Individual W Polarised Cross-Sections

Figure 9.1 shows the differential cross-sections for the production of transversely and longitudinally polarised W bosons obtained from the 189 GeV data by the procedure described in the previous chapter. Represented are the differential cross-sections for leptonically decaying W bosons and hadronically decaying W bosons, along with the sum of all W bosons.

Figure 9.1: The differential cross-sections for producing transversely (T) and longitudinally (L) polarised W bosons calculated from the 189 GeV data (points). The first two plots are for the leptonically decaying W boson in the pair. The next two are for the hadronically decaying W boson in the pair. The last two are for all W bosons. Overlaid are the predictions for the Standard Model (solid line), $\tilde{\kappa}_{z}$= +1.0 (dotted line) and $\tilde{\lambda}_{z}$= -1.0 (dashed line). The dotted-dashed line shows the zero.

Integrating over $\cos\theta_{\rm W}$ and dividing by the total cross-section gives the fraction of each polarisation. Table 9.1 gives the results for the 189 GeV data along with the predicted fractions calculated from generator level EXCALIBUR Monte Carlo. The results from the data have both a statistical error and a systematic error. The sources of possible systematic uncertainty investigated to calculate the second of these errors are described in detail in chapter 10.

The polarisation of the leptonically and hadronically decaying W bosons in a W-pair were obtained independently of each other. However these are not independent measurements, the correlation between them was found to be^9.1 0.071 $\pm$ 0.030. The total fraction of longitudinal W bosons was calculated by taking the average of the leptonic and hadronic fractions. The correlation was included when calculating the statistical error on this value.

Table 9.1: The fractions longitudinally polarised W bosons. The expected values are from generator level EXCALIBUR Monte Carlo. The first error on the measured values is statistical and the second is the systematic uncertainty. Also shown is the total cross-section these fractions relate to at 189 GeV.

	$\sigma_{\rm L}/\sigma_{\rm total}$	$\sigma_{\rm L}$ (pb)
Data
W $\rightarrow \ell{\nu}$	0.158 $\pm$ 0.046 $\pm$ 0.023	1.11 $\pm$ 0.32 $\pm$ 0.16
W $\rightarrow {\rm q}{\rm q}$	0.279 $\pm$ 0.045 $\pm$ 0.025	1.96 $\pm$ 0.32 $\pm$ 0.18
All	0.219 $\pm$ 0.034 $\pm$ 0.016	3.08 $\pm$ 0.50 $\pm$ 0.23
Standard Model Expectation
W $\rightarrow \ell{\nu}$	0.254 $\pm$ 0.005	1.86 $\pm$ 0.04
W $\rightarrow {\rm q}{\rm q}$	0.259 $\pm$ 0.005	1.90 $\pm$ 0.04
All	0.257 $\pm$ 0.004	3.76 $\pm$ 0.06

Taking the total integrated luminosity as $183.05 \pm 0.16({\rm stat.}) \pm 0.37({\rm syst.})$ pb$^{-1}$ [101], the total cross-section for the process ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\ell\bar{\nu}_{\ell}$ was measured at 189 GeV in [66] as $7.04 \pm 0.22({\rm sys.}) \pm 0.10({\rm stat.})$ pb. This means the total cross-section for production of longitudinal W bosons in ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\ell\bar{\nu}_{\ell}$ events is $\sigma_{\rm L} = 3.08\pm0.50$(stat.)$\pm0.23$(syst.) pb. The expected cross-section at 189 GeV is 3.76 pb.