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Results, systematic uncertainties, and conclusions.

The left and right halves of the Si detector had different number of working channels: 225 on the left side, 245 on the right, out of 256 on either side in total. In the analysis, a $\delta$-free side of the detector is used for each sign. This is the ``left'' (Saleve) side for the positive, and ``right'' (Jura) side for the negative settings. After the radiation damage correction (Table  4.4) is applied, a comparison of the so corrected multiplicities, measured in the samples of identical centrality by the left and right parts of the detector, is performed to test the quality of the multiplicity measurement. In all cases we look at $\delta$-free side, so it takes a change in the sign of magnetic field to compare the two sides. Fig.  4.7 shows the comparison where each point represents a particular setting of the Cherenkov trigger, angle and magnetic field strength. The abscissa and the ordinate represent average multiplicity of charged tracks, measured in the 4% centrality sample, in the positive and negative runs respectively, by one half of the detector. Corrections for the dead pads (= $\times 256/(256-N_{dead}))$ are applied.

Figure 4.7: Comparison of the average charged track multiplicities measured independently by the left and right sides of the Si detector in the runs with different field sign. See text of Subsection  4.2.10.

This comparison reveals a systematic trend for the right side of the detector to give somewhat higher multiplicity. Most likely this is due to geometrical misalignment which was not calibrated out in the '95 data set. The center of gravity of the set of points is displaced from the diagonal representing the perfect correlation. In other words, the right side of the Si detector shows systematically larger multiplicity than the left side. The cause of this could be a horizontal displacement of the beam with respect to the Si. The magnitude of the left-right asymmetry in the mean number of tracks in the data samples of the same centrality $(\langle$   Right$\rangle-\langle$   Left$\rangle)/ (\langle$   Right$\rangle+\langle$   Left$\rangle)$ - this number indicates by what fraction one would have to move an individual point, in order to eliminate the asymmetry) is about 3.5%, which is better than the accuracy of a centrality calibration in an individual spectrometer setting (6-8%, see below). This level of systematics seems acceptable.

The estimate of the systematic uncertainty in the centrality determination is based on the following considerations. Once the set of T0 thresholds at fixed centralities is established for every physics setting, a comparison of the Si multiplicities between different runs can be performed for every centrality bin. The variance of the Si multiplicity $dN/d\eta$ between different run periods (at fixed centrality) characterizes the uncertainty of the absolute normalization. The fractional error bar of $c$ is slightly better for high centrality points in agreement with my intuitive view that selection of high multiplicity samples and measurements of high multiplicity should be more reliable, because statistical fluctuation of a larger number is relatively smaller. For the interesting range of centralities ($c \le 0.1$) the $\sigma(c)/c = 0.06$. For kaons, because the Si is involved twice, I multiply the above mentioned centrality uncertainty by $\sqrt 2$. Table  4.5 summarizes the centralities.

Table 4.5: Trigger centrality $c$ of the physics settings.

momentum	4 GeV		8 GeV
$p_T$ setting	low	high	low	high
$\pi^{+}$	0.145$\pm$ 0.008	0.152 $\pm$0.009	0.17 $\pm$0.01	0.116$\pm$0.007
$K^{+}$	0.145$\pm$0.011	0.152$\pm$ 0.012	0.17 $\pm$ 0.014	0.116$\pm$0.009
$\pi^{-}$	0.129$\pm$ 0.007	0.128$\pm$0.007	0.143$\pm$ 0.008	0.127 $\pm$0.007
$K^{-}$	0.129$\pm$0.010	0.128$\pm$0.010	0.145 $\pm$ 0.012	0.127 $\pm$ 0.010

The advantage of this method of normalization is that it utilizes the Si multiplicity to solve the problem of normalization which is otherwise difficult to solve without making ungrounded assumptions, idealizing the experiment, e.g. the assumption that the top $x$% of T0 amplitudes are the top $x$% of the most central events, or that requirement of a spectrometer track in the trigger (with the ``jaws'' !) makes no effect on the centrality of the data sample so selected.

I have used RQMD simulation to link the acceptances of Si and spectrometer. I believe that any other normalization technique using T0 would, too, need simulations to fully understand the shape of minimum bias distribution in T0, and the effect of the spectrometer requirement in order to determine the trigger performance to the degree of realism needed for absolute normalization at the 6-8 % systematic error level. My approach reduces the simulation problem to the one which is quite tractable and relies on RQMD features not more sophisticated than the gross shape of $\,dN/\,d\eta$ distribution.