Jet Reconstruction

Extensive studies of back-to-back jets at LEP ${\rm Z}^{0}$ energies have been carried out. By comparing the data with the Monte Carlo events, the accuracy of the jet reconstruction can be measured. It was found that the uncertainties in the resolutions of the three parameters, energy, $\cos\theta_{\rm W}$ and $\phi_{W}$, were about 10%. A possible systematic shift of 0.5% was found in the absolute jet energy. For calculating the systematic uncertainty in the SDM elements due to the uncertainty in jet reconstruction a large sample of EXCALIBUR Monte Carlo was generated and then modified to form new samples by smearing the resolution of the jet parameters by 10% and shifting the jet energy by 0.5%. This was done to both the hadronic and the $\tau$ jets, although studies into the $\tau$ jet uncertainties have not been carried out, so it is only an assumption that the uncertainty will be the same.

The SDM elements and $\cos\theta_{\rm W}$ distribution were calculated for each sample and compared to the original Monte Carlo sample. The differences were taken as the systematic uncertainty. The systematics for each bin were added in quadrature to give an overall systematic due to jet reconstruction, these can be seen in table 10.3.

Table 10.3: The systematic uncertainty due to jet reconstruction. 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
$\cos\theta_{\rm W}$	0.25	0.10	0.11	0.27	0.34	0.31	0.17	0.59
$\rho_{++}$	0.10	0.19	0.17	0.14	0.09	0.85	1.42	1.09
$\rho_{--}$	0.07	0.18	0.11	0.05	0.08	0.13	0.15	0.13
$\rho_{00}$	0.09	0.19	0.16	0.11	0.08	0.12	0.11	0.14
Re($\rho_{+-}$)	0.09	0.16	0.11	0.47	0.11	0.12	0.09	0.12
Re($\rho_{+0}$)	0.12	0.11	0.09	0.06	0.10	0.12	0.06	0.06
Re($\rho_{-0}$)	0.09	0.17	0.07	0.08	0.09	0.15	0.09	0.13
Im($\rho_{+-}$)	0.11	0.13	0.14	0.09	0.14	0.16	0.05	0.05
Im($\rho_{+0}$)	0.08	0.07	0.06	0.06	0.16	0.15	0.07	0.06
Im($\rho_{-0}$)	0.06	0.13	0.81	0.18	0.21	0.15	0.08	0.06

For the helicity studies, the helicity fractions were calculated for each sample and compared to the original sample. The differences were added in quadrature and the total result was taken as the systematic uncertainty shown in table 10.9.

Further studies in estimating the possible systematic shift in the reconstructed direction of the boson have been carried out by looking at radiative ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ events. The possible shift in $\vert$$\mbox{$\cos\theta_{\rm W}$}$$\vert$ was found to be less than 0.01 [102].