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A very general saddle point nuclear shape may be found as a solution of an integro-differential equation without giving apriori any shape parametrization. By introducing phenomenological shell corrections one obtains minima of deformation energy for binary fission of parent nuclei at a finite (non-zero) mass asymmetry. Results are presented for reflection asymmetric saddle point shapes of thorium and uranium even-mass isotopes with A=226-238 and A=230-238 respectively.
We show that an unambiguous way of determining the universal limiting fragmentation region is to consider the derivative (d 2 n / d eta 2) of the pseudo-rapidity distribution per participant pair. In addition, we find that the transition region between the fragmentation and the central plateau regions exhibits a second kind of universal behavior that is only apparent in d 2 n / d eta 2. The sqrt s dependence of the height of the central plateau (d n / d eta) eta=0 and the total charged particle multiplicity n total critically depend on the behavior of this universal transition curve. Analyzing available RHIC data, we show that (dn/d eta) eta=0 can be bounded by ln 2 s and n total can be bounded by ln 3 s. We also show that the deuteron-gold data from RHIC has the exactly same features as the gold-gold data indicating that these universal behaviors are a feature of the initial state parton-nucleus interactions and not a consequence of final state interactions. Predictions for LHC energy are also given.
We discuss modifications of the gyromagnetic moment of electrons and muons due to a minimal length scale combined with a modified fundamental scaleMf . First-order deviations from the theoretical standard model value for g-2 due to these String Theory-motivated e ects are derived. Constraints for the new fundamental scale Mf are given.
String theory suggests modifications of our spacetime such as extra dimensions and the existence of a mininal length scale. In models with addidional dimensions, the Planck scale can be lowered to values accessible by future colliders. Effective theories which extend beyond the standart-model by including extra dimensions and a minimal length allow computation of observables and can be used to make testable predictions. Expected effects that arise within these models are the production of gravitons and black holes. Furthermore, the Planck-length is a lower bound to the possible resolution of spacetime which might be reached soon.
We compare multiplicities as well as rapidity and transverse momentum distributions of protons, pions and kaons calculated within presently available transport approaches for heavy ion collisions around 1 AGeV. For this purpose, three reactions have been selected: Au+Au at 1 and 1.48 AGeV and Ni+Ni at 1.93 AGeV.
We present a detailed study of chemical freeze-out in nucleus-nucleus collisions at beam energies of 11.6, 30, 40, 80 and 158A GeV. By analyzing hadronic multiplicities within the statistical hadronization approach, we have studied the strangeness production as a function of centre of mass energy and of the parameters of the source. We have tested and compared different versions of the statistical model, with special emphasis on possible explanations of the observed strangeness hadronic phase space under-saturation. We show that, in this energy range, the use of hadron yields at midrapidity instead of in full phase space artificially enhances strangeness production and could lead to incorrect conclusions as far as the occurrence of full chemical equilibrium is concerned. In addition to the basic model with an extra strange quark non-equilibrium parameter, we have tested three more schemes: a two-component model superimposing hadrons coming out of single nucleon-nucleon interactions to those emerging from large fireballs at equilibrium, a model with local strangeness neutrality and a model with strange and light quark non-equilibrium parameters. The behaviour of the source parameters as a function of colliding system and collision energy is studied. The description of strangeness production entails a non-monotonic energy dependence of strangeness saturation parameter gamma_S with a maximum around 30A GeV. We also present predictions of the production rates of still unmeasured hadrons including the newly discovered Theta^+(1540) pentaquark baryon.
We suggest that the fluctuations of strange hadron multiplicity could be sensitive to the equation of state and microscopic structure of strongly interacting matter created at the early stage of high energy nucleus-nucleus collisions. They may serve as an important tool in the study of the deconfinement phase transition. We predict, within the statistical model of the early stage, that the ratio of properly filtered fluctuations of strange to non-strange hadron multiplicities should have a non-monotonic energy dependence with a minimum in the mixed phase region.
The data on mT spectra of K0S K+ and K- mesons produced in all inelastic p + p and p + pbar interactions in the energy range sqrt(s)NN=4.7-1800GeV are compiled and analyzed. The spectra are parameterized by a single exponential function, dN/(m_T*dm_T)=C exp(-m_T/T), and the inverse slope parameter T is the main object of study. The T parameter is found to be similar for K0S, K+ and K- mesons. It increases monotonically with collision energy from T~30MeV at sqrt(s)NN=4.7GeV to T~220MeV at sqrt(s)NN=1800GeV. The T parameter measured in p+p and p+pbar interactions is significantly lower than the corresponding parameter obtained for central Pb+Pb collisions at all studied energies. Also the shape of the energy dependence of T is different for central Pb+Pb collisions and p+p(pbar) interactions.
We propose a method to experimentally study the equation of state of strongly interacting matter created at the early stage of nucleus--nucleus collisions. The method exploits the relation between relative entropy and energy fluctuations and equation of state. As a measurable quantity, the ratio of properly filtered multiplicity to energy fluctuations is proposed. Within a statistical approach to the early stage of nucleus-nucleus collisions, the fluctuation ratio manifests a non--monotonic collision energy dependence with a maximum in the domain where the onset of deconfinement occurs.
Production of Lambda and Antilambda hyperons was measured in central Pb-Pb collisions at 40, 80, and 158 A GeV beam energy on a fixed target. Transverse mass spectra and rapidity distributions are given for all three energies. The Lambda/pi ratio at mid-rapidity and in full phase space shows a pronounced maximum between the highest AGS and 40 A GeV SPS energies, whereas the anti-Lambda}/pi ratio exhibits a monotonic increase. PACS numbers: 25.75.-q
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.
The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type I_n factor as algebra of observables, including I_infinity. Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von Neumann algebra R without summands of types I_1 and I_2, using a known result on two-valued measures on the projection lattice P(R). Some connections with presheaf formulations as proposed by Isham and Butterfield are made.
To be published in J. Phys. G - Proceedings of SQM 2004 : We review the results from the various hydrodynamical and transport models on the collective flow observables from AGS to RHIC energies. A critical discussion of the present status of the CERN experiments on hadron collective flow is given. We emphasize the importance of the flow excitation function from 1 to 50 A.GeV: here the hydrodynamic model has predicted the collapse of the v2-flow ~ 10 A.GeV; at 40 A.GeV it has been recently observed by the NA49 collaboration. Since hadronic rescattering models predict much larger flow than observed at this energy we interpret this observation as evidence for a first order phase transition at high baryon density r b. Moreover, the connection of the elliptic flow v2 to jet suppression is examined. It is proven experimentally that the collective flow is not faked by minijet fragmentation. Additionally, detailed transport studies show that the away-side jet suppression can only partially (< 50%) be due to hadronic rescattering. Furthermore, the change in sign of v1, v2 closer to beam rapidity is related to the occurence of a high density first order phase transition in the RHIC data at 62.5, 130 and 200 A.GeV.
We investigate hadron production and transverse hadron spectra in nucleus-nucleus collisions from 2 A·GeV to 21.3 A·TeV within two independent transport approaches (UrQMD and HSD) based on quark, diquark, string and hadronic degrees of freedom. The enhancement of pion production in central Au+Au (Pb+Pb) collisions relative to scaled pp collisions (the ’kink’) is described well by both approaches without involving a phase transition. However, the maximum in the K+ p+ ratio at 20 to 30 A·GeV (the ’horn’) is missed by ~ 40%. Also, at energies above ~5 A·GeV, the measured K± mT-spectra have a larger inverse slope than expected from the models. Thus the pressure generated by hadronic interactions in the transport models at high energies is too low. This finding suggests that the additional pressure - as expected from lattice QCD at finite quark chemical potential and temperature - might be generated by strong interactions in the early pre-hadronic/partonic phase of central heavy-ion collisions. Finally, we discuss the emergence of density perturbations in a first-order phase transition and why they might affect relative hadron multiplicities, collective flow, and hadron mean-free paths at decoupling. A minimum in the collective flow v2 excitation function was discovered experimentally at 40 A·GeV - such a behavior has been predicted long ago as signature for a first order phase transition.
We investigate the effects of strong color fields and of the associated enhanced intrinsic transverse momenta on the phi-meson production in ultrarelativistic heavy ion collisions at RHIC. The observed consequences include a change of the spectral slopes, varying particle ratios, and also modified mean transverse momenta. In particular, the composition of the production processes of phi-mesons, that is, direct production vs. coalescence-like production, depends strongly on the strength of the color fields and intrinsic transverse momenta and thus represents a sensitive probe for their measurement.