In-Medium Kaon Potential and Nuclear Equation of State Measured in Nucleus–Nucleus Collisions

The kaon production in heavy ion collisions at intermediate energies provides a sensitive probe to study the in-medium properties and nuclear equation of state of hadrons. Properties of kaons in dense hadronic matter are important for a better understanding of both, the possible restoration of chiral symmetry in dense hadronic matter and the properties of nuclear matter at high densities. We investigated the in-medium kaon potential and nuclear equation of state by transverse mass spectra of K ⁺ mesons in heavy ion collisions. We use quantum molecular dynamics (QMD) models based on covariant kaon dynamics to simulate ${_{28}^{58}Ni +_{28}^{58}Ni}$ collisions at 1.93 A GeV, to analyze the transverse mass spectra of K ⁺. Calculated results with a repulsive in-medium K ⁺N potential can reasonably describe the features of KaoS data. They also shown that the transverse mass spectrum of K ⁺ mesons is a sensitive observable to probe the kaon in-medium potential in dense nuclear matter.     

The effect of Lorentz-like force on collective flows of <Emphasis Type="Italic">K</Emphasis><Superscript>+</Superscript> in Au+Au collisions at 1.5 GeV/nucleon

Producing kaon mesons in heavy-ion collisions at beam energies below their threshold energy is an important way to investigate the properties of dense nuclear matter. In this study, based on the newly updated version of the ultrarelativistic quantum molecular dynamics model, we introduce the kaon-nucleon (KN) potential, including both the scalar and vector (also dubbed Lorentz-like) aspects. We revisit the influence of the KN potential on the collective flow of K⁺ mesons produced in Au+Au collisions at E_lab = 1.5 GeV/nucleon and find that the contribution of the newly included Lorentz-like force is very important, particulary for describing the directed flow of K⁺. Finally, the corresponding KaoS data of both directed and elliptic flows can be simultaneously reproduced well.     

Strange mesons in dense nuclear matter

Experimental data on the production of kaons and antikaons in heavy-ion collisions at relativistic energies are presented and discussed with respect to in-medium effects. The K ^?/K⁺ ratios measured in nucleus-nucleus collisions are 1–2 orders of magnitude larger than in proton-proton collisions. The azimuthal angle distributions of K ⁺ mesons indicate a repulsive kaon-nucleon potential. Microscopic transport calculations consistently explain both the yields and the emission patterns of kaons and antikaons when assuming that their properties are modified in dense nuclear matter. The K ⁺ production excitation functions measured in light and heavy collision systems provide evidence for a soft nuclear equation-of-state.     

Antikaon production in proton-nucleus reactions and the K− properties in nuclear matter

We calculate the momentum-dependent potentials for K⁺ and K⁻ mesons in a dispersion approach at nuclear density ϱ₀ using the information from the vacuum K⁺N and K⁻N scattering amplitudes, however, leaving out the resonance contributions for the in-medium analysis. Whereas the K⁺ potential is found to be repulsive (≈ + 25 MeV) and to show only a moderate momentum dependence, the K⁻ self-energy at normal nuclear matter density turns out to be ≈ − 140 ± 25 MeV at zero momentum roughly in line with K⁻ atomic data, however, decreases rapidly in magnitude for higher momenta. The antikaon production in p + A reactions is calculated within a coupled channel transport approach and compared to the data at KEK including different assumptions for the antikaon potentials. Furthermore, detailed predictions are made for p+¹²C and p+²⁰⁷Pb reactions at 2.5 GeV in order to determine the momentum-dependent antikaon potential experimentally.     

Kaon production in heavy ion collisions — Which observable is best suited to observe in-medium potentials?

A review of kaon production in heavy ion collisions at incident energies of 1–2 A GeV is presented. Two conflicting interpretations are discussed: Microscopic transport models can describe most of the observed features when in-medium modifications of kaons are taken into account. In contrast, statistical models in a canonical formulation are able to describe the particle yields only by using masses of free hadrons. Different inverse slope parameters and unequal azimuthal distributions are observed for K⁺ and K^- mesons. Interpretations are discussed.     

Kaon production in hadronic matter

Subthreshold kaon production has been studied in symmetric nucleus-nucleus collisions as a function of the nucleus mass, beam energy and centrality. In Au+Au collsions at 1 AGeV theK ⁺ multiplicity increases more than linearly with increasing number of participating nucleons. Transport calculations have to assume a soft equation of state in order to reproduce the data. The in-mediumK ^? cross section measured in Ni+Ni collisions is enhanced by about a factor of 7 as compared to the free cross section when using theK ⁺ cross section at equivalent beam energies as a normalization.     

Partonic effect on anisotropic flows of Ω baryon for Au+Au at 62.4 and 200 GeV/c

The elliptic flow v₂ and the fourth order anisotropic flow v₄ of (Ω+Ω̄) have been studied in the framework a parton–hadronic transport model, namely a multi-phase transport (AMPT) model, for ¹⁹⁷Au+¹⁹⁷Au collisions at = 200 GeV and 62.4 GeV. The transverse momentum (p_T) and the transverse kinetic energy (m_T-m₀) dependence of v₂ and v₄ are presented. The calculation in the AMPT model seems consistent with the STAR data. The results show that the v₂ of (Ω+Ω̄) in 200 GeV obeys the constituent quark number scaling that has been observed for other mesons and baryons. Comparison of (Ω+Ω̄) elliptic flow v₂ in the default version of AMPT, the melting version of AMPT and the RQMD model calculation, shows that the parton cascade process is important to reproduce the sizeable v₂, and the string melting AMPT model preferably reproduces (Ω+Ω̄) elliptic flow v₂ in ¹⁹⁷Au+¹⁹⁷Au collisions at = 200 GeV. The v₂ of (Ω+Ω̄) in the 62.4 and 200 GeV collisions seem similar, and the p_T dependence of (Ω+Ω̄) baryons’ v₄ in 62.4 GeV and 200 GeV looks also similar in the string melting AMPT model, which indicates that a similar partonic matter phase has been reached in both energies.     

Di-lepton production in heavy-ion collisions and the QCD phase diagram

We reproduce di-electron spectra in the region of 0 < m _e+e < 4 GeV in both minimum bias and central Au+Au collisions at $\sqrt {s_{NN} } $ = 200 GeV measured by the STAR experiment. A cocktail simulation, incorporating STAR acceptance and detector responses, is able to describe the ??enhancement?? of the low mass region by including an in-medium modification of vector mesons and a thermal di-lepton calculation. We also predict the di-lepton mass spectra in RHIC lower energies via an extrapolation method. The evolution of Di-lepton mass spectra, effective temperature, and possible medium modifications versus colliding energies are studied to explore the QCD phase diagram.     

Subthreshold K+ production in proton-nucleus collisions

Double differential K⁺cross sections have been measured in p+C collisions at 1.2, 1.5 and 2.5 GeV beam energy and in p+Pb collisions at 1.2 and 1.5 GeV. The K⁺ spectrum taken at 2.5 GeV can be reproduced quantitatively by a model calculation which takes into account first chance proton-nucleon collisions and internal momentum with energy distribution of nucleons according to the spectral function. At 1.2 and 1.5 GeV beam energy the K⁺ data excess significantly the model predictions for first chance collisions. When taking secondary processes into account the results of the calculations are in much better agreement with the data.     

Elliptic flow of ν ands <Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> mesons in heavy-ion collisions at 2 <Emphasis Type="Italic">A</Emphasis> GeVmesons in heavy-ion collisions at 2 <Emphasis Type="Italic">A</Emphasis> GeV

Elliptic flow of ν and π ⁰ mesons emitted at midrapidity are studied in collisions of 1.9 A GeV ⁵⁸Ni+⁵⁸Ni and 2 A GeV ⁴⁰Ca+^natCa. The observed anisotropy corresponds to a negative elliptic flow signal for ν mesons, indicating a preferred emission perpendicular to the reaction plane. In contrast, only small azimuthal anisotropies are observed for π ⁰ mesons. This may indicate that ν mesons freeze out earlier from the central interaction region than pions.     

Subthreshold K+ production in proton-nucleus collisions

Double differential K⁺ cross sections have been measured in p+C collisions at 1.2, 1.5 and 2.5 GeV beam energy and in p+Pb collisions at 1.2 and 1.5 GeV. The K⁺ spectrum taken at 2.5 GeV can be reproduced quantitatively by a model calculation which takes into account first chance proton-nucleon collisions and internal momentum with energy distribution of nucleons according to the spectral function. At 1.2 and 1.5 GeV beam energy the K⁺ data excess significantly the model predictions for first chance collisions. When taking secondary processes into account the results of the calculations are in much better agreement with the data.     

Deep processes in nuclei and in-medium dressing of the nucleons and mesons

K⁺ scattering and quasielastic electron scattering from nuclei are expected to provide information about the nucleons and mesons in the inner regions of nuclei. The K⁺- nucleus cross sections and the quasielastic electron-nucleus response functions have been calculated taking into account the same in-medium dressing of the nucleons and the same coupling of the σ and ω mesons to the polarization of nuclear matter. We obtain a good agreement with experimental data for the two processes.     

Energy and system size dependence of charged hadron transverse momentum spectra from Cu+Cu and Au+Au collisions at √S NN =62.4 and 200 GeV

The PHOBOS Collaboration has measured transverse momentum distributions of charged hadrons produced in Cu+Cu collisions at √s _NN =200 and 62.4 GeV. The nuclear modification factor R _AA ^N _part is calculated relative to p+p data at both collision energies as a function of collision centrality. For the same number of participating nucleons, R _AA ^N _part is essentially the same in both systems over the full range of p Tthat is measured. In addition, we observe that within experimental uncertainties, the ratio of 200 GeV to 62.4 GeV Cu+Cu yields has only a moderate centrality dependence and is consistent with the value previously measured in Au+Au collisions for a broad range of p _T.     

What can we learn from high-p<Subscript>T</Subscript> correlations of neutral strange baryons and mesons at RHIC?

We present results on two-particle azimuthal correlations of neutral strange baryons (Λ, Λ̄) and mesons (K_S ⁰) for p_T=2–6 GeV/c associated with non-identified charged particles in d+Au and Au+Au collisions at  =200 GeV measured by the STAR experiment. We investigate in detail the associated yield of charged particles as a function centrality of the collision and transverse momentum of trigger and associated particles to look for possible flavor, baryon/meson and particle/anti-particle differences. We compare our results to the proton and pion triggered correlations as well as to a fragmentation and recombination model. PACS 25.75.-q; 25.75.Gz     

K + production inp-nucleus collisions

We present a non-perturbative dynamical study ofK ⁺ meson production in proton-nucleus collisions from 1.2 to 2.5 GeV bombarding energy. The dynamical evolution of the proton-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type evolving phase-space distribution functions for nucleons, δ’s,N(1440)’s,N(1535)’s, poins and η’s with their isospin degrees of freedom. We incorporate all known sources forK ⁺ production and study their momentum and angular distributions, and the excitation function. We show that at lower energies (E _b<1.5 GeV)NΔ andNN* channels dominate the kaon yield for light systems, and the πN channel for heavy systems. At higher bombarding energies the directNN channel accounts for almost the whole cross-section.     

Production of charged pions, kaons and antikaons in relativistic C + C and C + Au collisions

Production cross-sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(π⁺)/<A _part> is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K⁺ multiplicities per participating nucleon M(K⁺)/ <A _part> are independent of the target size at 1 AGeV and at 1.8 AGeV. The K^- multiplicity per participating nucleon M(K^-)/ <A _part> is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K^-/K⁺ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K-mesons are neglected. Received: 10 December 1999 / Accepted: 14 November 2000     

Event-by-event net charge fluctuations

We present analyses of event-by-event dynamical net charge fluctuations measured in 130 and 200 GeV Au+Au collisions with the STAR detector. The dynamical net charge fluctuations are evaluated using the ν _+-,dyn observable. Dynamical fluctuations measured in Au+Au collisions at 130 and 200 GeV are finite, and exceed charge conservation limits. They deviate from a perfect 1/N scaling and provide an indication that the collision dynamics varies with collision centrality.     

Investigation of the high-p<Subscript>T</Subscript> strange baryon anomalies at RHIC

Results from RHIC have shown that there is an enhanced baryon/meson ratio in the intermediate transverse momentum range (2<p_T<6 GeV/c) in Au+Au collisions at both  =130 and 200 GeV. This was initially demonstrated by measurements of the p̄/π^- ratio which was then extended in p_T by the Λ/K⁰ _S ratio. The data were successfully described by models utilising different hadronization mechanisms: those having recombination of quarks and others having an interplay between flow, jet quenching and incorporating baryon junction loops. The strange particle data from the first Au+Au run at  =200 GeV gave tantalising hints that the observed enhancement of baryons compared to mesons was diminished by a p_T of 6 GeV/c, but a lack of statistics in this range made a definitive statement impossible. Here we present an extended analysis of identified strange baryons and mesons in Au+Au collisions at  =200 GeV using data obtained by the STAR experiment from the 2004 running period. The increase in statistics extends the measurement of Λ hyperons out to at least 7 GeV/c and K⁰ _S mesons out to 9 GeV/c. This data allows us to place limits on the range where in-vacuum fragmentation functions are applicable and the effect of baryon dominance is reduced. We also discuss the prospects for making these measurements using multiply-strange baryons and mesons (Ω and ϕ).     

Pion-production in heavy-ion collisions at SIS energies

We investigate the production of pions in heavyion collisions in the energy range of 1–2 GeV/A. The dynamics of the nucleus-nucleus collisions is described by a set of coupled transport equations of the Boltzmann-Uehling-Uhlenbeck type for baryons and mesons. Besides theN(938) and theΔ(1232) we also take into account nucleon resonances up to masses of 1.95 GeV/c² as well asπ-,η- andρ-mesons. We study in detail the influence of the higher baryonic resonances and the 2π-production channels (NN→NNππ) on the pion spectra in comparison toπ ^? data fromAr+KCl collisions at 1.8 GeV/A andπ ⁰-data forAu+Au at 1.0GeV/A. We, furthermore, present a detailed comparison of differential pion angular distributions with the BEVALAC data forAr+KCl at 1.8 GeV/A. The general agreement obtained indicates that the overall reaction dynamics is well described by our novel transport approach.     

Event-by-event hadron ratio fluctuations from Au+Au collisions at RHIC-STAR

We present measurements of event-by-event fluctuations on hadron multiplicity ratios (K/??, p/??, K/p) in Au+Au collisions at $\sqrt {s_{NN} } $ and 200 GeV using the STAR detector at RHIC. The magnitude of dynamical fluctuations ?? _dyn for p/?? and K/p ratios change smoothly from a large negative value at 7.7 GeV to a smaller negative value at 200 GeV while that for the K/?? ratios exhibits no significant beam energy dependence. The dynamical fluctuations related to pair production ?? _dyn ^pair dyn for the p/K, K/p, K ^?/K ⁺ and p/p ratios at 200 GeV all exhibit a maximum at the mid-central collisions and decrease at the most peripheral and most central collisions.