Scaling of v2v_2 in heavy ion collisions

We interpret the scaling of the corrected elliptic flow parameter w.r.t. the corrected multiplicity, observed to hold in heavy ion collisions for a wide variety of energies and system sizes. We use dimensional analysis and power-counting arguments to place constraints on the changes of initial conditions in systems with different center of mass energy $\sqrt{s}$. Specifically, we show that a large class of changes in the (initial) equation of state, mean free path, and longitudinal geometry over the observed $\sqrt{s}$ are likely to spoil the scaling in $v_2$ observed experimentally. We therefore argue that the system produced at most Super Proton Synchrotron (SPS) and Relativistic Heavy Ion Collider (RHIC) energies is fundamentally the same as far as the soft and approximately thermalized degrees of freedom are considered. The ``sQGP'' (Strongly interacting Quark-Gluon Plasma) phase, if it is there, is therefore not exclusive to RHIC. We suggest, as a goal for further low-energy heavy ion experiments, to search for a ``transition'' $\sqrt{s}$ where the observed scaling breaks.Comment: Accepted for publication by Phys. Rev. C Based on presentation in mini-symposium on QGP collective properties, Frankfurt. Discussion expanded, results adde

A statistical model analysis of K/πK/\pi fluctuations in heavy ion collisions

We briefly describe two statistical hadronization models, based respectively on the presence and absence of light quark chemical equilibrium, used to analyze particle yields in heavy ion collisions. We then try to distinguish between these models using $K/\pi$ fluctuations data. We find that while the non-equilibrium model provides an acceptable description of fluctuations at top SPS and RHIC energies, both models considerably under-estimate fluctuations at low SPS energies.Comment: References updated Poster in QM2006 conference, Shangha

Hadron Resonances and Phase Threshold in Heavy Ion Collisions

We show that a measurement of the reaction energy dependence of relative hadron resonance yields in heavy ion collisions can be used to study the phase structure of the dense QCD matter created in these collisions, and investigate the origin of the trends observed in the excitation functions of certain soft hadronic observables. We show that presence of chemical nonequilibrium in light quark abundance imparts a characteristic signature on the energy dependence of resonance yields, that differs considerably from what is expected in the equilibrium picture.Comment: In press, Phys. Rev.

Hanbury-Brown--Twiss Analysis in a Solvable Model

The analysis of meson correlations by Hanbury-Brown--Twiss interferometry is tested with a simple model of meson production by resonance decay. We derive conditions which should be satisfied in order to relate the measured momentum correlation to the classical source size. The Bose correlation effects are apparent in both the ratio of meson pairs to singles and in the ratio of like to unlike pairs. With our parameter values, we find that the single particle distribution is too distorted by the correlation to allow a straightforward analysis using pair correlation normalized by the singles rates. An analysis comparing symmetrized to unsymmetrized pairs is more robust, but nonclassical off-shell effects are important at realistic temperatures.Comment: 21 pages + 9 figures (tarred etc. using uufiles, submitted separately), REVTeX 3.0, preprint number: DOE/ER/40561-112/INT93-00-3

Search for the QCD critical point in nuclear collisions at the CERN SPS

Pion production in nuclear collisions at the SPS is investigated with the aim to search, in a restricted domain of the phase diagram, for power-laws in the behavior of correlations which are compatible with critical QCD. We have analyzed interactions of nuclei of different size (p+p, C+C, Si+Si, Pb+Pb) at 158$A$ GeV adopting, as appropriate observables, scaled factorial moments in a search for intermittent fluctuations in transverse dimensions. The analysis is performed for $\pi^+\pi^-$ pairs with invariant mass very close to the two-pion threshold. In this sector one may capture critical fluctuations of the sigma component in a hadronic medium, even if the $\sigma$-meson has no well defined vacuum state. It turns out that for the Pb+Pb system the proposed analysis technique cannot be applied without entering the invariant mass region with strong Coulomb correlations. As a result the treatment becomes inconclusive in this case. Our results for the other systems indicate the presence of power-law fluctuations in the freeze-out state of Si+Si approaching in size the prediction of critical QCD.Comment: 31 pages, 11 figure

Source Dimensions in Ultrarelativistic Heavy Ion Collisions

Recent experiments on pion correlations, interpreted as interferometric measurements of the collision zone, are compared with models that distinguish a prehadronic phase and a hadronic phase. The models include prehadronic longitudinal expansion, conversion to hadrons in local kinetic equilibrium, and rescattering of the produced hadrons. We find that the longitudinal and outward radii are surprisingly sensitive to the algorithm used for two-body collisions. The longitudinal radius measured in collisions of 200 GeV/u sulfur nuclei on a heavy target requires the existence of a prehadronic phase which converts to the hadronic phase at densities around 0.8-1.0 GeV/fm$^3$. The transverse radii cannot be reproduced without introducing more complex dynamics into the transverse expansion.Comment: RevTeX 3.0, 28 pages, 6 figures, not included, revised version, major change is an additional discussion of the classical two-body collision algorithm, a (compressed) postscript file of the complete paper including figures can be obtained from Authors or via anonymous ftp at ftp://ftp_int.phys.washington.edu/pub/herrmann/pisource.ps.

Boundary and Coulomb Effects on Boson Systems in High-Energy Heavy-Ion Collisions

The boundary of a boson system plays an important role in determining the momentum distribution of the bosons. For a boson system with a cylindrical boundary, the momentum distribution is enhanced at high transverse momenta but suppressed at low transverse momenta, relative to a Bose-Einstein distribution. The boundary effects on systems of massless gluons and massive pions are studied. For gluons in a quark-gluon plasma, the presence of the boundary may modify the signals for the quark-gluon plasma. For pions in a pion system in heavy-ion collisions, Coulomb final-state interactions with the nuclear participants in the vicinity of the central rapidity region further modify the momentum distribution at low transverse momenta. By including both the boundary effect and the Coulomb final-state interactions we are able to account for the behavior of the $\pi^{-}$ transverse momentum spectrum observed in many heavy-ion experiments, notably at low transverse momenta.Comment: 15 pages Postscript uuencoded tar-comprssed file, 9 Postscript figures uuencoded tar-compressed fil

Dynamic ham-sandwich cuts in the plane

We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n1/3+ε) amortized time and O(n4/3+ε) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O(logn) time and ham-sandwich queries in O(klog4n) time. In addition, if each point set has convex peeling depth k , then we can maintain the decomposition automatically using O(klogn) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O(klog4n) time plus the O((kb)polylog(kb)) time required to approximate the root of a polynomial of degree O(k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.Engineering and Applied Science

System-size and centrality dependence of charged kaon and pion production in nucleus-nucleus collisions at 40A GeV and158A GeV beam energy

Measurements of charged pion and kaon production are presented in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV beam energy as well as in semi-central C+C and Si+Si interactions at 40A GeV. Transverse mass spectra, rapidity spectra and total yields are determined as a function of centrality. The system-size and centrality dependence of relative strangeness production in nucleus-nucleus collisions at 40A GeV and 158A GeV beam energy are derived from the data presented here and published data for C+C and Si+Si collisions at 158A GeV beam energy. At both energies a steep increase with centrality is observed for small systems followed by a weak rise or even saturation for higher centralities. This behavior is compared to calculations using transport models (UrQMD and HSD), a percolation model and the core-corona approach.Comment: 32 pages, 14 figures, 4 tables, typo table II correcte

Proton -- Lambda Correlations in Central Pb+Pb Collisions at sqrt(s_{NN}) = 17.3 GeV

The momentum correlation between protons and lambda particles emitted from central Pb+Pb collisions at sqrt(s_{NN}) = 17.3 GeV was studied by the NA49 experiment at the CERN SPS. A clear enhancement is observed for small relative momenta (q_{inv} < 0.2 GeV). By fitting a theoretical model, which uses the strong interaction between the proton and the lambda in a given pair, to the measured data a value for the effective source size is deduced. Assuming a static Gaussian source distribution we derive an effective radius parameter of R_G = 3.02 \pm 0.20$(stat.)^{+0.44}_{-0.16}(syst.) fm.Comment: 14 pages, 9 figures, submitted to Phys. Rev.