Jet Fragmentation

The modelling of the quark fragmentation into jets is another possible source of uncertainty. This process is not well understood, so it is an important area to investigate. The fragmentation simulation program most commonly used is JETSET. This program was used as the fragmentation scheme in the EXCALIBUR Monte Carlo employed for both the TGC fit and the helicity studies. To evaluate the uncertainty, large samples of grc4f Monte Carlo which use different fragmentation schemes are compared. Both samples have identical initial four-vectors, but one has then used the JETSET fragmentation scheme, and the other utilises the HERWIG fragmentation scheme. As before, the extracted SDM elements and $\cos\theta_{\rm W}$ are compared and the difference in each bin is assigned as the uncertainty on that bin. The plots of the single W SDM elements can be seen in figure 10.2. The magnitude of the systematic uncertainty on each bin is given in table 10.2.

The helicity fractions are calculated for both these samples and the differences are taken as the systematic uncertainty. These are shown in table 10.9.

Table 10.2: The systematic uncertainty due to jet hadronisation 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
$\cos\theta_{\rm W}$	0.01	0.38	0.25	0.14	0.04	0.27	0.29	0.17
$\rho_{++}$	0.10	0.14	0.47	0.06	0.18	0.07	0.05	0.18
$\rho_{--}$	0.23	0.19	0.11	0.04	0.06	0.11	0.21	0.02
$\rho_{00}$	0.20	0.21	0.39	0.01	0.08	0.04	0.18	0.06
Re($\rho_{+-}$)	0.28	0.12	0.12	0.08	0.02	0.01	0.11	0.04
Re($\rho_{+0}$)	0.25	0.35	0.27	0.13	0.08	0.10	0.01	0.07
Re($\rho_{-0}$)	0.08	0.12	0.40	0.22	0.14	0.06	0.04	0.01
Im($\rho_{+-}$)	0.07	0.04	0.01	0.15	0.08	0.07	0.29	0.21
Im($\rho_{+0}$)	0.34	0.46	0.13	0.01	0.29	0.05	0.51	0.28
Im($\rho_{-0}$)	0.32	0.48	0.35	0.09	0.04	0.05	0.08	0.19

Figure 10.2: Single W SDM elements extracted from two samples of fully detector simulated grc4f Monte Carlo. Both samples were initially the same, however, for jet fragmentation, one uses the JETSET fragmentation scheme (closed circles) and the other the HERWIG fragmentation scheme (open circles).