Background

Determining the contribution of background events within the data sample is important throughout the analysis. For fitting the TGCs, the expected contribution is added to the Monte Carlo sample that is compared to data, and for the helicity studies the expected contribution is removed from the data sample.

Calculating any possible systematic uncertainties in this area is then vital. The shape of the ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ background is varied by using a sample of HERWIG Monte Carlo instead of the PYTHIA to simulate these events. The SDM elements and $\cos\theta_{\rm W}$ distribution extracted from the standard fit sample of Monte Carlo are compared to those calculated for the same sample, except the ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ background contribution is replaced with a HERWIG sample.

The modelling of the two-photon background is much less understood. To calculate any possible systematic shift due to this, the two-photon background is removed from the standard fit sample and then the SDM elements and $\cos\theta_{\rm W}$ distribution are compared to those from the standard fit sample. This procedure is repeated, except this time the two-photon background is doubled. The total uncertainty due to background contributions formed by adding the uncertainties from each source in quadrature can be seen in table 10.4.

For the helicity studies, the background contribution subtracted from the data sample is varied in a similar way as described above, and then the differences in the calculated helicity proportions are taken as the systematic uncertainty. The total systematic uncertainties due to background studies are shown in table 10.9.

Table 10.4: The systematic uncertainty due to background modelling. The numbers represent the size of the error as a fraction of the statistical error from the data sample on each bin of each variable used in the TGC fits.

	1	2	3	4	5	6	7	8
$\cos\theta_{\rm W}$	0.06	0.02	0.02	0.02	0.01	0.01	0.02	0.03
$\rho_{++}$	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
$\rho_{--}$	0.01	0.03	0.04	0.05	0.01	0.03	0.01	0.01
$\rho_{00}$	0.01	0.01	0.01	0.01	0.01	0.02	0.01	0.01
Re($\rho_{+-}$)	0.18	0.06	0.04	0.06	0.02	0.03	0.01	0.01
Re($\rho_{+0}$)	0.17	0.01	0.02	0.04	0.01	0.03	0.01	0.01
Re($\rho_{-0}$)	0.06	0.05	0.06	0.08	0.02	0.04	0.01	0.01
Im($\rho_{+-}$)	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
Im($\rho_{+0}$)	0.02	0.01	0.01	0.01	0.01	0.01	0.01	0.01
Im($\rho_{-0}$)	0.02	0.01	0.01	0.01	0.01	0.01	0.01	0.01