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Relativistic collisions of heavy ions

An ultrarelativistic collision of heavy ions presents a phenomenon whose most interesting features are conditioned by the large multitude of degrees of freedom involved, and yet offer an opportunity for the fundamental physics of the strong interaction to manifest itself. From a particle physicist's point of view, "Relativistic Heavy Ions are a complicated mess raised to the power of a complicated mess" (a statement ascribed to D. Perkins). Particle physicists are used to comparing their experimental measurements with predictions obtained from perturbative theories (electro-weak theory or perturbative QCD). However, the most interesting aspects of strong interaction can not be described perturbatively. Luckily, perturbative expansion is not the only successful problem-solving technique in quantum physics. An approach with a somewhat complimentary area of success is the quasi-classical (WKB) approximation. Therefore, in order to address phenomena undescribable perturbatively, it is only natural to turn to systems which look like ``a complicated mess'', but (due to the large size and high excitation of the system) are quasi-classical.

The very notion of a phase transition in such systems (a subject of intense experimental and theoretical investigation) is of (quasi)macroscopic, multiparticle nature. On the theoretical side, the multiparticle, quasi-macroscopic, quasi-classical view favours statistical, thermodynamical, or hydrodynamical descriptions. The choice of an adequate description is a particularly challenging problem since the conditions (size, energy density, identities of the particles) of the system change dramatically over a short interval of time. At the end of this dramatic change, the hadronic interactions cease and the system freezes out in a state of free expansion. The measurements are performed long after that.

The macroscopic quantities that figure in the interpretation sections of experimental papers (temperature $T$, chemical potential $\mu$, velocity of collective flow) are derived (often in a model-dependent way, under simplifying assumptions, including that of equilibrium) from single- and double-particle observables - spectra, radius parameters obtained from the Hanbury-Brown - Twiss (HBT for short) interferometry[25], and yields. Truly multiparticle observables, defined on an event-by-event basis, are of paramount interest.

By event-by-event (EbyE for short) we will mean the kind of analysis where the quantity(ies) of interest can be extracted from a single event. Event mixing can be used to create artificial events which retain certain reproducible morphological features of real events, especially those arising due to effects related to the process of measurement, and are devoid of physical correlations.

In Spring 1999, when we started an event-by-event analysis in NA44 (presented in Chapters  6 and  7), certain examples of EbyE analyses in high energy hadron collisions existed in cosmic ray works  [5,2,6], in $pp$ collisions at ISR [7], and in the reaction plane determination and elliptic flow [8,9,10] analyses in heavy ion collisions. The recently published event-by-event analyses of the SPS $Pb+Pb$ data either deal with a few events [11] or analyze properties of a large ensemble of events by comparing different ensemble averages based on a single observable (transverse momentum $p_T$) [12]. In the first case [11], the path taken is essentially that of imaging, with the question of accumulation of feature information from large sets of events remaining open. In the second case [12], the difficulty lies in the fact that the ensemble averages (such as any RMS global fluctuation) on a set of post-freeze-out events can hardly be regarded as representative of a pre-freeze-out history of those events, due to the dramatic non-stationarity of the open system, with a consequent lack of ergodicity. More importantly, any symmetry breaking breaks ergodicity as well [13], thus causing any ergodicity-based measure to lose logical ground and become hard to interpret precisely when it is expected to signal a QCD phase transition.

Therefore, we prefer to concentrate on texture, or local fluctuation observables, where a single event is self-sufficient to determine its own fluctuation content. The idea to search for critical behaviour in particle distributions in rapidity $y$ [14,15] was inspired by a Ginzburg-Landau type of multihadron production theory [14], where the hadronic field probability amplitude $\Pi(y)$ plays the role of an order parameter in a hadronization transition. Naturally, enhanced correlations of hadrons in $y$ at the critical point would manifest critical fluctuations in the order parameter. Recently, Stephanov et al. [16] revitalized the interest in the topic by pointing to the possibility for a second order QCD phase transition point to be found under certain initial conditions within the reach of the today's experiments, emphasising the importance of scanning a broad range of energies and impact parameters and of critical fluctuations as a signature to look for.

Chapters 6 and 7 present a power spectrum analysis of event texture in pseudorapidity $\eta$ and azimuthal angle $\zeta$ (2D) , based on a Discrete Wavelet Transformation (DWT)[17], and performed on a number of large event ensembles sampled according to their multiplicity, thereby studying the impact parameter dependence of the observables. DWT quantifies contributions of different $\zeta$ and $\eta$ scales into the overall event's texture, thus testing the possible large scale enhancement - a classical [18] experimental signature of patterns formed in the vicinity of a critical point. A DWT-based power spectrum estimator is known [19] to overcome the problems of finite size and varying mean density of a sample.

While considering the texture analysis a fascinating topic with a promising future, we paid the due tribute of respect to the more traditional single particle observables. This part of work was chronologically the first (1996-1999); its methods and results are covered in chapters 4 and 5. We concentrated on the measurement of charged pions and kaons in $Pb+Pb$ collisions at SPS. One of the signatures of the deconfinement phase transition is enhancement of strangeness (discussed in Section 5). Interactions between liberated gluons in the deconfined phase are predicted [20,21,22] to enhance the rate of strangeness production compared to the non-QGP scenarios. Being the lightest strange hadrons, kaons are expected to dominate the strange sector by virtue of canonical thermodynamics [23]. The observed kaon multiplicity yields information about the mechanism of strangeness production, hadronization and subsequent evolution in the hadron gas, before the gas becomes sufficiently dilute that the interactions cease. Inelastic hadronic rescattering can enrich the strangeness content of the system [24]. We will report the yields and distributions of charged kaons and pions measured by the NA44 Experiment, and discuss implications of these data on the physics of the above-mentioned hadronic processes.