Global observables at PHENIX

We present PHENIX recent results on charged particle and transverse energy densities measured at mid-rapidity in Au?Au collisions at $\sqrt {s_{NN} } = 130$ GeV and 200 GeV over a broad range of centralities. The mean transverse energy per charged particle is derived. The first PHENIX measurements at $\sqrt {s_{NN} } = 19.6$ GeV are also presented. A comparison with calculations from various theoretical models is performed.     

Resonances and Correlations in heavy ion collisions

Results of resonance production from RHIC at $\sqrt {s_{NN} } = 200$ GeV and SPS at $\sqrt {s_{NN} } = 17$ GeV are presented and discussed in context with a possible hadronic interaction phase after chemical freeze-out in a heavy ion collision. Momentum spectra and yield may change due to rescattering and regeneration of hadronic decaying resonances. We compare the decays of resonances into leptonic and hadronic channels in order to discuss the impact of a the possible medium modifications on the resonance and their decay products. Microscopic model calculations predicts that high momentum resonances are almost unaffected by the hadronic medium. This raises the idea of using high transverse momentum selection criteria in order to extract resonances created at an early stage of a heavy ion collision.     

K S 0 , Λ and ≡ production at intermediate to high pT from Au+Au collisions at \sqrt {s_{NN} } = 39, 11.5 and 7.7 GeV

We report on the p _T dependence of nuclear modification factors (R _CP) for K _S ⁰ , ??, ?? and the $\bar NK_S^0 $ ratios at mid-rapidity from Au+Au collisions at $\sqrt {s_{NN} } $ = 39, 11.5 and 7.7 GeV. At $\sqrt {s_{NN} } $ = 39 GeV, the R _CP data show a baryon/meson separation at intermediate p _T and a suppression for K _S ⁰ for p _T up to 4.5 GeV/c; the $\bar \Lambda K_S^0 $ shows baryon enhancement in the most central collisions. However, at $\sqrt {s_{NN} } $ = 11.5 and 7.7 GeV, R _CP shows less baryon/meson separation and $\bar NK_S^0 $ shows almost no baryon enhancement. These observations indicate that the matter created in Au+Au collisions at $\sqrt {s_{NN} } $ = 11.5 or 7.7 GeV might be distinct from that created at $\sqrt {s_{NN} } $ = 39 GeV.     

Rules of thumb for theZ line shape

In this paper the theoretical parameters of theZ line shape, such asM _Z andΓ _Z, and the one photon exchange diagram are related to a set of parameters characterizing the experimental line shape. The latter are the peak height σ_max, peak position \(\sqrt {s_{\max } } \) and half peak positions \(\sqrt {s_ \pm } \) . The rules of thumb are accurate within 10 MeV. As a result we obtain approximate formulae which expressM _Z and Γ_Z in the measured \(\sqrt {s_{\max } } \) and \(\sqrt {s_ + } - \sqrt {s_ - } \) .     

Resonance studies at STAR

Preliminary results from measurements of resonances (K ^*0(892), $\overline {K*^0 } (892)$ , Φ(1020), and ρ(770)) and weakly decaying particles (Λ(1116), $\bar \Lambda (1116)$ , and K _S ⁰ (498)) are presented. The measurements are performed at mid-rapidity by the STAR detector in $\sqrt {s_{NN} } = 130$ GeV Au?Au collisions at RHIC. The ratios K ^*0/h?, $\overline {K*^0 } /K$ , and $\bar \Lambda /\Lambda $ are compared to measurements at different energies and colliding systems. Estimates of thermal parameters, such as temperature and baryon chemical potential, are also presented.     

Identified particle production in p+p, d+Au and Au+Au collisions at RHIC

Measurements of identified particle production with the PHENIX experiment at RHIC have reached a mature state, where a multitude of nuclear systems at different colliding energies have been studied. The discovery configurations of $\sqrt {s_{NN} } = 130$ and 200 GeV Au+Au collisions have now been supplemented by additional Au+Au and Cu+Cu configurations at various energies, along with baseline p+p and d+Au runs at $\sqrt {s_{NN} } = 130$ GeV. In this work we present a systematic study of the Cronin effect in d+Au collisions and recent results from p+p collisions. We then proceed to make a critical comparison of pion, kaon and proton production in heavy ion and baseline systems, and discuss the observed nuclear effects on hadron production.     

Elliptic flow measurements from STAR

In these proceedings some of the highlights of the elliptic flow measurements from STAR at $\sqrt {s_{NN} } = 130$ and 200 GeV for Au + Au collisions are presented.     

Resonance production in STAR

The recent results from resonance production in central Au+Au and p+p collisions at $\sqrt {s_{NN} } = 200$ GeV from the STAR experiment at RHIC are presented and discussed.     

Balance functions at RHIC

The balance function is based on the principle that charge is locally conserved when particles are pair produced. Balance functions have been measured for all charged pairs, identified pion pairs, and identified charged kaon pairs in Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV and p+p collisions at $\sqrt {s_{NN} } = 200$ GeV at the Relativistic Heavy Ion Collider using STAR. Balance functions for all charged particles from Au+Au scale smoothly with centrality to the p+p value. Balance functions for charged particles and pions are narrower in central collisions than in peripheral collisions consistent with trends predicted by models incorporating the concept of late hadronization. Balance functions for kaon pairs represent a strangeness balance. Balance functions for kaons are narrower than those for pion pairs and may show less dependence on centrality.     

Matter radii and wave function admixtures in 2n halo nuclei

We analyze longitudinal pion spectra from $\ensuremath \sqrt{s_{NN}}=2$ GeV to $\ensuremath \sqrt{s_{NN}}=20$ GeV within Landau??s hydrodynamical model and the UrQMD hybrid approach. From the measured data on the widths of the pion rapidity spectra, we extract the sound velocity c _s ² in the dense stage of the reactions. It is found that the sound velocity has a local minimum (indicating the softest point in the equation of state, EoS) at $\ensuremath \sqrt{s_{NN}}=4\mbox{--}9$ GeV, an energy range accessible at the Facility for Antiproton and Ion Research (FAIR) as well as the RHIC-Beam Energy Scan (RHIC-BES). This softening of the EoS is compatible with the formation of a QGP at the onset of deconfinement. The extracted sound velocities are then used to calculate an excitation function for the mean transverse mass of pions from the hybrid model. We find that, above $\ensuremath \sqrt{s_{NN}} \approx 10$ GeV, even the lowest c _s ² gives a considerably larger $\ensuremath \langle m_T\rangle$ of pions compared to data.     

Characteristics of charged particle production in relativistic heavy-ion collisions

Inclusive spectra of charged particles at midrapidity in Au+Au collisions at $\sqrt {s_{NN} } = 130$ GeV and 200 GeV were measured with the STAR detector at RHIC. The measured mean transverse momentum 〈p _T 〉 shows a characteristic dependence on charged particle multiplicity and beam energy in Au+Au collisions that is distinctly different from pp, $p\bar p$ and e⁺e^? collisions. A 32%±3%(syst) increase in 〈p _T 〉 from pp to Au+Au collisions was observed at 200 GeV. While the charged multiplicity was found to increase by 19%±5%(syst) from $\sqrt {s_{NN} } = 130$ GeV to 200 GeV, no significant difference in 〈p _T 〉 was found between the two energies. A comparison with model predictions is discussed.     

On AB Bond Percolation on the Square Lattice and AB Site Percolation on Its Line Graph

We prove that AB site percolation occurs on the line graph of the square lattice when $p \in (1 - \sqrt {1 - p_c } ,\sqrt {1 - p_c } )$ , where p _c is the critical probability for site percolation in $\mathbb{Z}^2$ . Also, we prove that AB bond percolation does not occur on $\mathbb{Z}^2$ for p = $\frac{1}{2}$ .     

Open charm production at RHIC: Recent results from STAR

We report recent measurements on the open charm production in d+Au and p+p collisions at $\sqrt {s_{NN} } = 200$ GeV from the STAR detector at RHIC. The two independent measurements — direct open charm hadron (D⁰, D^* etc.) reconstruction and non-photonic single electron spectrum — provide consistent results. The mid-rapidity charm differential cross section per nucleon-nucleon collision from d+Au collisions at RHIC is $d\sigma _{c\bar c}^{NN} /dy = 0.30 \pm 0.04(stat.) \pm 0.09(syst.)$ mb, which is higher than predictions from most of the NLO pQCD calculations. Implications for charmonium production in Au+Au collisions will also be discussed.     

Highlights from the STAR experiment at RHIC

Ultra-relativistic heavy-ion collisions produced at RHIC differ significantly from a superposition of proton-proton collisions. Evidence of collective expansion has been gathered. The yield of high transverse momentum particles has been found to be lower in head-on Au?Au collisions than is expected by scaling p-p collisions. Di-jet processes, which are frequent in p-p collisions, are almost absent in head-on Au?Au collisions. The current results from RHIC indicate that Au?Au collisions at $\sqrt {S_{NN} } = 130$ GeV and $\sqrt {S_{NN} } = 200$ GeV yield an expanding system that is opaque to high momentum partons.     

Singular $$ \mathcal{R}$$ -Matrices and Drinfeld's Comultiplication

We compute the $\mathcal{R}$ -matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for ${\text{U}}_q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ . This $\mathcal{R}$ -matrix contains terms proportional to the δ-function. We construct the algebra $A\left( \mathcal{R} \right)$ generated by the elements of the matrices L^±(z) with relations determined by $\mathcal{R}$ . In the category of highest-weight representations, there is a Hopf algebra isomorphism between $A\left( \mathcal{R} \right)$ and an extension $\overline {\text{U}} _q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ of Drinfeld's algebra.     

Probing longitudinal dynamics at RHIC

Particle production of charged hadrons in Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV bas been studied as a function of rapidity by the BRAHMS Collaboration at RHIC. Selected recent results are presented with emphasis on longitudinal dynamics of particle production. The rapidity dependence of particle production imposes more stringent constraints on theoretical models describing dynamics of nuclear matter created by high-energy heavy ion collisions.     

Recent results from PHOBOS

The PHOBOS Collaboration has measured charged particles emitted over the range ?5.4<η<5.4 for Au+Au collisions at energies of $\sqrt {s_{NN} } = 19.6$ , 62.4, 130 and 200 GeV. In this contribution I will present recent results on the pseudorapidity distributions, total charged-particle production, and collective flow of particles obtained from these measurements.     

Stopping in relativistic heavy ion reactions_— from SIS to RHIC

The status of stopping in heavy ion reactions is reviewed by comparing available data in pp, pA and AA systems over the energy regime $\sqrt {s_{NN} } \approx 2.5 - 130$ GeV. The data consist of average rapidity losses, anti-proton over proton ratios, and net-baryon values at mid-rapidity. The overall features of nuclear stopping are reasonably well described by simple extrapolations of pp and pA collisions to AA.     

Probing the QCD phase boundary with elliptic flow in relativistic heavy ion collisions at STAR

We present measurement of elliptic flow, v ₂, for charged and identified particles at midrapidity in Au+Au collisions at $\sqrt {s_{NN} } $ = 7.7?C39 GeV. We compare the inclusive charged hadron v ₂ to those from transport model calculations, such as the UrQMD model, AMPT default model and AMPT string-melting model. We discuss the energy dependence of the difference in v ₂ between particles and anti-particles. The v ₂ of ? meson is observed to be systematically lower than other particles in Au+Au collisions at $\sqrt {s_{NN} } $ = 11.5 GeV.     

Analysis of multi-strange hyperon production in p+p and Au+Au collisions at RHIC

The analysis of multi-strange hyperon production (Ξ^?, Ω^? and their anti-particles) at mid-rapidity is part of the program covered by the STAR experiment at RHIC. We report on preliminary results in Au+Au and p+p collisions at $\sqrt {s_{NN} } = 130$ and 200 GeV. Measurements of particle ratios are presented and production yields and spectra are discussed for both collision systems.