Dielectron measurements during heavy ion collisions at \sqrt {s_{NN} } = 200 GeV in the PHENIX experiment at RIHC

The production of dielectron pairs is measured in PHENIX experiment during p + p, d + Au, Cu + Cu, and Au + Au collisions at $\sqrt {s_{NN} }$ = 200 GeV. In the mass region between φ and J/ψ mesons, the yield is consistent with expectations from correlated production. In the mass region below φ mesons, the p + p and d+ Au spectra are well described by known contributions from light meson decays. In contrast, the Au + Au minimum bias spectrum in this region is enhanced by a factor of 4.7, concentrated at low p _T < 1.5 GeV/s and rapidly rising with centrality. Existing theoretical models cannot describe the observed enhancement.     

Hadron production at forward and backward rapidities in \sqrt {s_{NN} } = 200 GeV d+Au collisions

Understanding normal nuclear medium effects present in heavy ion collisions is essential for understanding the following dynamics of the high density matter produced in the collision. Asymmetric collisions, such as deuteron + gold, provide a key tool for studying these effects since particles produced in the forward and backward directions may be subject to different phenomena. Particle production has been studied in d+Au collisions for various kinematic regions at the RHIC facility. PHENIX has measured charged hadron production as a function of pT for different centrality classes using the PHENIX muon spectrometers for d+Au collisions at $\sqrt {s_{NN} } = 200$ GeV. The PHENIX muon spectrometers have coverage in both forward and backward directions in the rapidity range 1.2 |η| < 2.4. The R _cp measurement, the ratio of central to peripheral production, is presented and discussed. Comparisons are also made with some relevant theoretical calculations.     

Dile pton production in p+ p,Cu+Cu and Au+Au collisions at $\sqrt{s} = 200$ GeV

We study dilepton production in proton–proton, Cu+Cu as well as in Au+Au collisions at the center-of-mass energy \(\sqrt{s} =200\) GeV per participating nucleon pair within an extended statistical hadronization model. In extension to earlier studies we incorporate transport calculations for an estimate of uncorrelated e ⁺ e ^? -pairs from semileptonic D meson decays. While the invariant mass spectrum of dielectrons is well understood in the p+p collisions, severe discrepancies among different model scenarios based on hadronic degrees of freedom and recent data from the PHENIX Collaboration are found in heavy-ion collisions in the low-mass region from 0.15 to 0.6 GeV as well as in the intermediate mass regime from 1.1 to 3 GeV when employing the standard dilepton sources. We investigate, furthermore, the background from correlated dileptons that are not emitted as a pair from a parent hadron but emerge from semileptonic decays of two correlated daughter hadrons. Our calculations suggest a sizeable contribution of such sources in central heavy-ion collisions in the low-mass region. However, even the upper limits of our calculations are found to be far below the dilepton mass spectra of the PHENIX Collaboration.     

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.     

Antiproton and charged kaon production in \sqrt {s_{NN} } = 130 GeV Au+Au collisions at RHICGeV Au+Au collisions at RHIC

Preliminary results on antiproton and charged kaon spectra and the net-proton number at mid-rapidity are reported for Au+Au collisions at $\sqrt {s_{NN} } = 130$ GeV as measured by the STAR experiment at RHIC. Inverse slope parameters of the transverse mass distributions increase with the collision centrality, consistent with a strong radial flow. The antiproton and charged kaon extrapolated yields, normalized to the uncorrected negatively charged hadron yield, increase with the collision centrality. A finite but small number of net-baryons is found to be present at mid-rapidity.     

High p T identified particles in PHENIX: Data vs. theory

Two of the most interesting experimental results of heavy-ion reactions at RHIC collider energies are in the hard scattering sector where central Au+Au data show a very different behaviour compared to p+p and peripheral Au+Au collisions. The so-called “high p _T π ⁰ suppression” and the “anomalous” baryon/meson ratio observed by PHENIX in central Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV are reviewed and compared to various theoretical calculations based on different strongly interacting medium scenarios.     

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.     

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.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.     

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.     

Direct photon measurement at RHIC-PHENIX

Results on direct photon measurements from the PHENIX experiment at RHIC are presented. The direct photon yields for P _T >6GeV/c as a function of centrality in Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV are found to be consistent with NLO pQCD calculation scaled by the number of binary collisions. The results suggest that the photons observed are emitted from the initial stage of hard scattering. Comparisons with several theoretical calculations are also presented.     

Centrality dependence of freeze-out parameters from Au+Au collisions at \sqrt {s_{NN} } = 7.7, 11.5 and 39 GeV

The RHIC beam energy scan program in its first phase collected data for Au+Au collisions at beam energies of 7.7, 11.5 and 39 GeV. The event statistics collected at these lower energies allow us to study the centrality dependence of various observables in detail, and compare to fixed-target experiments at SPS for similar beam energies. The chemical and kinetic freeze-out parameters can be extracted from the experimentally measured yields of identified hadrons within the framework of thermodynamical models. These then provide information about the system at the stages of the expansion where inelastic and elastic collisions of the constituents cease. We present the centrality dependence of freeze-out parameters for Au+Au collisions at midrapidity for $\sqrt {s_{NN} } $ = 7.7, 11.5, and 39 GeV from the STAR experiment. The chemical freeze-out conditions are obtained by comparing the measured particle ratios (involving ??, K, p, and p) to those from the statistical thermal model calculations. The kinetic freeze-out conditions are extracted at these energies by simultaneously fitting the invariant yields of identified hadrons (??, K, and p) using Blast Wave model calculations.     

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.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Photonic decays involving the2^{ + + } \left( {\bar bb} \right): Partial widths and jets from tensor meson dominance

Tensor meson dominance combined with vector meson dominance, QCD-potentials and the experimental leptonic widths of Γ and Γ′ predicts $$\Gamma _{\Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right)} = 2.8keV$$ and $$\Gamma _{2^{ + + } \left( {\bar bb} \right) \to \gamma \Upsilon \left( {9.46} \right)} = 134keV.$$ The angular distributions of the γ and the jetsj resulting from the decays $$e^ + e^ - \to \Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right) \to \gamma gg \to \gamma jj$$ and $$e^ + e^ - \to \Upsilon '\left( {10.01} \right) \to \gamma 2^{ + + } \left( {\bar bb} \right) \to \gamma \bar qq \to \gamma jj$$ with massless vector gluonsg, (coupled gauge invariantly) and quarksq are uniquely determined in TMD. The result for the first process agrees with that of perturbative QCD. No perturbative QCD-prediction for the latter is known.     

Multi-strange baryon elliptic flow in Pb-Pb collisions at \sqrt {s_{NN} } = 2.76 TeV measured with the ALICE detector

We present the results on elliptic flow with multi-strange baryons produced in Pb-Pb collisions at $\sqrt {s_{NN} } $ = 2.76 TeV. The analysis is performed with the ALICE detector at LHC. Multi-strange baryons are reconstructed via their decay topologies and the v ₂ measurements are analyzed with the two-particle scalar product method. The p _T differential v ₂ values are compared to the viscous hydrodynamical (VISH2+1) model calculation and to the STAR measurements in Au-Au collisions at $\sqrt {s_{NN} } $ = 200 GeV. We found that the model describes ?? and ??v ₂ measurements within uncertainties. The differential v ₂ of ?? and ?? is similar to the STAR measurements at 200 GeV in Au-Au collisions.     

Contribution of vector resonances to the \bar{B}_{d}^{0}\to\bar {K}^{*0}\mu^{+}\mu^{-} decay

The fully differential angular distribution for the rare flavor-changing neutral current decay $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) \mu^{+}\mu^{-} $ is studied. The emphasis is placed on accurate treatment of the contribution from the processes $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) V $ with intermediate vector resonances V=??(770),??(782),?(1020),J/??,??(2S),?? decaying into the ?? ⁺ ?? ^? pair. The dilepton invariant-mass dependence of the branching ratio, longitudinal polarization fraction f _L of the $\bar{K}^{*0}$ meson, and forward?Cbackward asymmetry A _FB is calculated and compared with data from Belle, CDF and LHCb. It is shown that inclusion of the resonance contribution may considerably modify the branching ratio, calculated in the SM without resonances, even in the invariant-mass region far from the so-called charmonia cuts applied in the experimental analyses. This conclusion crucially depends on values of the unknown phases of the B ⁰??K ^?0 J/?? and B ⁰??K ^?0 ??(2S) decay amplitudes with zero helicity.     

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.     

Charged hadron suppression in Au+Au collisions at high p T from STAR

We report high statistics measurements of inclusive charged hadron production in Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV and 130 GeV. A large, approximately constant hadron suppression is observed in central Au+Au collisions for 5 ‖p _T ‖ 12 GeV/c. The collision energy dependence of the yields and the centrality and p _T dependence of the suppression provide stringent constraints on theoretical models of suppression. Models incorporating initial-state gluon saturation or partonic energy loss in dense matter are largely consistent with observations. The p _T -dependent suppression expected from models incorporating jet attenuation in cold nuclear matter or absorption of fragmentation hadrons is not observed.     

Z 0 boson decays to B^{(*)}_{c} meson and its uncertainties

The planned new e ⁺ e ^? collider with high luminosity shall provide another useful platform to study the properties of the doubly heavy B _c meson in addition to the hadronic colliders as LHC and TEVATRON. In the ‘New Trace Amplitude Approach’, we calculate the production of the spin-singlet B _c and the spin-triplet $B^{*}_{c}$ mesons through the Z ⁰ boson decays, where uncertainties for the production are also discussed. Our results show $\varGamma_{(^{1}S_{0})}=81.4^{+102.1}_{-40.5}$  KeV and $\varGamma_{(^{3}S_{1})}=116.4^{+163.9}_{-62.8}$  KeV, where the errors are caused by varying m _b and m _c within their reasonable regions.