}$

Table 8: $W\to e \nu + \ge$ n jet cross section. The total uncertainty is separated into the statistical uncertainty, which includes the statistical uncertainty on the number of events as well as all the statistical uncertainties which scale as the square root of the number of events, the common systematic uncertainty, related to the inclusive cross section measurement, and the systematic uncertainty. For this table the systematics are always the maximum between the plus and minus systematic errors. In the last column the ratio $\sigma (n)/\sigma (n-1)$ is reported. The error is due to the combination of all the uncertainties mentioned before. (.ps)

	BR$\times\sigma$(pb)	Stat.	Common	Syst.	$\frac{\sigma(n)}{\sigma(n-1)}$
		Error	Error	Error
W+$\ge$ 1 jets	526.2	$\pm$4.7	$\pm$15.5	$\pm$84	0.197 $\pm$0.031
W+$\ge$ 2 jets	113.7	$\pm$2.5	$\pm$3.36	$\pm$30	0.216 $\pm$0.020
W+$\ge$ 3 jets	22.3	$\pm$1.2	$\pm$0.65	$\pm$8.9	0.196 $\pm$0.020
W+$\ge$ 4 jets	4.3	$\pm$0.57	$\pm$0.12	$\pm$2.2	0.193 $\pm$0.017

Figure 5: Systematics.

Figure 6: $W+\ge$ n jets cross section measured in Run II ($\sqrt {s}=1.96$ TeV) compared to the Run I measurement ($\sqrt {s}=1.8$ TeV). In the lower plot the ratio between the two measurements is compared to Monte Carlo prediction calculated at the two center of mass energies.

Figure 7: $W+\ge$ n jets cross section compared to theoretical prediction. The filled circles are the data measurements with the statistical and systematic uncertainties represented by two different error bars. The filled band indicates the variation of the theoretical prediction with the renormalization scale. the $W+\ge$ 0 jets is independent of this parameter.

Figure 8: Ratio of data to theory for $W+\ge$ n jets cross section as a function of the jet multiplicity. The theoretical prediction is extracted for two different renormalization scales: $M^2_W$ (red open circles), $<p_T^2>$ (blue filled circles).

Figure 9: The ratio $R_{n/(n-1)}$ as a function of the jet multiplicity. The error bars represent the sum in quadrature of the statistical and systematic uncertainties, theory is assumed to be free of errors. The open and close circles correspond respectively to theoretical predictions at two different renormalization scales: $M^2_W$ and $<p_T^2>$.

Figure 10: The ratio of data to theory for the quantity $R_{n/(n-1)}$ is plotted. The error bars represent the sum in quadrature of the statistical and systematic uncertainties, theory is assumed to be free of errors. The open and close circles correspond respectively to theoretical predictions at two different renormalization scales: $M^2_W$ and $<p_T^2>$.