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Sensitivity of the method

The sensitivity study was performed using the multifireball event generator created specially for this purpose and described in Section 7.2. Writing an event generator with a very simple physics behind it was preferred to searching for an existing one with potentially deep, relevant and interesting physics, for the following reasons:

• an argument, based on a result obtained from an event generator with a simple-minded simulation of the interesting physics effects, is more general than the one made on the basis of a detailed, physically deep calculation of one particular theoretical scenario, with one particular set of assumptions
• a calibration of the sensitivity of the method, that is, the job of establishing the quantitative connection between a standard effect and the response of the experiment is best done with an immutable standard

Figure 7.5: Coarse scale $\eta$ texture correlation in the NA44 data, shown by $\bigcirc$ (from the top right plot of Figure 7.1), is compared with that from the multifireball event generator for three different fireball sizes. Detector response is simulated. The boxes represent systematic errorbars (see caption to Fig. 7.1).

The longitudinal flow of fireballs manifests itself primarily in the rapidity mode. We simulated average fireball multiplicities of 10, 50, 90 (with RMS fluctuation of 3) and larger. The average fireball multiplicity is referred to as a ``clustering parameter'', and characterizes the ``grain coarseness'' of the pseudorapidity texture. More detailed description of the model is given in Section 7.2. Fig. 7.5 shows comparison of our data with the simulated pseudorapidity texture. For clustering parameters 50 and 90, on a statistics of $\sim 10^4$ events the detector+software sees a difference between the hadronizations with different mean fireball multiplicities. The signal grows with the multiplicity and with the clustering parameter. Fig. 7.5 provides quantitative information on the sensitivity of the texture measurements by relating the expected strength of response to the strength of texture via Monte Carlo simulation. The sensitivity is limited by systematic errors of the measurement, discussed in Section 6.9. We continue with a qualitative discussion of the sensitivity. It is instructive to compare sensitivity of this method with other methods; in particular with two point correlators.

The sensitivity of the method is remarkable indeed if one takes into account that statistics in the fifth multiplicity bin for each of the three event generator points is below $3\times10^4$ events - too scarce, e.g., to extract three source radius parameters via HBT analysis even with a well optimized spectrometer! In this context, it can be mentioned that sensitivity of HBT interferometry to first order phase transition with droplet hadronization has been discussed [85]; for a hadronization scenario with droplets evaporating slowly as they participate in the transverse flow of the matter, abnormally large values of $R_{out}$ are expected. We emphasize that in our approach, we are able to see the signal without such particularities of dynamics. In fact, neither the concept of ``slow evaporation'' nor that of the transverse flow is present in the event generator we used for this sensitivity study. Another theoretical idea - to use two particle correlation in rapidity $R_2(y)$ to search for droplets - has been discussed in the context of $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV (at FNAL)[86]. The $R_2$ was reported to decrease with multiplicity, so that it would not be expected to be visible for $\,dN/\,dy$ above $\approx$20; the signal would be weaker in a scenario with correlated droplets.

In the same multiplicity bin, with total number of hadrons at freeze-out around $1.5\times10^2$, a typical fraction of particles coming from the same fireball for the clustering parameters of 50 would be 3%, and, respectively, 6% for 90. In either case there is little hope of seeing any trace of such dynamics either in ensemble-averaged $\,dN/dy$ or in $\,dN/dy$ of a single event.

The data is consistent with clustering parameters below 50. Discussion of the implications of the results presented so far will be carried out separately in the context of the first (Section 7.4) and second order (Section 7.5) phase transition models.