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Static and dynamic texture. Event mixing as a way to subtract the static contribution.

Figure 6.11: Power spectra of $7\times 10^3$ events in the multiplicity bin $326<\,dN/\,d\eta<398$. $\bigcirc$ - true events, $\bigtriangleup$ - mixed events, $\Box$ - the average event.

Figure 6.11 shows such power spectra for one multiplicity range. The unit on the vertical scale ( $\sigma^2/\langle dE_{MIP} \rangle^2$) is chosen so that the power of the fluctuation whose variance $\sigma^2$ equals the squared mean energy loss by a minimum ionising particle traversing the detector, is the unit. The first striking feature is that the power spectra of physical events are indeed enhanced on the coarse scale. The task of the analysis is to quantify and, as much as possible, eliminate ``trivial'' and experiment-specific reasons for this enhancement.

The average event, formed by summing amplitude images of the measured events in a given multiplicity bin, and dividing by the number of events, has a much reduced texture as statistical fluctuations cancel (shown as $\Box$ in Fig.6.11). Average events retain the texture associated with the shape of $\,d^2N/\,d\eta\,d\zeta$, with the dead channels and the finite beam geometrical cross-section (though this is only partially visible in the average event, due to the fact that event averaging is done without attempting to select events according to the vertex position). $P^\lambda(m)$ is proportional to the variance, or squared fluctuation $\sigma^2$. Therefore, for Poissonian statistics of hits in a pad, the event averaging over $M$ events should decrease $P^\lambda(m)$ by a factor of $M$. The average event whose power spectrum is shown on Fig. 6.11 is formed by adding $7\times 10^3$ events, however its $P^\lambda(m)$ is down less than $7\times 10^3$ compared to that of the single events. This demonstrates that the average event's texture is not due to statistical fluctuations, but rather, predominantly due to the systematic uncertainties listed. Consequently, we can use the average event's $P^\lambda(m)$ to estimate the magnitude of the static texture-related systematics. As seen from Fig. 6.11, the systematics are orders of magnitude below the $P^\lambda(m)$ of single events (true or mixed), with the exception of pseudorapidity, where non-constancy of $\,dN/\,d\eta$ over the detector's acceptance is visible.

The way to get rid of the ``trivial'' or static texture is to use mixed events, taking different channels from different events. The mixed events preserve the texture associated with the detector position offset, the inherent $\,dN/\,d\eta$ shape and the dead channels. This is static texture as it produces the same pattern event after event while we are searching for evidence of dynamic texture. We reduce sources of the static texture in the power spectra by empty target subtraction and by subtraction of mixed events power spectra, thus obtaining the dynamic texture $P^\lambda(m)_{true} - P^\lambda(m)_{mix}$. In order to reproduce the electronics cross-talk effects in the mixed event sample, the mixing is done sector-wise, i.e. the sectors constitute the subevents subjected to the event number scrambling. Its multiplicity dependence is plotted on Figure 7.1.

For comparison with models, a MC simulation (done with RQMD [57]) includes the known static texture effects and undergoes the same elimination procedure. This allows the effects irreducible by the subtraction methods to be taken into account in the comparison. One such example is the finite beam size, which has been shown by the MC studies to cause the RQMD points to rise with $\,dN/\,d\eta$.