A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature

I retrace the developments from Hagedorn's concept of a limiting temperature for hadronic matter to the discovery and characterization of the quark-gluon plasma as a new state of matter. My recollections begin with the transformation more than 30 years ago of Hagedorn's original concept into its modern interpretation as the "critical" temperature separating the hadron gas and quark-gluon plasma phases of strongly interacting matter. This was followed by the realization that the QCD phase transformation could be studied experimentally in high-energy nuclear collisions. I describe here my personal effort to help develop the strangeness experimental signatures of quark and gluon deconfinement and recall how the experimental program proceeded soon to investigate this idea, at first at the SPS, then at RHIC, and finally at LHC. As it is often the case, the experiment finds more than theory predicts, and I highlight the discovery of the "perfectly" liquid quark-gluon plasma at RHIC. I conclude with an outline of future opportunities, especially the search for a critical point in the QCD phase diagram.Comment: To appear in {\em Melting Hadrons, Boiling Quarks} by Rolf Hagedorn and Johan Rafelski (editor), Springer Publishers, 2015 (open access

Evaluating Frequency, Diagnostic Quality, and Cost of Lyme Borreliosis Testing in Germany: A Retrospective Model Analysis

Background. Data on the economic impact of Lyme borreliosis (LB) on European health care systems is scarce. This project focused on the epidemiology and costs for laboratory testing in LB patients in Germany. Materials and Methods. We performed a sentinel analysis of epidemiological and medicoeconomic data for 2007 and 2008. Data was provided by a German statutory health insurance (DAK) company covering approx. 6.04 million members. In addition, the quality of diagnostic testing for LB in Germany was studied. Results. In 2007 and 2008, the incident diagnosis LB was coded on average for 15,742 out of 6.04 million insured members (0.26%). 20,986 EIAs and 12,558 immunoblots were ordered annually for these patients. For all insured members in the outpatient sector, a total of 174,820 EIAs and 52,280 immunoblots were reimbursed annually to health care providers (cost: 2,600,850€). For Germany, the overall expected cost is estimated at 51,215,105€. However, proficiency testing data questioned test quality and standardization of diagnostic assays used. Conclusion. Findings from this study suggest ongoing issues related to care for LB and may help to improve future LB disease management

Kinetic equation with exact charge conservation

We formulate the kinetic master equation describing the production of charged particles which are created or destroyed only in pairs due to the conservation of their Abelian charge.Our equation applies to arbitrary particle multiplicities and reproduces the equilibrium results for both canonical (rare particles) and grand canonical (abundant particles) systems. For canonical systems, the equilibrium multiplicity is much lower and the relaxation time is much shorter than the naive extrapolation from the grand canonical ensemble results. Implications for particle chemical equilibration in heavy-ion collisions are discussed.Comment: 4 Pages in RevTe

Relativistic mass distribution in event-anti-event system and ``realistic'' equation of state for hot hadronic matter

We find the equation of state $p,\rho \propto T^6,$ which gives the value of the sound velocity $c^2=0.20,$ in agreement with the ``realistic'' equation of state for hot hadronic matter suggested by Shuryak, in the framework of a covariant relativistic statistical mechanics of an event--anti-event system with small chemical and mass potentials. The relativistic mass distribution for such a system is obtained and shown to be a good candidate for fitting hadronic resonances, in agreement with the phenomenological models of Hagedorn, Shuryak, {\it et al.} This distribution provides a correction to the value of specific heat 3/2, of the order of 5.5\%, at low temperatures.Comment: 19 pages, report TAUP-2161-9

Recent results in relativistic heavy ion collisions: from ``a new state of matter'' to "the perfect fluid"

Experimental Physics with Relativistic Heavy Ions dates from 1992 when a beam of 197Au of energy greater than 10A GeV/c first became available at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL) soon followed in 1994 by a 208Pb beam of 158A GeV/c at the Super Proton Synchrotron (SPS) at CERN (European Center for Nuclear Research). Previous pioneering measurements at the Berkeley Bevalac in the late 1970's and early 1980's were at much lower bombarding energies (~ 1 A GeV/c) where nuclear breakup rather than particle production is the dominant inelastic process in A+A collisions. More recently, starting in 2000, the Relativistic Heavy Ion Collider (RHIC) at BNL has produced head-on collisions of two 100A GeV beams of fully stripped Au ions, corresponding to nucleon-nucleon center-of-mass energy, sqrt(sNN)=200 GeV, total c.m. energy 200A GeV. The objective of this research program is to produce nuclear matter with extreme density and temperature, possibly resulting in a state of matter where the quarks and gluons normally confined inside individual nucleons (r < 1 fm) are free to act over distances an order of magnitude larger. Progress from the period 1992 to the present will be reviewed, with reference to previous results from light ion and proton-proton collisions where appropriate. Emphasis will be placed on the measurements which formed the basis for the announcements by the two major laboratories: "A new state of matter", by CERN on Feb 10, 2000 and "The perfect fluid", by BNL on April 19, 2005.Comment: 62 pages, 39 figures. Review article published in Reports on Progress in Physics on June 23, 2006. In this published version, mistakes, typographical errors, and citations have been corrected and a subsection has been adde

Hadron and hadron-cluster production in a hydrodynamical model including particle evaporation

We discuss the evolution of the mixed phase at RHIC and SPS within boostinvariant hydrodynamics. In addition to the hydrodynamical expansion, we also consider evaporation of particles off the surface of the fluid. The back-reaction of the evaporation process on the dynamics of the fluid shortens the lifetime of the mixed phase. In our model this lifetime of the mixed phase is <12 fm/c in Au+Au at RHIC and <6.5 fm/c in Pb+Pb at SPS, even in the limit of vanishing transverse expansion velocity. Strangeness separation occurs, especially in events (or at rapidities) with relatively high initial net baryon and strangeness number, enhancing the multiplicity of MEMOs (multiply strange nuclear clusters). If antiquarks and antibaryons reach saturation in the course of the pure QGP or mixed phase, we find that at RHIC the ratio of antideuterons to deuterons may exceed 0.3 and even anti-helium to helium>0.1. Due to fluctuations, at RHIC even negative baryon number at midrapidity is possible in individual events, so that the antibaryon and antibaryon-cluster yields exceed those of the corresponding baryons and clusters.Comment: 17 pages, Latex, epsfig stylefil

Pion Multiplicity Distribution in Proton-Antiproton Annihilation at Rest

The pion multiplicity distribution is widely believed to reflect the statistical aspects of $\bar{p}p$ annihilation at rest. We try to reproduce it in a grand canonical picture with explicit conservation of electric charge, isospin, total angular momentum, and the parity quantum numbers $P$, $C$, and $G$ via the projection operator formalism. Bose statistics is found to be non-negligible, particularly in fixing the interaction volume. The calculated pion multiplicity distribution for $\left\langle n_{\pi} \right\rangle = 5$ turns out to depend strongly on the conservation of the angular momentum and connected quantum numbers, as well as on the spin state occupation in S-wave annihilation. However, the empirical Gaussian pion multiplicity distribution cannot be reproduced. This calls in question either the statistical ansatz or the rather old data themselves.Comment: 13pages, TPR-94-3

Signatures of Quark-Gluon-Plasma formation in high energy heavy-ion collisions: A critical review

A critical review on signatures of Quark-Gluon-Plasma formation is given and the current (1998) experimental status is discussed. After giving an introduction to the properties of QCD matter in both, equilibrium- and non-equilibrium theories, we focus on observables which may yield experimental evidence for QGP formation. For each individual observable the discussion is divided into three sections: first the connection between the respective observable and QGP formation in terms of the underlying theoretical concepts is given, then the relevant experimental results are reviewed and finally the current status concerning the interpretation of both, theory and experiment, is discussed. A comprehensive summary including an outlook towards RHIC is given in the final section.Comment: Topical review, submitted to Journal of Physics G: 68 pages, including 39 figures (revised version: only minor modifications, some references added