NA49 physics results regarding the search for Quark-Gluon Matter
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We want to comment here about four experimental NA49 results which, in particular, have the most immediate connection to the search for the QCD phase transition between partons (i.e. quarks and gluons) and hadrons (i.e. pions , kaons, protons etc.).
How can we know that the energy density created in head-on Pb+Pb collisions at 158 GeV per nucleon in the projectile nucleus suffices to get beyond the "critical" energy density epsilon_c at which the transition occurs - i.e. beyond 1-1.5 GeV per cubic fermi which is the QCD estimate for epsilon_c?
To this end one first measures the total internal energy content at the center of the fireball, then employs an estimate for the corresponding volume - to get an energy density. This approach was suggested almost 20 years ago by J. D. Bjorken of Fermilab.
NA49 adapted a large calorimeter inherited from former SPS experiments to measure the so-called transverse energy ET radiated outward from the primordial interaction zone created in Pb+Pb collisions.
The range of created ET extends from mere grazing collisions, with low ET, to near head-on collisions which show more than 500 GeV of transverse energy. The Bjorken estimate of that fraction of the primordial volume which is covered by the calorimeter acceptance amounts to 150-200 cubic fermis.
The figure shows the cross sections as a function of transverse energy ET in Pb+Pb (NA49) and S+Au (NA35) collisions near midrapidity. The highest values of ET are reached in central collisions. Using the Bjorken hydrodynamical model one obtains an estimate of about 3 GeV pre cubic fermi for the energy density in the early phase of central Pb+Pb collisions.
The transverse energy density can thus be estimated to be about 3 GeV per cubic fm: well sufficient to let the system enter the domain above the QCD estimate for epsilon_c. The SPS energy thus appears to be just high enough to probe into deconfined partonic matter.
The primordial fireball volume develops an enormous pressure that drives it into expansion. This pressure is related to its energy density (it is proportional to epsilon).
We have estimated the latter above, albeit in the units of GeV pre cubic fermi that are appropriate to microscopic physics. Translated into our more familiar classical physics terminology the initial pressure amounts to about 3x1032 kg per cm2, again past any imagination but it may help to realize that this amounts to about the weight total of 150 solar masses pressing on one square centimeter.
From our above argument this should be the pressure prevailing at an instant of time before the pressure driven expansion enters the QCD parton to hadron phase transition. The above findings are relevant to the dynamics of the cosmological expansion at the early microsecond stage, whence the Big Bang is about to undergo the parton to hadron phase transition.
Likewise, in our mini-bangs, the primordial pressure drives the interaction volume into an expansion mode. The characteristics of this "explosive" mode is recaptured in the experimental observation of a radially symmetric "blast wave" collective velocity field which drives the fireball particles into free space.
The figure shows the result, from NA49 analysis of the spectra of emitted particles, combined with an analysis of the constructive interference effect imposed on emitted pion pairs by their Bose statistics, which provides for an alternative microscope of their collective, "blast wave" mode emission. It is shown that all data coincide at a collective emission velocity of hadrons, driven by the primordial high energy and pressure, of beta ~ 0.6, i.e. at 60 % of light velocity: the final remnant of the initial high density fireball explosion.
The determination of the collective radial flow velocity and the temperature at freezeout of the fireball produced in a central Pb+Pb collision is based on the spectra of negative hadrons (mostly pions) and deuterons. The transverse mass distributions can be fitted in a fireball model by any set of parameters T and beta_T within the bands labeled h- and d shown in the figure. The observed systematics in the measurement of the two-pion Bose-Einstein interferometry in the same events can be fitted by the same fireball model by an other set of parameters as given by the band labeled BE. The region where there is a common solution for the three different observables is given by the hatched area.
The two above examples of NA49 data illustrate, first the primordial energy density in the collision fireball which is well above the QCD prediction for the critical energy density of the parton to hadron phase transition, and the final emission of produced particles in a "blast wave" explosive expansion mode.
This captures a moment far below the critical density, as the hadrons decouple from the strong interaction force fields and travel into free streaming - eventually to be detected in the experimental apparatus.
Under guidance from recent Lattice QCD results, that predict the transition from deconfined quarks and gluons to the finally observed hadrons to occur at an energy density of about 1 GeV per cubic fermi we now entertain the hypothesis that the initial fireball volume, estimated to reach up to about 3 GeV per cubic fermis, is indeed in a state of partonic matter. It expands toward lower energy density and should thus hit the critical QCD point, at which hadrons are to be formed that continue to expand, giving rise to the observed final "blast wave" collective expansion mode.
In order to recapture the conditions at phase transition we need an observable quantity which is sensitive to this special point in the expansion dynamics of the fireball. This point falls in between of the primordially formed state reflected by the Bjorken estimate (which marks the beginning of expansion), and the very end of this expansion phase in collectively ordered velocity fields.
We now employ the "hadron thermometer" idea. Measuring all hadronic production rates, in central Pb+Pb collisions, for pions, kaons, antiprotons etc., up to the doubly strange Xi-hyperon makes use of the large acceptance and the high particle discrimination provided by the NA49 setup. The set of the production rates, or their ratios contains essentially one single information - but a very valuable one: the temperature and energy density prevailing at the birth of the hadronic phase. This should be very close to the critical values T_c and epsilon_c of the phase transition.
The figure shows the data and an analysis by F. Becattini of Florence University who employs a thermodynamic model, in the footsteps of R. Hagedorn of CERN. The phase space integrated multiplicities of various identified particle species measured by NA49 in central Pb+Pb reactions at 158 GeV per nucleon are compared to a statistical model fit. Fitted parameters of the model are the temperature T, the baryochemical potential, the strangeness suppression parameter and the fireball volume V.
See also the CERN Courier article of 39/9/5 for more information
We obtain T = 176 (pm 10) MeV corresponding to epsilon = 1.1 (pm 0.2) GeV per cubic fermi. These are, thus, our results concerning the critical parameters, and the outcome agrees with the prediction of lattice QCD. The parton-hadron phase transition is thus located.
The Big Bang theorists world consider our mini-bang physics complete if we could not only pin down T_c and epsilon_c but also obtain insight into the nature of the phase transformation. The lattice QCD model is still uncertain about this question. For Big Bang dynamics it would be of particular importance to know whether or not the transformation is a first order phase transition because that would be of influence to the early synthesis of light nuclear species (helium, lithium, beryllium) in the Big Bang.
In the Pb+Pb collisions a first order phase transition with a large latent heat jump might manifest itself by a long life-time of the fireball at the transition point. In principle, the pion Bose correlation effect provides for a reaction time estimate but the NA49 data do not show a slowing of the expansion rate (to the contrary as we have seen in section (b)).
Also large fluctuations of the hadronization point would be expected due to supercooloing - reheating processes that vary from one collision event to the other. NA49 records about 1200 hadrons in each event which enable one to measure certain quantities for each single event, for example the kaon to pion ratio which is sensitive to the creation temperature of the hadronic phase (see in section (c)).
The figure shows the histogram of Kaon to pion ratios found in individual central Pb+Pb collision events. Its width and shape can be almost completely understood by a simulation that incorporates only the trivial effects due to finite number counting statistics, experimental Kaon to pion ratios resolution etc.
This lack of dynamical fluctuations indicates equilibration of the produced matter, as may be expected if the reaction proceeded through a QGP stage.
Thus we might take this as a first indication that the transition is not first order or, at least, features no large latent heat jump. However, this conclusion is still subject to a vivid theoretical discussion.
Caption Event-by-event fluctuations of the ratio of the produced numbers of charged kaons and pions (a measure of the strangeness content of the event) in central Pb+Pb collisions at 158 GeV per nucleon (data points) are reduced to the level of finite particle number statistics (histograms). This lack of dynamical fluctuations indicates equilibration of the produced matter, as may be expected if the reaction proceeded through a QGP stage.
We conclude that the SPS Lead beam program has led to very interesting data that give a first outline of the QCD deconfinement properties in extended matter of extreme energy density.
The results of all experiments and theory have been intensively discussed at the recent Quark Matter '99 conference in Torino, and the interested reader is referred to the Proceedings of QM99 that have appeared as a special volume of the journal Nuclear Physics series A, volume 661 (1999), Elsevier Publishers.