The chemical equilibration volume: measuring the degree of thermalization

We address the issue of the degree of equilibrium achieved in a high energy heavy-ion collision. Specifically, we explore the consequences of incomplete strangeness chemical equilibrium. This is achieved over a volume V of the order of the strangeness correlation length and is assumed to be smaller than the freeze-out volume. Probability distributions of strange hadrons emanating from the system are computed for varying sizes of V and simple experimental observables based on these are proposed. Measurements of such observables may be used to estimate V and as a result the degree of strangeness chemical equilibration achieved. This sets a lower bound on the degree of kinetic equilibrium. We also point out that a determination of two-body correlations or second moments of the distributions are not sufficient for this estimation.Comment: 16 pages, 15 figures, revtex

System-size dependence of the pion freeze-out volume as a potential signature for the phase transition to a Quark Gluon Plasma

Hanburry-Brown-Twiss (HBT) correlation functions and radii of negatively charged pions from C+C, Si+Si, Cu+Cu, and In+In at lower RHIC/SPS energies are calculated with the UrQMD transport model and the CRAB analyzing program. We find a minimum in the excitation function of the pion freeze-out volume at low transverse momenta and around $E_{lab}\sim 20-30A$GeV which can be related to the transition from hadronic to string matter (which might be interpreted as a pre-cursor of the QGP). The existence of the minimum is explained by the competition of two mechanisms of the particle production, resonance decays and string formation/fragmentation.Comment: 12 pages, 4 fig

Measurement of event-by-event transverse momentum and multiplicity fluctuations using strongly intensive measures Δ[PT,N]\Delta[P_T, N] and Σ[PT,N]\Sigma[P_T, N] in nucleus-nucleus collisions at the CERN Super Proton Synchrotron

Results from the NA49 experiment at the CERN SPS are presented on event-by-event transverse momentum and multiplicity fluctuations of charged particles, produced at forward rapidities in central Pb+Pb interactions at beam momenta 20$A$, 30$A$, 40$A$, 80$A$, and 158$A$ GeV/c, as well as in systems of different size ($p+p$, C+C, Si+Si, and Pb+Pb) at 158$A$ GeV/c. This publication extends the previous NA49 measurements of the strongly intensive measure $\Phi_{p_T}$ by a study of the recently proposed strongly intensive measures of fluctuations $\Delta[P_T, N]$ and $\Sigma[P_T, N]$. In the explored kinematic region transverse momentum and multiplicity fluctuations show no significant energy dependence in the SPS energy range. However, a remarkable system size dependence is observed for both $\Delta[P_T, N]$ and $\Sigma[P_T, N]$, with the largest values measured in peripheral Pb+Pb interactions. The results are compared with NA61/SHINE measurements in $p+p$ collisions, as well as with predictions of the UrQMD and EPOS models.Comment: 12 pages, 14 figures, to be submitted to PR

The K/pi ratio from condensed Polyakov loops

We perform a field-theoretical computation of hadron production in large systems at the QCD confinement phase transition associated with restoration of the Z(3) global symmetry. This occurs from the decay of a condensate for the Polyakov loop. From the effective potential for the Polyakov loop, its mass just below the confinement temperature T_c is in between the vacuum masses of the pion and that of the kaon. Therefore, due to phase-space restrictions the number of produced kaons is roughly an order of magnitude smaller than that of produced pions, in agreement with recent results from collisions of gold ions at the BNL-RHIC. From its mass, we estimate that the Polyakov loop condensate is characterized by a (spatial) correlation scale of 1/m_\ell ~ 1/2 fm. For systems of deconfined matter of about that size, the free energy may not be dominated by a condensate for the Polyakov loop, and so the process of hadronization may be qualitatively different as compared to large systems. In that vein, experimental data on hadron abundance ratios, for example K/pi, in high-multiplicity pp events at high energies should be very interesting.Comment: 7 pages, 4 figures; discussion of the two-point function of Polyakov Loops in small versus large systems adde

Antideuteron and deuteron production in mid-central Pb+Pb collisions at 158AA GeV

Production of deuterons and antideuterons was studied by the NA49 experiment in the 23.5% most central Pb+Pb collisions at the top SPS energy of $\sqrt{s_{NN}}$=17.3 GeV. Invariant yields for $\bar{d}$ and $d$ were measured as a function of centrality in the center-of-mass rapidity range $-1.2<y<-0.6$. Results for $\bar{d}(d)$ together with previously published $\bar{p}(p)$ measurements are discussed in the context of the coalescence model. The coalescence parameters $B_2$ were deduced as a function of transverse momentum $p_t$ and collision centrality.Comment: 9 figure

Multiplicity fluctuations in nuclear collisions at 158 A GeV

System size dependence of multiplicity fluctuations of charged particles produced in nuclear collisions at 158 A GeV was studied in the NA49 CERN experiment. Results indicate a non-monotonic dependence of the scaled variance of the multiplicity distribution with a maximum for semi-peripheral Pb+Pb interactions with number of projectile participants of about 35. This effect is not observed in a string-hadronic model of nuclear collision HIJING.Comment: Presented at "Focus on Multiplicity", 17-19 of June, Bari, Ital

Bose-Einstein correlations of pion pairs in central Pb+Pb collisions at CERN SPS energies

Measurements of Bose-Einstein correlations of pion pairs in central Pb+Pb collisions were performed with the NA49 detector at the CERN SPS for beam energies of 20A, 30A, 40A, 80A, and 158A GeV. Correlation functions were measured in the longitudinally co-moving ``out-side-long'' reference frame as a function of rapidity and transverse momentum in the forward hemisphere of the reaction. Radius and correlation strength parameters were obtained from fits of a Gaussian parametrization. The results show a decrease of the radius parameters with increasing transverse momentum characteristic of strong radial flow in the pion source. No striking dependence on pion-pair rapidity or beam energy is observed. Static and dynamic properties of the pion source are obtained from simultaneous fits with a blast-wave model to radius parameters and midrapidity transverse momentum spectra. Predictions of hydrodynamic and microscopic models of Pb+Pb collisions are discussed.Comment: 22 pages, 23 figure

System size dependence of strange particle yields and spectra at sqrt(s)=17.3 GeV

Yields and spectra of strange hadrons (K+, K-, phi, Lambda and Antilambda) as well as of charged pions were measured in near central C+C and Si+Si collisions at 158 AGeV beam energy with the NA49 detector. Together with earlier data for p+p, S+S and Pb+Pb reactions the system size dependence can be studied. Relative strangeness production rises fast and saturates at about 60 participating nucleons; the net hyperon spectra show an increasing shift towards midrapidity for larger colliding nuclei. An interpretation based on the formation of coherent systems of increasing volume is proposed. The transverse mass spectra can be described by a blast wave ansatz. Increasing flow velocity is accompanied by decreasing temperatures for both kinetic and chemical freeze out. The increasing gap between inelastic and elastic decoupling leaves space for rescattering.Comment: 8 pages, 6 figures, Proceedings of the Hot Quarks 2004 worksho

Event-by-Event Fluctuations of Particle Ratios in Central Pb+Pb Collisions at 20 to 158 AGeV

In the vicinity of the QCD phase transition, critical fluctuations have been predicted to lead to non-statistical fluctuations of particle ratios, depending on the nature of the phase transition. Recent results of the NA49 energy scan program show a sharp maximum of the ratio of K+ to Pi+ yields in central Pb+Pb collisions at beam energies of 20-30 AGeV. This observation has been interpreted as an indication of a phase transition at low SPS energies. We present first results on event-by-event fluctuations of the kaon to pion and proton to pion ratios at beam energies close to this maximum.Comment: 4 pages, 4 figures, Quark Matter 2004 proceeding