Invariant elliptic curves as attractors in the projective plane

Let f be a rational self-map of P^2 which leaves invariant an elliptic curve C with strictly negative transverse Lyapunov exponent. We show that C is an attractor, i.e. it possesses a dense orbit and its basin is of strictly positive measure

Production of deuterium, tritium, and 3^3He in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV at the CERN SPS

Production of $d$, $t$, and $^3$He nuclei in central Pb+Pb interactions was studied at five collision energies ($\sqrt{s_{NN}}=$ 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and $^3$He were determined as a function of transverse mass at all energies.Comment: 22 pages, 29 figures, 8 tables, for submission to Phys. Rev.

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

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

Energy dependence of kaon-to-proton ratio fluctuations in central Pb+Pb collisions from sNN\sqrt{s_{NN}} = 6.3 to 17.3 GeV

Kaons and protons carry large parts of two conserved quantities, strangeness and baryon number. It is argued that their correlation and thus also fluctuations are sensitive to conditions prevailing at the anticipated parton-hadron phase boundary. Fluctuations of the $(\mathrm{K}^+ + \mathrm{K}^-)/(\mathrm{p}+\bar{\mathrm{p}})$ and $\mathrm{K}^+/\mathrm{p}$ ratios have been measured for the first time by NA49 in central Pb+Pb collisions at 5 SPS energies between $\sqrt{s_{NN}}$= 6.3 GeV and 17.3 GeV. Both ratios exhibit a change of sign in $\sigma_{\mathrm{dyn}}$, a measure of non-statistical fluctuations, around $\sqrt{s_{NN}}$ = 8 GeV. Below this energy, $\sigma_{\mathrm{dyn}}$ is positive, indicating higher fluctuation compared to a mixed event background sample, while for higher energies, $\sigma_{\mathrm{dyn}}$ is negative, indicating correlated emission of kaons and protons. The results are compared to UrQMD calculations which which give a good description at the higher SPS energies, but fail to reproduce the transition to positive values.Comment: 5 pages, 4 figure

Centrality dependence of proton and antiproton spectra in Pb+Pb collisions at 40A GeV and 158A GeV measured at the CERN SPS

The yields of (anti-)protons were measured by the NA49 Collaboration in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV. Particle identification was obtained in the laboratory momentum range from 5 to 63 GeV/c by the measurement of the energy loss dE/dx in the TPC detector gas. The corresponding rapidity coverage extends 1.6 units from mid-rapidity into the forward hemisphere. Transverse mass spectra, the rapidity dependences of the average transverse mass, and rapidity density distributions were studied as a function of collision centrality. The values of the average transverse mass as well as the midrapidity yields of protons when normalized to the number of wounded nucleons show only modest centrality dependences. In contrast, the shape of the rapidity distribution changes significantly with collision centrality, especially at 40A GeV. The experimental results are compared to calculations of the HSD and UrQMD transport models.Comment: 25 pages, 12 figures, submitted to PR

System-size and centrality dependence of charged kaon and pion production in nucleus-nucleus collisions at 40A GeV and158A GeV beam energy

Measurements of charged pion and kaon production are presented in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV beam energy as well as in semi-central C+C and Si+Si interactions at 40A GeV. Transverse mass spectra, rapidity spectra and total yields are determined as a function of centrality. The system-size and centrality dependence of relative strangeness production in nucleus-nucleus collisions at 40A GeV and 158A GeV beam energy are derived from the data presented here and published data for C+C and Si+Si collisions at 158A GeV beam energy. At both energies a steep increase with centrality is observed for small systems followed by a weak rise or even saturation for higher centralities. This behavior is compared to calculations using transport models (UrQMD and HSD), a percolation model and the core-corona approach.Comment: 32 pages, 14 figures, 4 tables, typo table II correcte

Search for the QCD critical point in nuclear collisions at the CERN SPS

Pion production in nuclear collisions at the SPS is investigated with the aim to search, in a restricted domain of the phase diagram, for power-laws in the behavior of correlations which are compatible with critical QCD. We have analyzed interactions of nuclei of different size (p+p, C+C, Si+Si, Pb+Pb) at 158$A$ GeV adopting, as appropriate observables, scaled factorial moments in a search for intermittent fluctuations in transverse dimensions. The analysis is performed for $\pi^+\pi^-$ pairs with invariant mass very close to the two-pion threshold. In this sector one may capture critical fluctuations of the sigma component in a hadronic medium, even if the $\sigma$-meson has no well defined vacuum state. It turns out that for the Pb+Pb system the proposed analysis technique cannot be applied without entering the invariant mass region with strong Coulomb correlations. As a result the treatment becomes inconclusive in this case. Our results for the other systems indicate the presence of power-law fluctuations in the freeze-out state of Si+Si approaching in size the prediction of critical QCD.Comment: 31 pages, 11 figure

High p_T Spectra of Identified Particles Produced in Pb+Pb Collisions at 158A GeV Beam Energy

Results of the NA49 collaboration on the production of hadrons with large transverse momentum in Pb+Pb collisions at 158A GeV beam energy are presented. A range up to p_T = 4 GeV/c is covered. The nuclear modification factor R_CP is extracted for pions, kaons and protons, and the baryon to meson ratios p/pi+, pbar/pi- and Lambda/K^0_s are studied. All results are compared to other measurements at SPS and RHIC and to theoretical calculations.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 5 pages, 3 figure