Overall Systematic Uncertainty

For the TGC fit the overall systematic uncertainty on each observable is calculated by adding in quadrature all the calculated uncertainties discussed above. These are then included into the fit as described by equation 7.1 in chapter 7. The overall systematic uncertainty on each data observable as a fraction of the statistical error on the data can be seen in table 10.8.

The overall systematic uncertainty on the helicity fractions are calculated by adding in quadrature all the uncertainties calculated from each area described above. These are shown in table 10.9. The overall systematic uncertainties are added in quadrature with the statistical error to give the overall uncertainty on each polarised cross-section measured from the data.

Table: The total systematic uncertainty on the SDM observables and $\cos\theta_{\rm W}$ distribution. These were calculated by adding in quadrature the values of the all systematic uncertainties discussed in this chapter. 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
$\cos\theta_{\rm W}$	0.31	0.63	0.47	0.34	0.45	0.42	0.41	0.66
$\rho_{++}$	0.50	0.41	0.60	0.31	0.40	0.91	1.47	1.15
$\rho_{--}$	0.61	0.41	0.32	0.28	0.31	0.47	0.52	0.61
$\rho_{00}$	0.67	0.34	0.51	0.22	0.22	0.36	0.32	0.38
Re($\rho_{+-}$)	0.65	0.35	0.32	0.62	0.23	0.28	0.47	0.34
Re($\rho_{+0}$)	0.51	0.59	0.35	0.26	0.56	0.29	0.30	0.20
Re($\rho_{-0}$)	0.50	0.40	0.59	0.32	0.79	0.23	0.25	0.30
Im($\rho_{+-}$)	0.37	0.56	0.47	0.22	0.25	0.29	0.34	0.26
Im($\rho_{+0}$)	0.42	0.52	0.53	0.31	0.36	0.41	0.57	0.30
Im($\rho_{-0}$)	0.42	0.65	1.14	0.58	0.58	0.32	0.24	0.45

Table 10.9: The contribution to the systematic uncertainty on the polarised cross-section fractions from the sources discussed in this chapter. The total uncertainty is calculated by adding each of the uncertainties in quadrature.

Systematic		TT	LL	TL	T,L
MC Generator	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.015	0.013	0.028	0.001
	W $\rightarrow \ell{\nu}$	-	-	-	0.004
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.006
Jet Reconstruction	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.013	0.004	0.008	0.007
	W $\rightarrow \ell{\nu}$	-	-	-	0.005
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.011
Hadronisatation	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.016	0.002	0.014	0.009
	W $\rightarrow \ell{\nu}$	-	-	-	0.003
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.021
Background	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.004	0.001	0.004	0.002
	W $\rightarrow \ell{\nu}$	-	-	-	0.003
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.004
Lepton id	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.017	0.005	0.014	0.010
	W $\rightarrow \ell{\nu}$	-	-	-	0.017
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.003
Detector Effect Correction	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.004	0.008	0.012	0.002
	W $\rightarrow \ell{\nu}$	-	-	-	0.009
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.005
Lepton Charge/Momentum	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.007	0.001	0.008	0.005
	W $\rightarrow \ell{\nu}$	-	-	-	0.011
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.001
Total	WW $\rightarrow{\rm q}{\rm q}\ell{\nu}$	0.032	0.017	0.038	0.016
	W $\rightarrow \ell{\nu}$	-	-	-	0.023
	W $\rightarrow {\rm q}{\rm q}$	-	-	-	0.025