The inverse Laplace transform as the ultimate tool for transverse mass spectra

New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using the inverse Laplace transform. The problems with its inherent ill-definedness can be overcome and several applications in other fields like biology, chemistry or optics have already shown its feasability. Moreover, the method also promises to deliver upper bounds on the total information content of the spectra, which is of big importance for all other means of analysis. Here we compute several Laplace inversions from different thermal scenarios, both analytically and numerically, to test the efficiency of the method. Especially the case of a two component structure, related to a possible first order phase transition to a quark gluon plasma, is closer investigated and it is shown that at least a signal to noise ratio of $10^4$ is necessary to resolve two individual components.Comment: 13 pages (PostScript, including figures), BNL-NTHES

Thermal phenomenology of hadrons from 200 AGeV S+S collisions

We develop a complete and consistent description for the hadron spectra from heavy ion collisions in terms of a few collective variables, in particular temperature, longitudinal and transverse flow. To achieve a meaningful comparison with presently available data, we also include the resonance decays into our picture. To disentangle the influences of transverse flow and resonance decays in the $m_T$-spectra, we analyse in detail the shape of the $m_T$-spectra.Comment: 31 pages, 13 figs in seperate uuencoded file, for LaTeX, epsf.sty and dvips, TPR-93-16 and BNL-(no number yet

Hydrodynamical assessment of 200 AGeV collisions

We are analyzing the hydrodynamics of 200 A GeV S+S collisions using a new approach which tries to quantify the uncertainties arising from the specific implementation of the hydrodynamical model. Based on a previous phenomenological analysis we use the global hydrodynamics model to show that the amount of initial flow, or initial energy density, cannot be determined from the hadronic momentum spectra. We additionally find that almost always a sizeable transverse flow deve- lops, which causes the system to freeze out, thereby limiting the flow velocity in itself. This freeze-out dominance in turn makes a distinction between a plasma and a hadron resonance gas equation of state very difficult, whereas a pure pion gas can easily be ruled out from present data. To complete the picture we also analyze particle multiplicity data, which suggest that chemical equilibrium is not reached with respect to the strange particles. However, the over- population of pions seems to be at most moderate, with a pion chemical potential far away from the Bose divergence.Comment: 19 pages, 11 figs in separate uuencoded file, for LateX, epsf.tex, dvips, TPR-94-5 and BNL-(no number yet

Time evolution of the chiral phase transition during a spherical expansion

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps