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Triple differential cross sections d3 sigma /dp3 for charged pions produced in symmetric heavy-ion collisions were measured with the KaoS magnetic spectrometer at the heavy-ion synchrotron facility SIS at GSI. The correlations between the momentum vectors of charged pions and the reaction plane in 197Au+197Au collisions at an incident energy of 1 GeV/nucleon were determined. We observe, for the first time, an azimuthally anisotropic distribution of pions, with enhanced emission perpendicular to the reaction plane. The anisotropy is most pronounced for pions of high transverse momentum in semicentral collisions.
Nuclear resonance fluorescence experiments with linearly polarized bremsstrahlung were performed to determine parities of strong dipole transitions in 40Ar. A total of 14 transitions—ten of them previously unknown—in the energy range from 4.7 to 10.2 MeV could be identified. From this experiment it is evident that the main dipole strength to bound states is due to E1 excitations. An upper limit of B(M1) [up arrow] <0.5 µN2 was found for individual magnetic dipole excitations in 40Ar in the energy region below neutron threshold.
Electric charge correlations were studied for p+p, C+C, Si+Si, and centrality selected Pb+Pb collisions at sqrt[sNN]=17.2 GeV with the NA49 large acceptance detector at the CERN SPS. In particular, long-range pseudorapidity 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.
The properties of two measures of charge fluctuations D-tilde and DeltaPhiq are discussed within several toy models of nuclear collisions. In particular their dependence on mean particle multiplicity, multiplicity fluctuations, and net electric charge are studied. It is shown that the measure DeltaPhiq is less sensitive to these trivial biasing effects than the originally proposed measure D-tilde. Furthermore the influence of resonance decay kinematics is analyzed and it is shown that it is likely to shadow a possible reduction of fluctuations due to QGP creation.
Dt. Fassung: Der Umgang mit Rechtsparadoxien: Derrida, Luhmann, Wiethölter. In: Christian Joerges und Gunther Teubner (Hg.) Rechtsverfassungsrecht: Recht-Fertigungen zwischen Sozialtheorie und Privatrechtsdogmatik. Nomos, Baden-Baden 2003, 249-272.
Analysis of Lambda and associative pion production in relativistic nucleus-nucleus collisions
(1984)
The transverse momentum and rapidity distributions of negative hadrons and participant protons have been measured for central 32S+ 32S collisions at plab=200 GeV/c per nucleon. The proton mean rapidity shift < Delta y>~1.6 and mean transverse momentum <pT>~0.6 GeV/c are much higher than in pp or peripheral AA collisions and indicate an increase in the nuclear stopping power. All pT spectra exhibit similar source temperatures. Including previous results for K0s Lambda , and Lambda -bar, we account for all important contributions to particle production.
The NA35 experiment has collected a high statistics set of momentum analyzed negative hadrons near and forward of midrapidity for central collisions of 200A GeV/c 32S+S, Cu, Ag, and Au. Using momentum space correlations to study the size of the source of particle production, the transverse source radii are found to decrease by ~40% at midrapidity and ~20% at forward rapidity while the longitudinal radius RL is found to decrease by ~50% as pT increases over the interval 50<pT<600 MeV/c. Calculations using a microscopic phase space approach (relativistic quantum molecular dynamics) reproduce the observed trends of the data. PACS: 25.75.+r
Transverse momenta and rapidities of Lambda 's produced in central nucleus-nucleus collisions at 4.5 GeV/c·u (C-C,...,O-Pb) were studied and compared with those from inelastic He-Li interactions at the same incident momentum. Polarization of the Lambda hyperons was found to be consistent with zero ( alpha P=-0.06=0.11 for Lambda 's from central collisions). An upper limit of the Lambda -bar / Lambda production ratio was estimated to be less than 4.5 x 10-3. The experiment was performed in a triggered streamer chamber.
Difficulties of the thermodynamical model approach to pion production in relativistic ion collisions
(1983)
Thermodynamical models with various forms of partial transparency of nuclear matter are considered. It is shown that the introduction of transparency, however, significantly improves agreement with pion data concerning multiplicities and transverse momenta leads to a serious discrepancy with average rapidities of pions. Qualitative arguments are given that difficulties of the thermodynamical approach can be overcome if one assumes hydrodynamical expansion in the first stage of nuclear interactions.
A detailed study of pion production in inelastic and central nucleus-nucleus collisions was carried out using a 2 m streamer spectrometer. Nuclear targets mounted inside the streamer chamber were exposed to nuclear beams of 4.5 GeV/c/nucleon momentum. A systematic study of the influence of the central trigger on observed data is performed. The data on multiplicities, rapidities, transverse momenta, and emission angles of negative pions are presented for various pairs of colliding nuclei. Intercorrelations between various characteristics are studied and discussed. The results are compared with predictions of some theoretical models. It is shown that the main features of the pion production in nuclear collisions can be satisfactorily described by a model assuming independent nucleon-nucleon collisions with subsequent cascading process. However, the observed correlation between Lambda and pion characteristics seems to be unexplained by this picture.
We argue that the recent analysis of strangeness production in nuclear collisions at 200 A GeV/c performed by Topor Pop et al. is flawed. The conclusions are based on an erroneous interpretation of the data and the numerical model results. The term "strangeness enhancement" is used in a misleading way.
Pion and strangeness puzzles
(1996)
Data on the mean multiplicity of strange hadrons produced in minimum bias proton--proton and central nucleus--nucleus collisions at momenta between 2.8 and 400 GeV/c per nucleon have been compiled. The multiplicities for nucleon--nucleon interactions were constructed. The ratios of strange particle multiplicity to participant nucleon as well as to pion multiplicity are larger for central nucleus--nucleus collisions than for nucleon--nucleon interactions at all studied energies. The data at AGS energies suggest that the latter ratio saturates with increasing masses of the colliding nuclei. The strangeness to pion multiplicity ratio observed in nucleon--nucleon interactions increases with collision energy in the whole energy range studied. A qualitatively different behaviour is observed for central nucleus--nucleus collisions: the ratio rapidly increases when going from Dubna to AGS energies and changes little between AGS and SPS energies. This change in the behaviour can be related to the increase in the entropy production observed in central nucleus-nucleus collisions at the same energy range. The results are interpreted within a statistical approach. They are consistent with the hypothesis that the Quark Gluon Plasma is created at SPS energies, the critical collision energy being between AGS and SPS energies.
In the current globalization debate the law appears to be entangled in economic and political developments which move into a new dimension of depoliticization, de-centralization and de-individualization. For all the correct observations in detail, though, this debate is bringing about a drastic (polit)economic reduction of the role of law in the globalization process that I wish to challenge in this paper. Here one has to take on Wallerstein’s misconception of “worldwide economies” according to which the formation of the global society is seen as a basically economic process. Autonomous globalization processes in other social spheres running parallel to economic globalization need to be taken seriously. In protest against such (polit)economic reductionism several strands of the debate, among them the neo-institutionalist theory of “global culture”, post-modern concepts of global legal pluralism, systems theory studies of differentiated global society and various versions of “global civil society” have shaped a concept of a polycentric globalization. From these angles the remarkable multiplicity of the world society, in which tendencies to re-politicization, re-regionalization and re-individualization are becoming visible at the same time, becomes evident. I shall contrast two current theses on the globalization of law with two less current counter-theses: First thesis: globalization is relevant for law because the emergence of global markets undermines the control potential of national policy, and therefore also the chances of legal regulation. First counter-thesis: globalization produces a set of problems intrinsic to law itself, consisting in a change to the dominant lawmaking processes. Second thesis: globalization means that the law institutionalizes the worldwide shift in power from governmental actors to economic actors. Second counter-thesis: globalization means that the law has a chance of contributing to a dual constitution of autonomous sectors of world society.
The main results obtained within the energy scan program at the CERN SPS are presented. The anomalies in energy dependence of hadron production indicate that the onset of deconfinement phase transition is located at about 30 A GeV. For the first time we seem to have clear evidence for the existence of a deconfined state of matter in nature. PACS numbers: 24.85.+p
We present the measured correlation functions for pi+ pi-, pi- pi- and pi+ pi+ pairs in central S+Ag collisions at 200 GeV per nucleon. The Gamov function, which has been traditionally used to correct the correlation functions of charged pions for the Coulomb interaction, is found to be inconsistent with all measured correlation functions. Certain problems which have been dominating the systematic uncertainty of the correlation analysis are related to this inconsistency. It is demonstrated that a new Coulomb correction method, based exclusively on the measured correlation function for pi+ pi- pairs, may solve the problem.
The pion multiplicity per participating nucleon in central nucleus-nucleus collisions at the energies 2-15 A GeV is significantly smaller than in nucleon-nucleon interactions at the same collision energy. This effect of pion suppression is argued to appear due to the evolution of the system produced at the early stage of heavy-ion collisions towards a local thermodynamic equilibrium and further isentropic expansion.
It is shown that data on pion and strangeness production in central nucleus-nucleus collisions are consistent with the hypothesis of a Quark Gluon Plasma formation between 15 A GeV/c (BNL AGS) and 160 A GeV/c (CERN SPS) collision energies. The experimental results interpreted in the framework of a statistical approach indicate that the effective number of degrees of freedom increases by a factor of about 3 in the course of the phase transition and that the plasma created at CERN SPS energy may have a temperature of about 280 MeV (energy density $\approx$ 10 GeV/fm^3). Experimental studies of central Pb+Pb collisions in the energy range 20-160 A GeV/c are urgently needed in order to localize the threshold energy, and study the properties of the QCD phase transition.
Using the NA49 main TPC, the central production of hyperons has been measured in CERN SPS Pb - Pb collisions at 158 GeV c-1. The preliminary ratio, studied at 2.0 < y < 2.6 and 1 < pT < 3 GeV c-1, equals ~ (13 ± 4)% (systematic error only). It is compatible, within errors, with the previously obtained ratios for central S + S [1], S + W [2], and S + Au [3] collisions. The fit to the transverse momentum distribution resulted in an inverse slope parameter T of 297 MeV. At this level of statistics we do not see any noticeable enhancement of hyperon production with the increased volume (and, possibly, degree of equilibration) of the system from S + S to Pb + Pb. This result is unexpected and counterintuitive, and should be further investigated. If confirmed, it will have a significant impact on our understanding of mechanisms leading to the enhanced strangeness production in heavy-ion collisions.
The data on average hadron multiplicities in central A+A collisions measured at CERN SPS are analysed with the ideal hadron gas model. It is shown that the full chemical equilibrium version of the model fails to describe the experimental results. The agreement of the data with the off-equilibrium version allowing for partial strangeness saturation is significantly better. The freeze-out temperature of about 180 MeV seems to be independent of the system size (from S+S to Pb+Pb) and in agreement with that extracted in e+e-, pp and p{\bar p} collisions. The strangeness suppression is discussed at both hadron and valence quark level. It is found that the hadronic strangeness saturation factor gamma_S increases from about 0.45 for pp interactions to about 0.7 for central A+A collisions with no significant change from S+S to Pb+Pb collisions. The quark strangeness suppression factor lambda_S is found to be about 0.2 for elementary collisions and about 0.4 for heavy ion collisions independently of collision energy and type of colliding system
The transverse momentum and rapidity distributions of net protons and negatively charged hadrons have been measured for minimum bias proton-nucleus and deuteron-gold interactions, as well as central oxygen-gold and sulphur-nucleus collisions at 200 GeV per nucleon. The rapidity density of net protons at midrapidity in central nucleus-nucleus collisions increases both with target mass for sulphur projectiles and with the projectile mass for a gold target. The shape of the rapidity distributions of net protons forward of midrapidity for d+Au and central S+Au collisions is similar. The average rapidity loss is larger than 2 units of rapidity for reactions with the gold target. The transverse momentum spectra of net protons for all reactions can be described by a thermal distribution with temperatures' between 145 +- 11 MeV (p+S interactions) and 244 +- 43 MeV (central S+Au collisions). The multiplicity of negatively charged hadrons increases with the mass of the colliding system. The shape of the transverse momentum spectra of negatively charged hadrons changes from minimum bias p+p and p+S interactions to p+Au and central nucleus-nucleus collisions. The mean transverse momentum is almost constant in the vicinity of midrapidity and shows little variation with the target and projectile masses. The average number of produced negatively charged hadrons per participant baryon increases slightly from p+p, p+A to central S+S,Ag collisions.
Preliminary inclusive spectra for K+, K-, Ks0, Λ, and are presented which were measured in central Pb + Pb collisions at 158 GeV per nucleon by the NA49 experiment. A comparison with data from lighter collision systems shows a strong change of the shape of the Λ rapidity distribution. The strangeness enhancement observed in S + S compared to p + p and p + A is not further increased in Pb + Pb.
The directed and elliptic flow of protons and charged pions has been observed from the semi-central collisions of a 158 GeV/nucleon Pb beam with a Pb target. The rapidity and transverse momentum dependence of the flow has been measured. The directed flow of the pions is opposite to that of the protons but both exhibit negative flow at low pt. The elliptic flow of both is fairly independent of rapidity but rises with pt. PACS numbers: 25.75.-q, 25.75.Ld
Preliminary data on phi production in central Pb + Pb collisions at 158 GeV per nucleon are presented, measured by the NA49 experiment in the hadronic decay channel phi - K+K-. At mid-rapidity, the kaons were separated from pions and protons by combining dE/dx and time-of-flight information; in the forward rapidity range only dE/dx identification was used to obtain the rapidity distribution and a rapidity-integrated mt-spectrum. The mid-rapidity yield obtained was dN/dy = 1.85 ± 0.3 per event; the total phi multiplicity was estimated to be 5.0 ± 0.7 per event. Comparison with published pp data shows a slight, but not very significant strangeness enhancement.
We demonstrate that a new type of analysis in heavy-ion collisions, based on an event-by-event analysis of the transverse momentum distribution, allows us to obtain information on secondary interactions and collective behaviour that is not available from the inclusive spectra. Using a random walk model as a simple phenomenological description of initial state scattering in collisions with heavy nuclei, we show that the event-by-event measurement allows a quantitative determination of this effect, well within the resolution achievable with the new generation of large acceptance hadron spectrometers. The preliminary data of the NA49 collaboration on transverse momentum fluctuations indicate qualitatively different behaviour than that obtained within the random walk model. The results are discussed in relation to the thermodynamic and hydrodynamic description of nuclear collisions.
Two-particle correlation functions of negative hadrons over wide phase space, and transverse mass spectra of negative hadrons and deuterons near mid-rapidity have been measured in central Pb+Pb collisions at 158 GeV per nucleon by the NA49 experiment at the CERN SPS. A novel Coulomb correction procedure for the negative two-particle correlations is employed making use of the measured oppositely charged particle correlation. Within an expanding source scenario these results are used to extract the dynamic characteristics of the hadronic source, resolving the ambiguities between the temperature and transverse expansion velocity of the source, that are unavoidable when single and two particle spectra are analysed separately. The source shape, the total duration of the source expansion, the duration of particle emission, the freeze-out temperature and the longitudinal and transverse expansion velocities are deduced.
Lambda and Antilambda reconstruction in central Pb+Pb collisions using a time projection chamber
(1997)
The large acceptance time projection chambers of the NA49 experiment are used to record the trajectory of charged particles from Pb + Pb collisions at 158 GeV per nucleon. Neutral strange hadrons have been reconstructed from their charged decay products. To obtain distributions of Λ, and Ks0 in discrete bins of rapidity, y, and transverse momentum, pT, calculations have been performed to determine the acceptance of the detector and the efficiency of the reconstruction software as a function of both variables. The lifetime distributions obtained give values of cτ = 7.8 ± 0.6 cm for Λ and cτ = 2.5 ± 0.3 cm for Ks0, consistent with data book values.
A brief review of a history of data collection and interpretation of the results on high energy A+A collisions is presented. Basic assumptions and main results of a statistical model of the early stage of the A+A collisions are discussed. It is concluded that a broad set of experimental data is in agreement with the hypothesis that QGP is created in central A+A (S+S and Pb+Pb) collisions at the SPS. Carefull experimental investigation of the A+A collisions in the energy region between top AGS and SPS energies is needed.
The large acceptance TPCs of the NA49 spectrometer allow for a systematic multidimensional study of two-particle correlations in different part of phase space. Results from Bertsch-Pratt and Yano-Koonin-Podgoretskii parametrizations are presented differentially in transverse pair momentum and pair rapidity. These studies give an insight into the dynamical space-time evolution of relativistic Pb+Pb collisions, which is dominated by longitudinal expansion.
A statistical model of the early stage of central nucleus--nucleus (A+A) collisions is developed. We suggest a description of the confined state with several free parameters fitted to a compilation of A+A data at the AGS. For the deconfined state a simple Bag model equation of state is assumed. The model leads to the conclusion that a Quark Gluon Plasma is created in central nucleus--nucleus collisions at the SPS. This result is in quantitative agreement with existing SPS data on pion and strangeness production and gives a natural explanation for their scaling behaviour. The localization and the properties of the transition region are discussed. It is shown that the deconfinement transition can be detected by observation of the characteristic energy dependence of pion and strangeness multiplicities, and by an increase of the event--by--event fluctuations. An attempt to understand the data on J/psi production in Pb+Pb collisions at the SPS within the same approach is presented.
Data on J/psi production in inelastic proton-proton, proton-nucleus and nucleus-nucleus interactions at 158 A GeV are analyzed and it is shown that the ratio of mean multiplicities of J/psi mesons and pions is the same for all these collisions. This observation is difficult to understand within current models of J/psi production in nuclear collisions based on the assumption of hard QCD creation of charm quarks.
This paper determines the cost of employee stock options (ESOs) to shareholders. I present a pricing method that seeks to replicate the empirics of exercise and cancellation as good as possible. In a first step, an intensity-based pricing model of El Karoui and Martellini is adapted to the needs of ESOs. In a second step, I calibrate the model with a regression analysis of exercise rates from the empirical work of Heath, Huddart and Lang. The pricing model thus takes account for all effects captured in the regression. Separate regressions enableme to compare options for top executives with those for subordinates. I find no price differences. The model is also applied to test the precision of the fair value accounting method for ESOs, SFAS 123. Using my model as a reference, the SFAS method results in surprisingly accurate prices.
Intangible assets as goodwill, licenses, research and development or customer relations become in high technology and service orientated economies more and more important. But comparing the book values of listed companies and their market capitalization the financial reports seems to fail the information needs of market participants regarding the estimate of the proper firm value. Moreover, with the introduction of Anglo-American accounting systems in Europe and Asia we can observe even in the accounts of companies sited in the same jurisdiction diverging accounting practices for intangible assets caused by different accounting standards. To assess the relevance of intangible assets in Japanese and German accounts of listed companies we therefore measure certain balance sheet and profit and loss relations according to goodwill and self-developed software. We compare and analyze valuation rules for goodwill and software costs according to German GAAP, Japanese GAAP, US GAAP and IAS to determine the possible impact of diverging rules in the comparability of the accounts. Our results show that the comparability of the accounts is impaired because of different accounting practices. The recognition and valuation of goodwill and self-developed software varies significantly according to the accounting regime applied. However, for the recognition of self-developed software, the effect on the average impact on asset coefficients or profit is not that high. Moreover, an industry bias can only be found for the financial industry. In contrast, for goodwill accounting we found major differences especially between German and Japanese Blue Chips. The introduction of the new goodwill impairment only approach and the prohibition of the pooling method may have a major impact especially for Japanese companies’ accounts.
We report measurements of Xi and Xi-bar hyperon absolute yields as a function of rapidity in 158 GeV/c Pb+Pb collisions. At midrapidity, dN/dy = 2.29 +/- 0.12 for Xi, and 0.52 +/- 0.05 for Xi-bar, leading to the ratio of Xi-bar/Xi = 0.23 +/- 0.03. Inverse slope parameters fitted to the measured transverse mass spectra are of the order of 300 MeV near mid-rapidity. The estimated total yield of Xi particles in Pb+Pb central interactions amounts to 7.4 +/- 1.0 per collision. Comparison to Xi production in properly scaled p+p reactions at the same energy reveals a dramatic enhancement (about one order of magnitude) of Xi production in Pb+Pb central collisions over elementary hadron interactions.
New data with a minimum bias trigger for 158 GeV/nucleon Pb + Pb have been analyzed. Directed and elliptic flow as a function of rapidity of the particles and centrality of the collision are presented. The centrality dependence of the ratio of elliptic flow to the initial space elliptic anisotropy is compared to models.
Net proton and negative hadron spectra for central \PbPb collisions at 158 GeV per nucleon at the CERN SPS were measured and compared to spectra from lighter systems. Net baryon distributions were derived from those of net protons, utilizing model calculations of isospin contributions as well as data and model calculations of strange baryon distributions. Stopping (rapidity shift with respect to the beam) and mean transverse momentum \meanpt of net baryons increase with system size. The rapidity density of negative hadrons scales with the number of participant nucleons for nuclear collisions, whereas their \meanpt is independent of system size. The \meanpt dependence upon particle mass and system size is consistent with larger transverse flow velocity at midrapidity for \PbPb compared to \SS central collisions.
We present first data on event-by-event fluctuations in the average transverse momentum of charged particles produced in Pb+Pb collisions at the CERN SPS. This measurement provides previously unavailable information allowing sensitive tests of microscopic and thermodynamic collision models and to search for fluctuations expected to occur in the vicinity of the predicted QCD phase transition. We find that the observed variance of the event-by-event average transverse momentum is consistent with independent particle production modified by the known two-particle correlations due to quantum statistics and final state interactions and folded with the resolution of the NA49 apparatus. For two specific models of non-statistical fluctuations in transverse momentum limits are derived in terms of fluctuation amplitude. We show that a significant part of the parameter space for a model of isospin fluctuations predicted as a consequence of chiral symmetry restoration in a non-equilibrium scenario is excluded by our measurement.
The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.
The statistical production of antibaryons is considered within the canonical ensemble formulation. We demonstrate that the antibaryon suppression in small systems due to the exact baryon number conservation is rather different in the baryon-free (B=0) and baryon-rich (B>1) systems. At constant values of temperature and baryon density in the baryon-rich systems the density of the produced antibaryons is only weakly dependent on the size of the system. For realistic hadronization conditions this dependence appears to be close to B/(B+1) which is in agreement with the preliminary data of the NA49 Collaboration for the antiproton/pion ratio in nucleus-nucleus collisions at the CERN SPS energies. However, a consistent picture of antibaryon production within the statistical hadronization model has not yet been achieved. This is because the condition of constant hadronization temperature in the baryon-free systems leads to a contradiction with the data on the antiproton/pion ratio in e+e- interactions.
The experimental results on the pion, strangeness and J/psi production in high energy nuclear collisions are discussed. The anomalous energy dependence of pion and strangeness production is consistent with the hypothesis that a transition to a deconfined phase takes place between the top AGS (15 AGeV) and the SPS (200 AGeV) energies. The J/psi production systematics at the SPS can be understood assuming that the J/psi mesons are created at hadronization according to the available hadronic phase space. This new interpretation of the J/psi data allows one to establish a coherent picture of high energy nuclear collisions based on the statistical approaches of the collision early stage and hadronization. Surprisingly, the statistical model of strong interactions is successful even in the region reserved up to now for pQCD based models.
The hypothesis of statistical production of J/psi mesons at hadronization is formulated and checked against experimental data. It explains in the natural way the observed scaling behavior of the J/psi to pion ratio at the CERN SPS energies. Using the multiplicities of J/psi and eta mesons the hadronization temperature T_H = 175 MeV is found, which agrees with the previous estimates of the temperature parameter based on the analysis of the hadron yield systematics.