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Fluctuations of charged particle number are studied in the canonical ensemble. In the infinite volume limit the fluctuations in the canonical ensemble are different from the fluctuations in the grand canonical one. Thus, the well-known equivalence of both ensembles for the average quantities does not extend for the fluctuations. In view of a possible relevance of the results for the analysis of fluctuations in nuclear collisions at high energies, a role of the limited kinematical acceptance is studied.
Report from NA49
(2004)
The most recent data of NA49 on hadron production in nuclear collisions at CERN SPS energies are presented. Anomalies in the energy dependence of pion and kaon production in central Pb+Pb collisions are observed. They suggest that the onset of deconfinement is located at about 30 AGeV. Large multiplicity and transverse momentum fluctuations are measured for collisions of intermediate mass systems at 158 AGeV. The need for a new experimental programme at the CERN SPS is underlined.
Preliminary results on pion-pion Bose-Einstein correlations in central Pb+Pb collisions measured by the NA49 experiment are presented. Rapidity as well as transverse momentum dependence of the HBT-radii are shown for collisions at 20, 30, 40, 80, and 158 AGeV beam energy. Including results from AGS and RHIC experiments only a weak energy dependence of the radii is observed. Based on hydrodynamical models parameters like lifetime and geometrical radius of the source are derived from the dependence of the radii on transverse momentum.
Event-by-event fluctuations of particle ratios in central Pb + Pb collisions at 20 to 158 AGeV
(2004)
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.
Results are presented on event-by-event electric charge fluctuations in central Pb+Pb collisions at 20, 30, 40, 80 and 158 AGeV. The observed fluctuations are close to those expected for a gas of pions correlated by global charge conservation only. These fluctuations are considerably larger than those calculated for an ideal gas of deconfined quarks and gluons. The present measurements do not necessarily exclude reduced fluctuations from a quark-gluon plasma because these might be masked by contributions from resonance decays.
System size and centrality dependence of the balance function in A + A collisions at √sNN = 17.2 GeV
(2004)
Electric charge correlations were studied for p+p, C+C, Si+Si and centrality selected Pb+Pb collisions at sqrt s_NN = 17.2$ GeV with the NA49 large acceptance detector at the CERN-SPS. In particular, long range pseudo-rapidity correlations of oppositely charged particles were measured using the Balance Function method. The width of the Balance Function decreases with increasing system size and centrality of the reactions. This decrease could be related to an increasing delay of hadronization in central Pb+Pb collisions.
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.
Let G be a Fuchsian group containing two torsion free subgroups defining isomorphic Riemann surfaces. Then these surface subgroups K and alpha-Kalpha exp(-1) are conjugate in PSl(2,R), but in general the conjugating element alpha cannot be taken in G or a finite index Fuchsian extension of G. We will show that in the case of a normal inclusion in a triangle group G these alpha can be chosen in some triangle group extending G. It turns out that the method leading to this result allows also to answer the question how many different regular dessins of the same type can exist on a given quasiplatonic Riemann surface.