Thermal Pions

I discuss the absorption and dispersion of pions in hot matter. A two-loop calculation in the framework of chiral perturbation theory is presented and its result is compactly written in terms of the two- and three-particle forward $\pi \pi$ scattering amplitudes. At modest temperatures, $T \le 100$ MeV, the change in the pion mass is small and its dispersion law closely resembles the free space one. At these temperatures, all quantities of interest are given to a good degree of accuracy by the first term in the virial expansion which is linear in the density. (BUTP-93/16, uses espcrc1.sty from North-Holland Publishing)Comment: 7 pp, LaTeX, uses espcrc1.sty from North-Holland Publishing, BUTP-93/1

ANALISIS PENGGUNAAN KANDOUSHI NO KANDOU DALAM DRAMA BOKU, UNMEI NO HITO DESU

Skripsi ini menganalisis mengenai interjeksi impresi atau kandoushi no kandou dalam bahasa Jepang. Penelitian ini merupakan penelitian kualitatif dengan analisis deskriptif. Tujuan penelitian ini yaitu untuk mengetahui : 1). Variasi kandoushi no kandou yang terdapat dalam drama jepang yang berjudul Boku, Unmei no Hito desu, 2). Fungsi serta penggunaan kandoushi no kandou yang terdapat dalam drama Jepang yang berjudul Boku, Unmei no Hito desu. Sumber penelitian ini adalah drama Jepang yang berjudul Boku, Unmei no Hito desu. Hasil penelitian menunjukan bahwa terdapat dua puluh lima variasi kandoushi no kandou yang ditemukan dalam drama Jepang Boku, Unmei no Hito desu. Masing-masing dari kandoushi no kandou tersebut memiliki fungsi serta penggunaannya yang berbeda dikarenakan konteks situasi tutur yang melatar belakanginya juga berbeda. This thesis analyzes the impression interjection or kandoushi no kandou in Japanese. This research is a qualitative research with descriptive analysis. The purpose of this research is to find out: 1). Variations on kandoushi no kandou found in Japanese drama titled Boku, Unmei no Hito desu, 2). The function and usage of kandoushi no kandou is contained in a Japanese drama entitled Boku, Unmei no Hito desu. The source of this research is a Japanese drama entitled Boku, Unmei no Hito desu. The results showed that there were twenty-five variations of the Kandoushi no kandou found in the Japanese drama Boku, Unmei no Hito desu. Each of the kandoushi no kandou has different functions and uses because the context of the speech situation underlying them is also different

Soft transverse expansion in Pb(158 AGeV) on Pb collisions: preequilibrium motion or 1st order phase transition?

Transverse expansion of centrally produced matter in Pb on Pb collisions at beam energies around 158 AGeV appears to be rather `soft'. Two possible reasons -- an extended preequilibrium stage and a first order phase transition from a quark-gluon-plasma into hadronic matter -- are discussed. The softening of transverse expansion caused by preequilibrium dynamics is estimated with the aid of the transport model RQMD which does not contain a first order phase transition. It is found that the anisotropy of transverse flow in non-central reactions is very different in the preequilibrium and hydrodynamic scenarios even if the latter are based on a strong 1st order transition.Comment: 14 pages LaTeX including 3 postscript figure

Matter-induced modification of resonances at RHIC freezeout

We discuss the physical effects causing a modification of resonance masses, widths and even shapes in a dilute hadronic gas at late stages of heavy ion collisions. We quantify the conditions at which resonances are produced at RHIC, and found that it happens at $T\approx 120 MeV$. Although in the pp case the ``kinematic'' effects like thermal weighting of the states is sufficient, in AA we see a clear effect of dynamical interaction with matter, both due to a variety of s-channel resonances and due to t-channel scalar exchanges. The particular quantity we focus mostly on is the $\rho$ meson mass, for which these dynamical effects lead to about -50 MeV shift, on top of about -20 MeV of a thermal effect: both agree well with preliminary data from STAR experiment at RHIC. We also predict a complete change of shape of $f_0(600)$ resonance, even by thermal effects alone.Comment: A comment about width modification added, some misspelling correcte

Equation of State, Flow, Fluctuations and J/ψJ/\psi suppression

Radial flow observed at AGS/SPS energies is very strong, with collective velocities of matter reaching about 0.5c for central collisions of the heaviest ions. The lattice-based Equation of State (EOS) is however rather soft, due to the QCD phase transition. We show that both statements are consistent only if proper kinetic-based treatment of the freeze-out is made. In fact chemical and thermal freeze-out happen at quite different conditions, especially at SPS. Event-by-event fluctuations can shed new light on this problem. We also propose new model of "anomalous" $J/\psi$ suppression found for PbPb collisions, related it to prolonged lifetime of dense matter due the "softest point" of the EOS.Comment: Plenary Talk at Quark Matter 97, Tsukuba, Dec.199

Pion dispersion relation at finite density and temperature

We study the behavior of the pion dispersion relation in a pion medium at finite density and temperature. We introduce a pion chemical potential to describe the finite pion number density and argue that such description is valid during the hadronic phase of a relativistic heavy-ion collision between chemical and thermal freeze-out. We make use of an effective Lagrangian that explicitly respects chiral symmetry through the enforcement of the chiral Ward identities. The pion dispersion relation is computed through the computation of the pion self-energy in a non-perturbative fashion by giving an approximate solution to the Schwinger-Dyson equation for this self-energy. The dispersion relation is described in terms of a density and temperature dependent mass and an index of refraction which is also temperature, density as well as momentum dependent. The index of refraction is larger than unity for all values of the momentum for finite $\mu$ and $T$. We conclude by exploring some of the possible consequences for the propagation of pions through the boundary between the medium and vacuum.Comment: 7 pages, 5 figures, 3 new references, published versio

Flow effects on the freeze-out phase-space density in heavy ion collisions

The strong longitudinal expansion of the reaction zone formed in relativistic heavy-ion collisions is found to significantly reduce the spatially averaged pion phase-space density, compared to naive estimates based on thermal distributions. This has important implications for data interpretation and leads to larger values for the extracted pion chemical potential at kinetic freeze-out.Comment: 5 pages, 3 figures included via epsfig, added discussion of different transverse density profiles, 1 new figur

Temperatures and Non-ideal Expansion in Ultrarelativistic Nucleus-Nucleus Collisions

The hadronic phase space distributions calculated with the transport model RQMD for central S(200 AGeV) on S and Pb(160AGeV) on Pb collisions are analyzed to study the deviations from ideal hydrodynamical evolution. After the preequilibrium stage, which lasts for approximately 4 (2) fm/c in Pb+Pb (S+S) the source stays in approximate kinetic equilibrium for about 2 fm/c at a temperature close to 140 MeV. The interactions of mesons last until around 14 (5) fm/c during which time strong transverse flow is generated. The interactions in the hadronic resonance gas are not sufficiently strong to maintain ideal fluid expansion. While pions acquire average transverse fluid velocities around 0.47-0.58 c, heavier particles like protons and kaons cannot keep up with the pionic fluid, since their average velocities are smaller by about 20 to 30 \%. Although kinetic equilibrium breaks down in the final dilute stage of $AA$ collisions, the system resembles a thermal system at a temperature of 130 MeV, if the free streaming of hadrons after freeze-out is suppressed. This freeze-out temperature is consistent with estimates based on mean free paths and expansion rates in a thermal fireball but lower than values derived from fits to measured particle ratios and transverse momentum spectra. The processes in RQMD to which the differences can be attributed to are the non-ideal expansion of the hadronic matter and the absence of chemical equilibrium at freeze-out.Comment: 12 pages + 3 postscript figures (uuencoded and included

Strangeness in ultrarelativistic nucleus-nucleus collisions

I discuss strangeness production in nucleus-nucleus reactions at ultrarelativistic energies (up to 200 AGeV). In these reactions matter may be created with densities and temperatures in the transition region between quark-gluon plasma (QGP) and hadron gas. Strange anti-baryon enhancement at 200 AGeV and probably even more so at 10 AGeV signals importance of interactions beyond hadron gas dynamics. The systematics of strangeness production indicates that energy and baryon density are key variables while the size of the production volume plays no visible role. Analysis of strangeness appears useful to explore thermalization, flow and the post-equilibrium stage in ultrarelativistic nucleus-nucleus collisions.Comment: 13 pages LaTeX including 6 postscript figures; needs style files espcrc1,floatfig,epsfig. Invited talk presented at 6th International Conference on Nucleus-Nucleus Collisions at Gatlinburg, June 2-6, 1997. To be published in Proceedings in Nuclear Physics

Elliptical flow -- a signature for early pressure in ultrarelativistic nucleus-nucleus collisions

Elliptical energy flow patterns in non-central Au(11.7AGeV) on Au reactions have been studied employing the RQMD model. The strength of these azimuthal asymmetries is calculated comparing the results in two different modes of RQMD (mean field and cascade). It is found that the elliptical flow which is readily observable with current experimental detectors may help to distinguish different reasonable expansion scenarios for baryon-dense matter. The final asymmetries are very sensitive to the pressure at maximum compression, because they involve a partial cancelation between early squeeze-out and subsequent flow in the reaction plane. This cancelation can be expected to occur in a broad energy region covered by the current heavy ion fixed-target programs at BNL and at CERN.Comment: 14 pages LaTeX including 3 postscript figure