Dear All, I attached the most recent version of my proceedings (v1.6). It contains comments that I get from Zbigniew, Flemming and Radek. Still one plot is missing (I should get it from Truls). Please, read it and comment. Thanks, Pawel. -- ---------------------------------------------------------------------- | Pawel Staszel | | Jagiellonian University | | Institute of Physics email: ufstasze@if.uj.edu.pl | | Reymonta 4 phone: (+48) 12 663 5712 | | Krakow 30059 FAX: (+48) 12 633 7086 | | Poland | ---------------------------------------------------------------------- %%%%%%%%%% espcrc1.tex %%%%%%%%%% % % $Id: espcrc1.tex,v 1.2 2004/02/24 11:22:11 spepping Exp $ % \documentclass[fleqn,12pt,twoside]{article} % \usepackage{espcrc1} % Use the option 'headings' if you want running headings \usepackage[headings]{espcrc1} \usepackage{epsfig} % identification \readRCS $Id: espcrc1.tex,v 1.2 2004/02/24 11:22:11 spepping Exp $ \ProvidesFile{espcrc1.tex}[\filedate \space v\fileversion \space Elsevier 1-column CRC Author Instructions] % change this to the following line for use with LaTeX2.09 % \documentstyle[12pt,twoside,fleqn,espcrc1]{article} % if you want to include PostScript figures \usepackage{graphicx} % if you have landscape tables \usepackage[figuresright]{rotating} % put your own definitions here: % \newcommand{\cZ}{\cal{Z}} % \newtheorem{def}{Definition}[section] % ... \newcommand{\rootsnn}[1]{$\sqrt{s_{NN}} = #1$~GeV} \newcommand{\pt}{p$_{T}$ } \newcommand{\dndeta}{dN$_{ch}$/d$\eta$ } %\newcommand{\pionr}{$N(\pi^{-})/N(\pi^{+})$ } \newcommand{\pionr}{$N_{\pi^{-}}/N_{\pi^{+}}$ } \newcommand{\pir}{$N_{\pi^{-}}/N_{\pi^{+}}$} \newcommand{\kaonr}{$N_{K^{-}}/N_{K^{+}}$ } \newcommand{\kar}{$N_{K^{-}}/N_{K^{+}}$} %\newcommand{\protr}{$N(\bar{{\rm p}})/N({\rm p})$ } \newcommand{\protr}{$N_{\bar{\rm p}}/N_{\rm p}$ } \newcommand{\pr}{$N_{\bar{\rm p}}/N_{\rm p}$} \newcommand{\Raa}{$R_{AA}$ } \newcommand{\Rnn}{$R_{AA}$ } \newcommand{\Rda}{$R_{dAu}$ } \newcommand{\Rcp}{$R_{CP}$ } \newcommand{\Npart}{N$_{part}$ } \newcommand{\Ncoll}{N$_{coll}$ } \newcommand{\ttbs}{\char'134} \newcommand{\AmS}{{\protect\the\textfont2 A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}} % add words to TeX's hyphenation exception list \hyphenation{author another created financial paper re-commend-ed Post-Script} % set the starting page if not 1 % \setcounter{page}{17} % declarations for front matter \title{Recent Results from the BRAHMS Experiment} \author{P. Staszel\address[KRA]{Jagiellonian University, Institute of Physics, \\ ul. Reymonta 4, 30-059 Krak{\'o}w, Poland} (for the BRAHMS Collaboration)\thanks{For the full BRAHMS Collaboration author list and acknowledgment see appendix 'Collaborations' of this volume} } % If you use the option headings, % the title is also used as the running title, % and the authors are also used as the running authors. % You can change that by using \runtitle and \runauthor. \runtitle{Recent Results from the BRAHMS Experiment} \runauthor{P. Staszel} \begin{document} % typeset front matter \maketitle \begin{abstract} We present results obtained by the BRAHMS experiment at the Relativistic Heavy Ion Collider (RHIC) for four colliding systems, namely: Au + Au and Cu + Cu at \rootsnn{200} and \rootsnn{62.4}, and d + Au and p + p at \rootsnn{200}. The focus here is to give an overview of the main results on the reaction dynamics and on the properties of hot and high energy density matter produced in utra-relativistic heavy ion collisions versus its longitudinal expansion. Measurement of particle production, particle spectra over a large rapidity interval as well as high \pt measurements related to nuclear modification in Au + Au and Cu + Cu and d + Au collision are discussed. The observed number of charged particles produced per unit of rapidity at the central rapidity region indicates that a high energy density systems are created at the initial stage of the Au + Au reaction. Analysis of anti-particle to particle ratios (including multi-strange baryon) as the function of rapidity and collision energy reveals that particles population at the chemical freeze-out stage for heavy ion reaction at and above SPS energies is controlled only by baryon chemical potential. >From the particle spectra we deduced significant radial expansion ($\beta \approx $ 0.75) which is consistent with the large initial energy density. We also measured the elliptic flow parameter $v_2$ versus rapidity and \pt. The weak dependency (if any) of the $v_{2}(p_T)$ is observed. We present rapidity dependent $p/\pi$ rations in $0 < y < 3$ for Au + Au and Cu + Cu \rootsnn{200}. The strong enhancement of proton and anti-proton yields compared to pion yields is seen, and the results are discuss in terms of collision energy, system size and rapidity dependency. We compare \Raa for Au + Au at \rootsnn{200} and \rootsnn{62.4}, and for Au + Au and Cu + Cu at \rootsnn{200}. The general observed trend is that \Raa increases with: decreasing collision energy, system size, and collision centrality. \Raa shows very weak dependency on rapidity (in $0 < y < 3.2$ interval), both for pions and protons. %Studying of \Rda and \Raa at forward rapidity reveals the %stronger pions suppression for Au + Au as compare to d + Au. \end{abstract} \section{INTRODUCTION} Reactions between heavy nuclei provides a unique opportunity to produce and study nuclear (hadronic) matter far from its ground state, at extremely high densities and temperatures. From the onset of the formulation of the quark model and the first understanding of the nature of the binding and confining potential between quarks about 30 years ago, it has been realized that at very high density and temperature the hadronic matter may undergo transition to the more primordial form of matter characterized by a strongly reduced interaction between its constituents, quarks and gluons, such that the partons would exist in the nearly free state~\cite{Collins}. This proposed state of matter has been named the quark gluon plasma (QGP). Experimental attempts to create the QGP in the laboratory by colliding heavy nuclei have been carried out for more than 20 years. During that period, center of mass energies per pair of colliding nucleons have risen steadily from the \rootsnn{1} domain of the Bevalac at LBNL, to energies of \rootsnn{5} at the AGS at BNL, and to \rootsnn{17} at the SPS at CERN. Although a number of signals suggesting the formulation of a very dense state of matter have been observed, no strong evidence for QGP formation was found at these energies. In mid-August 2001 systematic data collecting by the four RHIC experiments, namely BRAHMS, PHENIX, PHOBOS and STAR, began at the energy of \rootsnn{200}. The RHIC operations started a new era of systematic studies of strongly interacting matter created in ultra-relativistic nucleus-nucleus collision. The main results obtained up to present at RHIC are the large eliptic flow observed for central Au + Au collisions, that is consistent with the hydrodynamic evolution of the perfect fluid \cite{star_flow_papers,phenix_flow_paper,hydro1}, and the strong jet suppression \cite{br_PRL91} predicted within the Quantum Chromo-Dynamic theory, (QCD), as a consequence of creation of the dense colored medium \cite{khar_CGC}. The last observation was supplemented by d~+~Au measurement showing absence of suppression, and rather Cronin type enhancement at the central rapidity region that excluded alternative interpretation of suppression in terms of initial state parton saturation (CGC) effects. Another measurement that strongly supported the scenario of jet quenching was the discovery of mono-jet production \cite{star_Adler,star_Hardtke} in central Au~+~Au collisions, whereas, for d~+~Au and peripheral Au~+~Au near side and away side back-to-back jet correlation have been measured. The large rapidity range and \pt coverage allows BRAHMS to study the properties of the produced medium as a function of its longitudinal expansion. The measurement of rapidity evolution of the nuclear modification factor for d~+~Au performed by BRAHMS shown that at more forward rapidities the hadronic yields are suppressed as compared to scaled p~+~p interactions \cite{br_evordau}. The suppression was even stronger for central collisions. Both observations can be quantitatively described within the framework of CGC \cite{khar_CGC,marian}. \section{BRAHMS DETECTOR SETUP } The BRAHMS (Broad RAnge Hadron Magnetic Spectrometers) \cite{br_nim}, experimental setup consists of a set of global detectors and two spectrometer arms: Mid-Rapidity Spectrometer (MRS) that operates in the polar angle range from 30 to 95 degrees, and the Forward Spectrometer (FS) that operates in the range between 2 and 30 degrees. Global detectors can measure the global features of the collision like overall particle multiplicity and centrality, collision vertex position, and recently they provide also information on reaction plane orientation utilized in the azimuthal flow analysis. For the momentum measurements in the MRS we use two tracking devices and one dipol magnet. Particle identification (PID) is done by the Time of Flight (TOF) measurement and using Cherenkov detector C4. In the FS two Time Projection Chambers (TPC) and three Drift Chambers (DC) deliver particle track segments and for the momentum measurement we use three dipol magnets. The PID is provided by TOF measurements for low (TOF1) and medium (TOF2) particle momenta, and by the Ring Imaging Cherenkov detector (RICH) in the high momentum mode measurement. The BRAHMS PID ability is summarized in Table~\ref{tab_pid}. \begin{table}[htb] \caption{Upper range of the momentum for 2$\sigma$ separation (in GeV/c)} \label{tab_pid} \newcommand{\m}{\hphantom{$-$}} \newcommand{\cc}[1]{\multicolumn{3}{c}{#1}} \newcommand{\ccc}[1]{\multicolumn{3}{c|}{#1}} \renewcommand{\tabcolsep}{1pc} % enlarge column spacing \renewcommand{\arraystretch}{1.2} % enlarge line spacing \begin{tabular}{@{}lclclclclclcl} \hline {} & \ccc{$0 < \eta <1.0$} & \cc{$1.5 < \eta < 4.0$} \\ \hline {} & TOFW & TOFW2 & C4 & TOF1 & TOF2 & RICH \\ \hline $K/\pi$ & 2.0 & 2.5 & - & 3.0 & 4.5 & 25.0 \\ $K/p$ & 3.5 & 4.0 & 9.0 & 5.5 & 7.5 & 35.0 \\ \hline \end{tabular} \end{table} %Using 2$\sigma$ cut, in MRS we have $K/\pi$ separation up to $2.5$ GeV and $K/p$ %separation up to $4$ GeV, C4 allows to extend the $K/\pi$ separation up to $9$ GeV. %In the FS, the TOF measurement provide separation %up to $4.5$ GeV for $K/\pi$ and up to $7.5$ GeV for $K/p$. %RICH extends this ability up to $25$ GeV for $K/\pi$ and provides %proton id up to $35$ GeV. \section{OVERALL BULK CHARACTERISTICS} The multiplicity distribution of emitted particles is a fundamental observable in ultra-relativistic collisions. It is sensitive to all stages of the reaction and can address issues like the role of hard scatterings between partons and the interaction of these partons in the high-density medium \cite{khar_multi,br_mult1,br_mult2}. Figure \ref{dNdEta} shows the measured pseudo-rapidity density of charged hadrons, \dndeta, over a wide range of $\eta$ for the central $(0-5\%)$ Au~+~Au collisions at \rootsnn{200}, \rootsnn{130} and \rootsnn{62.4}. \begin{figure} \centering \epsfig{file=./figures/soft/dNdEta.eps,width=14.0cm} \vspace{-1.0cm} \caption{ Distributions of $dN_{ch}/d\eta$ measured by BRAHMS for $ 0-5\% $ central Au + Au reactions, at \rootsnn{200} (solid circles), \rootsnn{130} (open squares) and \rootsnn{62.4} (solid squares). Only statistical error (usually smaller than the symbol size) are shown. } \label{dNdEta} \end{figure} For the central collisions at \rootsnn{200} we observed about 4500 of charged particles within the rapidity range covered and the \dndeta\nolinebreak$|_{\eta=0}$ = 625 $\pm$ 56. %% removed because no plot %Figure \ref{syst} shows the energy %systematic \dndeta scaled with the number of participating nucleon pairs. %\begin{figure} % \centering % \epsfig{file=syst.eps,width=5.0cm} % \caption{\protect\footnotesize % Multiplicity density of charged particles, at $\eta$ = 0, normalised with the number % participant pair as a function of energy. % Systematics for nucleus - nucleus and p + p collisions are shown.} % \label{syst} %\end{figure} %It is seen that the production of charged particle in the central Au + Au collisions %exceeds the particle production per participant pair observed in elementary %p + $\bar{p}$ collisions at the same energy by 40-50\% \cite{alner}. The latter value exceeds the particle production per participant pair observed in elementary p + ${\rm \bar{p}}$ collisions at the same energy by 40-50\% \cite{alner}. This means that nucleus-nucleus collisions at the considered energies are far from being the simple superposition of elementary collisions. This simple measurement of charged particle density $dN_{ch}/d\eta$ can be used to estimate the so-called Bjorken energy density, $\varepsilon$ \cite{bjor}. The formula \begin{equation} \label{eq1} \varepsilon = \frac{3}{2} \times \frac{\langle E_{t}\rangle}{\pi R^{2}\tau_{o}} \times \frac{dN_{ch}}{d\eta} \end{equation} provides the value of about 4 GeV/fm$^3$. To obtained this result we assumed that $\tau_{o}$~~=~1 fm/c, $\langle E_{t}\rangle$ = 0.5 GeV and R = 6 fm. The factor 3/2 is due to the assumption that the charged particles carried out of the reaction zone only a fraction (2/3) of the total available energy. The more refined results obtained from the identified particle abundances and particle spectra leads to somewhat larger values of $\varepsilon$, namely 5 GeV/fm$^3$ at \rootsnn{200}, 4.4 GeV/fm$^3$ at \rootsnn{130}, and 3.7 GeV/fm$^3$ at \rootsnn{62.4}, \cite{br_meson}. All these values significantly exceed the predicted energy density $\varepsilon \approx 1$ GeV/fm$^3$ for the boundary between hadronic and partonic phases \cite{karsch}. %For \rootsnn{200} the energy density exceeds by factor of %30 the density of normal nuclear matter and by a factor of 5 the density of %a single baryon. \subsection{Hadrochemistry with BRAHMS data} BRAHMS measurements allow to derive the anti-particle to particle ratios for pions, \pir, kaons, \kar, and protons, \pr, over the large rapidity interval. The results, for Au + Au collision at \rootsnn{200} and \rootsnn{62.4} are presented on Figure \ref{ratiosVsY}. \begin{figure} \centering \epsfig{file=./figures/soft/ratiosAll.eps,width=11.0cm} \vspace{-1.0cm} \caption{ Ratios of anti-particles to particles (pions, kaons and protons) at a function of rapidity for \rootsnn{62.4}, \rootsnn{200}. Statistical and systematic errors are indicated. } \label{ratiosVsY} \end{figure} Whereas \pionr stays constant and is equal 1 in the whole covered rapidity range (0 $<$ y $<$ 3.2) for all RHIC energies, the \kaonr and \protr drop significantly with increasing rapidity. For \rootsnn{200} the \kaonr and \protr equal respectively 0.95 and 0.76 at $y \approx 0$, and reach values of 0.6 for \kaonr and 0.3 for \protr around rapidity 3. Comparing \rootsnn{200} and \rootsnn{62.4} we observe $11 \%$ and $40 \%$ decrease of ratios at mid-rapidity and $43 \%$ and $93 \%$ decrease at $y \approx 3$ for kaons and protons, respectively. The large difference in the \protr reduction for \rootsnn{200} and \rootsnn{62.4} is due to the fact that for the lower energy the rapidity $y \approx 3$ corresponds to the fragmentation region, whereas for \rootsnn{200} $y \approx 3$ is located about 1 unit of rapidity below the maximum in the net-baryon distribution \cite{br_stopping}. Figure \ref{ratiosKaons} shows the \kaonr as a function of corresponding \protr for various rapidities. The data are for central collisions for the three studied collision energies studied at RHIC. The AGS and SPS results are plotted for comparison. There is a striking correlation between the RHIC/BRAHMS kaon and proton ratios over 3 units of rapidity. %\begin{figure}[htb] %\begin{minipage}[t]{75mm} %\epsfig{file=./figures/soft/ratiosKaons.eps,width=7.8cm} % \vspace{-1.0cm} % \caption{Correlation between \kaonr and \protr. % The solid curve refer to statistical model calculation with a chemical freeze-out % temperature of 170 MeV. % } % \label{ratiosKaons} %\end{minipage} % %\hspace{\fill} % %\begin{minipage}[t]{75mm} % \epsfig{file=./figures/soft/ratiosHyperons.eps,width=8.3cm} % \vspace{-1.0cm} % \caption{Anti-particle to particle ratios % for $\Lambda$s, $\Xi$s and $\Omega$s as a function of % $\bar{p}/p$. Different points show mid-rapidity ratios measured by NA49 and STAR % collaboration at different collision energies. % Meaning of the plotted functions is explained in text}. % \label{ratiosHyperons} %\end{minipage} %\end{figure} \begin{figure}[htb] \centering \epsfig{file=./figures/soft/ratiosKaons.eps,width=9.8cm} \vspace{-1.0cm} \caption{Correlation between \kar and \pr. The solid curve refer to statistical model calculation with a chemical freeze-out temperature of 170 MeV. } \label{ratiosKaons} \end{figure} It is worth to note that the BRAHMS forward rapidity data measured at \rootsnn{62.4} overlap with the SPS points that were measured at much lower energy but at mid-rapidity. The solid line plotted on the figure refers to the fit with a statistical model to the \rootsnn{200} results assuming that the temperature at the chemical freeze-out is 170 MeV \cite{br_ratios,becatt}. It is seen that the data are very well described by the statistical model over the broad rapidity range with baryonic chemical potential changing from 27 MeV at mid-rapidity to 140 MeV at the most forward rapidities. %Assuming that we can use statistical model Using simple statistical model at the quark level with chemical and thermal equilibrium, the ratios can be written \begin{equation} \label{eq2} %\frac{N(\bar{p})}{N(p)} = e^{-6\mu_{u,d}/T}, \; \; \; \; \; \; \; \; %\frac{N(K^-)}{N(K^+)} = e^{-2(\mu_{u,d} - \mu_{s})/T}, \frac{N_{\bar{p}}}{N_p}= e^{-6\mu_{u,d}/T}, \; \; \; \; \; \; \; \; \frac{N_{K^-}}{N_{K^+}} = e^{-2(\mu_{u,d} - \mu_{s})/T}, \end{equation} where $\mu$ and $T$ are chemical potential and temperature, respectively. Substituting $\mu_s = 0$ into eqs. (\ref{eq2}), one gets \kaonr = [\pr]$^{1/3}$. This relation, represented by the dotted line on Figure \ref{ratiosKaons}, does not reproduce the observed correlation. The data are however well fitted by the function \kaonr = [\pr]$^{1/4}$ (dashed line) which can be derived from eqs. (\ref{eq2}) assuming $\mu_s = 1/4 \mu_{u,d}$. Recently, STAR and NA49 have measured mid-rapidity ratios $\bar{\Lambda}/\Lambda$, $\bar{\Xi}/\Xi$ and $\bar{\Omega}/\Omega$ versus \protr for set of energies from \rootsnn{10} up to \rootsnn{200}. % if anihyperons to hyperons are not shown -> These preliminary results can also be well discribed within statistical model of chemical and thermal equilibrium at the quark level and confirm the the strong correlation between $\mu_s$ and $\mu_{u,d}$ derived from BRAHMS data. % %These measurements of strange and multi-strange particles %ratios provide the possibility to test the relation between $\mu_s$ and $\mu_{u,d}$ found %for kaons. %From the statistical model of chemical and thermal equilibrium at the quark level one can %derive the following relations %\begin{equation} %\label{eq3} %\frac{N(\bar{H})}{N(H)} = \left[\frac{N(\bar{p})}{N(p)}\right]^{\lambda}, %\end{equation} %where $H$ stands for any hadronic states build of $u$, $d$ and/or $s$ quarks. %Taking $\mu_s = 1/4 \mu_{u,d}$, one can easily calculate that the $\lambda$ %is equal $3/4$ for $\Lambda$, $1/2$ for $\Xi$ and $1/4$ for $\Omega$. %The comparison between data points from NA49 and STAR measurements %and predictions from eqs. \ref{eq3} for $\bar{\Lambda}/\Lambda$, $\bar{\Xi}/\Xi$ and %$\bar{\Omega}/\Omega$ plotted on Fig. \ref{ratiosHyperons}. %The parameters $\lambda$ extracted from fits (not shown) are equal $0.74 \pm 0.02$, %$0.55 \pm 0.02$ and $0.21 \pm 0.08$ for $\Lambda$, $\Xi$ and $\Omega$, respectively. %The agreement between predictions based on $K^{-}/K^{+}$ ratios measured at different rapidities %with antihyperons-to-hyperons ratios measured at mid-rapidity is noticeable, and %the relation $\mu_s = 1/4 \mu_{u,d}$ calls for the theoretical explanation. \subsection{Radial flow} The properties of matter in the latest stage of the collision when the interactions between particles cease (kinetic freeze-out) can be studied from the shape of spectra of the emitted particles. This shape depends in general on the temperature of the emitting source and on the collective flow. For central collisions where one should not expect any azimuthal dependency only the so-called transverse (radial) flow is important \cite{hydro1}. In the blast-wave approach \cite{blast1} the spectrum is parametrized by a function depending on the freeze-out temperature, ($T_{fo}$), and on the transverse expansion velocity ($\beta_{T}$). Figure \ref{flowNpart} shows results from analysis of the particle spectra from the Au + Au reaction at \rootsnn{200} using the blast-wave model fit, simultaneously to $\pi^+$, $\pi^-$, K$^+$,K$^-$, protons and anti-protons, plotted versus number of participant pairs ($N_{part}$). \begin{figure}[htb] \begin{minipage}[t]{80mm} \centering \epsfig{file=./figures/oana/beta_npart.eps,width=8.3cm} \vspace{-1.0cm} \caption{ Kinetic freeze-out temperature and transverse flow velocity at mid-rapidity as a function of centrality for Au~+~Au at \rootsnn{200} (dots). For the comparison we show result for $0-10\%$ central Au~+~Au at \rootsnn{62.4} (star).} \label{flowNpart} \end{minipage} % \hspace{\fill} % \begin{minipage}[t]{70mm} \centering \epsfig{file=./figures/oana/flow_y.eps,width=7.8cm} \vspace{-1.0cm} \caption{ Kinetic freeze-out temperature and transverse flow velocity for central Au + Au at \rootsnn{200} as a function of rapidity. } \label{flow_y} \end{minipage} \end{figure} The obtained result indicates that the kinetic freeze-out temperature decreases with centrality from about 140 MeV for $40-50\%$ centrality bin to about 120 MeV for the most central collisions. The second quantity is lower than the temperature of the chemical freeze-out indicating that, as expected, the freeze-out of particle ratios occurs earlier than the kinetic freeze-out. The reversed trend is seen for the expansion velocity which is equal about 0.65c and 0.75c for $40-50\%$ centrality and $0-5\%$ centrality class, respectively. For comparison we show also the results for Au + Au collisions at \rootsnn{62.4}. Although for the same $N_{part}$ value the $T_{fo}$ for both energies is very similar, the reduction by about $20 \%$ in the expansion velocity is observed. Figure \ref{flow_y} shows the dependence of $T_{fo}$ and $\beta_{T}$ as a function of rapidity. The observed variations of $T_{fo}$ and $\beta_T$ on $N_{part}$ and rapidity are consistent with the hydrodynamic description in which the radial flow is the result of outwards gradients of pressure that exists in the expanding matter during the whole evolution. Thus the speed of expansion should increase with the density of the initially created system. The transverse flow velocity is larger than that observed at SPS energies what is consistent with a large initial density of the system created at RHIC. \subsection{Elliptic Flow} The powerful tool to study the dynamic that drives the initial evolution of systems created in heavy ion reactions is the analysis of the azimuthal distribution of the emitted particles relative to the reaction plane \cite{hydro1}. The triple differential distribution of emitted particles can be factorized as follow \begin{equation} \frac{dN}{dydp_Td\phi} = \frac{dN}{dydp_T} \frac{1}{2\pi} \times (1 + 2v_1(y,p_T)cos(\phi-\phi_r) + 2v_2(y,p_T)cos2(\phi-\phi_r) + ....). \label{eq_v2} \end{equation} where $\phi$ and $\phi_r$ denote the azimuthal angles of the particle and of the reaction plane, respectively. The first factor depends only on $y$ and $p_T$ and the second factor represents the expansion of the azimuthal dependence into the Fourier series. The coefficients at the first ($v_1$) and the second ($v_2$) harmonics are called direct and elliptic flow parameter, respectively, and in general they are functions of rapidity and transverse momentum. The calculations based on hydrodynamic models \cite{hydro1} show that the elliptic flow is substantially generated only during the highest density phase, before the initial spatial anisotropy of created medium disappears. Thus $v_2$ is sensitive to the very early phase in the system evolution and relatively insensitive to the late stage characterized by the dissipative expansion of the hadronic gas. Elliptic flow has been extensively measured by the STAR, PHENIX and PHOBOS experiments \cite{star_flow_papers,phenix_flow_paper,phobos_flow_paper}. Generally, the $v_2$ is an increasing function of \pt up to $1.5$ GeV/c, at which point it saturates. Up to roughly 1.5 GeV/c in \pt, hydrodynamic calculations show good agreement with experimental data for the $v_2$ dependence on \pt and centrality. BRAHMS has measured the \pt dependence of $v_2$ at set of rapidities \cite{qm05_hiro}, and the results for pions at $\eta = 0$ and at $\eta = 3.4$ are shown on Figure \ref{v2_ypt}. \begin{figure} \centering \epsfig{file=./figures/ellipticflow/plot_v2_pion.eps,width=10.0cm} \vspace{-1.0cm} \caption{ Pion elliptic flow parameter \pt dependence measured for Au + Au at \rootsnn{200} at $\eta = 0$ and at $\eta = 3.2$.} \label{v2_ypt} \end{figure} %The reaction plane was determined for each event by using %the array of azimuthally arranged silicon and tiles detectors \cite{br_nim}. %At mid-rapidity the emitted hadrons have been measured and identified %in the MRS and at forward rapidities by the FS (see \cite{qm05_hiro} for more details). $v_2$ for identified pions is an increasing function of \pt at both rapidities, with indication of saturation above 1.5 GeV/c. The dependence on pseudo rapidity is very small. These results are very similar to that obtained for charged hadrons \cite{qm05_hiro}. \section{BARYON TO MESON RATIOS} With its excellent particle identification capabilities BRAHMS can study the \pt and y dependency for different type of hadrons production. Preliminary results \cite{br_Claus,br_Yin} indicate that for Au + Au reactions in the intermediate \pt region the proton to meson ratio is significantly higher that one would expect from the parton fragmentation in vacuum. Several theoretical explanations in terms of partonic interactions like models of quark hadronization and quark coalescence \cite{eunjoo_Fries,eunjoo_Greco,eunjoo_Hwa} and models that incorporate the novel baryon dynamics \cite{eunJoo_Vitev,VTPop} have been proposed. The recent experimental data obtained for the p~+~p, Au~+~Au, and Cu~+~Cu colliding systems are expected to result in a better understanding of the underlying physics and verification of the proposed theoretical scenarios. Fig. \ref{btom1} shows a recent investigation by BRAHMS \cite{qm05_eunjoo}, of the $\bar{p}$ to $\pi^-$ ratios at mid-rapidity (circles) and at pseudo rapidity $\eta = 3.2$ (squares) for Au + Au collisions at \rootsnn{200} for different centrality classes indicated on the plot. The bottom panel shows the ratios for p + p at \rootsnn{200} measured by PHENIX at mid-rapidity and by BRAHMS at forward rapidity. \begin{figure}[htb] \begin{minipage}[t]{65mm} \epsfig{file=./figures/baryontomeson/fig1.eps,width=6.5cm} \vspace{-1.0cm} \caption{The $\bar{p}$ to $\pi^-$ ratios at mid-rapidity (circles) and at pseudo rapidity $\eta = 3.2$ (squares) for different centralities of Au + Au collisions at \rootsnn{200}. } \label{btom1} \end{minipage} % \hspace{\fill} % \begin{minipage}[t]{85mm} \epsfig{file=./figures/baryontomeson/fig4.eps,width=8.5cm} \vspace{-1.0cm} \caption{The averaged $\bar{p}/\pi^-$ versus \Npart for Au + Au (open symbols) and Cu + Cu (solid symbols) at \rootsnn{200}, for $y \approx 0$ (circles) and and for $\eta \approx 3.2$ (squers). } \label{btom2} \end{minipage} \end{figure} The data reveal smooth increase of $\bar{p}/\pi^-$ from peripheral to central collisions, however, the centrality dependence is stronger at mid-rapidity than at forward rapidity. The maxima in $\bar{p}/\pi^-$ ratio is lower at forward rapidity as compared to mid-rapidity. Figure~\ref{btom2} shows the $\bar{p}/\pi^-$ centrality dependence for Au~+~Au (open symbols) and Cu~+~Cu (solid symbols) at \rootsnn{200}. The data for $y = 0$ and $\eta=3.2$ are represented by circles and squares, respectively. One can see the strong increase of $\bar{p}/\pi^-$ as a functon of \Npart in the range from 0 to 100. For $N_{part} > 100$ the dependence saturates and the ratios reach values of about 0.6 and about 0.25 for mid and forward rapidity, respectively. For peripheral Au~+~Au collisions the data approach the p~+~p results. It is important to note that the Au + Au and Cu + Cu ratios are consistent with each other when plotted versus \Npart what indicates that the enhancement of $\bar{p}$ over $\pi^-$ is controlled by the initial size of the created systems. Fig. \ref{btom3} shows the comparison of BRAHMS and PHENIX data for the ratio of protons to positive pions measured at $y=0$ with the theoretical calculation. \begin{figure} \centering \epsfig{file=./figures/baryontomeson/fig2.eps,width=9.5cm} \vspace{-1.0cm} \caption{The $p/\pi^+$ versus \pt for Au + Au collisions at \rootsnn{200} measured at mid-rapidity by BRAHMS (circles) and by PHENIX (triangles). Squares represent BRAHMS results at $eta$ = 3.2. The plotted lines show model calculations (see text). } \label{btom3} \end{figure} The parton coalescence \cite{eunjoo_Greco} and recombination \cite{eunjoo_Hwa} models describe the observed ratios well at mid-rapidity. The three-dimentional hydrodynamic model \cite{eunjoo_Hirano_Nara} can not reproduce the observed shape of $p/\pi^+$, however it reproduces the overall level of enhancement. The current hydrodynamic calculations do not show a rapidity depencence which is in contrary to the experimental observation (see Fig. \ref{btom3}). This is presumably because the baryon and isospin chemical potentials are not included in this model. \section{HIGH \pt SUPPRESSION} Particles with high \pt (above 2 GeV/c) are primarily produced in hard scattering processes early in the collision. In high energy nucleon-nucleon reactions hard scattered partons fragment into jets of hadrons. However, in nucleus-nucleus collision hard scattered partons might travel in the medium. It was predicted that, if the medium is QGP, the partons will lose a large fraction of their energy by induced gluon radiation, effectively leading to suppression of jet production \cite{wang}. Experimentally this phenomenon, known as jet quenching, will be observed as a depletion of the high \pt region in hadron spectra. The measure commonly used to study the medium effects is called the nuclear modification factor, \Rnn. It is defined as a ratio of the particle yield produced in nucleus-nucleus collision, scaled with the number of binary collisions (\Ncoll), and the particle yield produced in elementary nucleon-nucleon collision \begin{equation} \label{eq5} R_{AA} = \frac{Yield(AA)}{N_{coll} \times Yield(NN)}. \end{equation} At high \pt the particles are predominantly produced by hard scatterings and in the absence of nuclear effects (when the nucleus-nucleus collision reduces to the superposition of elementary collisions) we expect \Rnn to be 1. At low \pt, where the production rate scales rather with \Npart, \Rnn should converge to N$_{part}$/\Ncoll which is roughly 1/3 for central Au~+~Au at RHIC energies. \Rnn $< 1$ at high \pt will indicate the suppression which, as has been discussed, is consistent with the jet quenching phenomenon. At SPS there is no suppression, in fact it is well known that there is enhancement for \pt~$>$~2~GeV/c and this so-called Cronin effect is attributed to initial multiple scattering of reacting partons. Another variable used to quantify nuclear effects, that does not depend on the elementary reference spectra, is \Rcp, defined as a ratio of \Rnn at central nucleus-nucleus collisions to \Rnn at peripheral collisions. The idea of using \Rcp bases on the expectation that any nuclear modification in peripheral collisions in not significant. We will show that the latter statement is not true for $R_{CP} = R_{AuAu}(0-10\%)/R_{AuAu}(40-60\%)$. \subsection{\Rnn evolution on collision centrality and collision energy for Au~+~Au and Cu~+~Cu systems} The large set of data collected during the RHIC run 4 has allowed us to carry out the study of the \Rnn evolution on collision centrality and collision energy for two colliding systems, namely Au~+~Au and Cu~+~Cu \cite{qm05_truls}. Figure \ref{auau200vs62} shows \Raa measured at $\eta \approx 0$ and $\eta \approx 1$ for Au + Au at \rootsnn{200} (upper row) and at \rootsnn{62.4} (bottom row), for different centrality ranges indicated on the plot. \begin{figure} \centering \epsfig{file=./figures/truls/auau200vs62.eps,width=5.0cm} \vspace{-1.0cm} \caption{\Raa measured at $\eta \approx 0$ and $\eta \approx 1$ for Au + Au at \rootsnn{200} (upper row) and at \rootsnn{62.4} (bottom row), for different centrality classes indicated on the plot. (p + p reference is based on ISR collider data) } \label{auau200vs62} \end{figure} For the most central reactions the \Raa shows suppression for both energies, however, the suppression is significantly stronger for the system colliding with higher energy. We observe a smooth increase of \Raa towards less central collisions, for \rootsnn{200}, resulting in approximate scaling with \Ncoll for $p_T > 2$ GeV/c for $40-50 \%$ centrality bin. However, at \rootsnn{62.4} scaling appears for more central collisions, and the Cronin peak in clearly visible already for $20-40 \%$ centrality class, where \Raa reaches value of about 1.3 in the \pt range between $2.0$ and $3.0$ GeV/c. This observations are qualitatively consistent with the picture in which there are two competing mechanisms that influence the nuclear modification in the intermediate and high \pt range, namely: the jet quenching that dominates at central collisions and Cronin type enhancement ($k_{T}$ broadening or/and quark recombination) that prevails for the more peripheral collisions. The next figure (Fig. \ref{auauvscucu62}), presents similar comparison as shown on Fig. \ref{auau200vs62} but this time we compare two different systems, namely Au~+~Au and Cu~+~Cu colliding at the same energy (\rootsnn{62.4}). \begin{figure} \centering \epsfig{file=./figures/truls/qm05_RAuAu_CuCu_63GeV.eps,width=15.0cm} \vspace{-1.0cm} \caption{\Rnn measured at mid-rapidity for Au + Au (upper row) and for Cu + Cu (bottom row) at \rootsnn{62.4} for different centrality classes indicated on the plot. (p + p reference is based on ISR collider data) } \label{auauvscucu62} \end{figure} For Cu + Cu at \rootsnn{62.4} the same trend of increasing \Rnn with decreasing collision centrality is seen, however, the Cronin type enhancement is present already for the most central collisions. Summarizing the whole set of observation we conclude that the level of suppression of the inclusive hadron spectra produced in the nucleus-nucleus collisions at RHIC energies in the \pt range above $2$ GeV increases with increasing collision energy, collision centrality and with the size of the colliding nuclei. The dependency on the last two variables can be replaced by only one dependency on \Npart. %The similarity %between value and the shape of \Raa for Au + Au $20-40 \%$ centrality and for Cu + Cu %$0-10 \%$ centrality is striking. {\sl PS comment: we haven't shown the direct argument for what is stated in the last sentence but plotting \Raa versus \Npart for (Au+Au and CuCu at 62) maybe would show that? It looks like it can be done for eta=1.} \subsection{\Raa for identified hadrons at forward rapidity for Au + Au at \rootsnn{200}} BRAHMS collaboration has already announced a large suppression of the nuclear modification factor (similar to that seen at mid-rapidity) measured at large pseudo rapidity of $\eta = 2.2$ in Au + Au at \rootsnn{200} \cite{br_PRL91}. However, the data did not allow to verify the mechanism responsible for the observed effect. %In this section we present the nuclear effects at forward rapidity %for identified hardons in hope that this more exlusive analysis will %lead us to better understanding of origin of suppression versus the %logitidunal expansion. In this section we present more exclusive analysis of nuclear effects at forward rapidity for identified pions, kaons and protons. Figure~\ref{AuAuRaaRcp} shows \Raa for identified hadrons at rapidity $y \approx 3.2$ for $0-10\%$ central Au~+~Au events at \rootsnn{200}. The shaded band around unity indicates systematic error associated with the uncertainty in the number of binary collisions. Both \Raa and \Rcp show suppression for pions (left panel) and for kaons (middle panel), however protons (right panel) \Rcp shows suppression whereas \Raa reveals the Cronin type enhancement with the peak at $p_T \approx 2$ GeV/c. \begin{figure} \centering \epsfig{file=./figures/radek/AuAuRaaRcp.eps,width=13.0cm} \vspace{-1.0cm} \caption{BRAHMS \Raa (upper row) and \Rcp (bottom row) for pions, kaons and protons, measured $y \approx 3.2$ in Au + Au \rootsnn{200}. The p + p reference was also measured by BRAHMS (see \cite{qm05_radek}). } \label{AuAuRaaRcp} \end{figure} The difference between \Raa and \Rcp is striking, indicating significant enhancement of protons (in respect to p + p) for the $40-60 \%$ collision centrality used in the definition of \Rcp. The same misleading behavior of \Rcp is seen for charged hadrons when comparing evolution of \Rnn and \Rcp on $\eta$ for Au + Au at \rootsnn{200} and \rootsnn{62.4} \cite{qm05_truls}. Figure~\ref{PhenixRaa} shows the nuclear modification factors calculated for $(\pi^{+} + \pi^{-})/2$ (left panel) and $(p + \bar{p})/2$ (right panel), respectively, at $y \approx 3.2$, for central Au + Au reaction. For the comparison we plotted the \Raa measured by the PHENIX Collaboration at mid-rapidity. \begin{figure}[htb] \centering \epsfig{file=./figures/radek/PhenixRaa.eps,width=15.0cm} \vspace{-1.0cm} \caption{ Comparison of \Raa measured for central Au + Au collisions at \rootsnn{200}, at mid-rapidity and $y \approx 3$ for pions (left panel) and protons (right panel). } \label{PhenixRaa} \end{figure} The \Raa measured for pions shows strong suppression (by factor of about 3 for $2 < p_T < 3$ GeV/c), both at mid and at forward rapidity. The consistency between mid and forward rapidity is seen also for protons, but in this case, \Raa reveals Cronin peak around $p_T = 2$ GeV/c. The similarity between \Raa at mid and forward rapidity observed simultaneously for pions and protons suggests the same mechanisms responsible for the nuclear modifications within the studied rapidity interval. It has been predicted \cite{gyulassy_quenching} that the magnitude of quenching should depend on size and density of the created absorbing medium, thus it is interesting to study the dependency of \Raa on centrality. In Figure~\ref{AuAuRaaNpart} we plotted the averaged \Raa measured for pions versus the \Npart for the mid-rapidity (squared shape symbols) and for forward rapidity (triangles). The averaging was performed in the \pt range from $2$ GeV/c to $3$ GeV/c. \begin{figure}[htb] \centering \epsfig{file=./figures/radek/AuAuRaaNpart.eps,width=15.0cm} \vspace{-1.0cm} \caption{Averaged \Raa in the range $2.0 < p_T < 3.0$ GeV at mid rapidity (PHENIX) and at forward rapidity as a function of collision centrality, expressed by the number of participants. } \label{AuAuRaaNpart} \end{figure} It is seen again, that for the most central Au + Au reaction, the mid and forward pion suppression is of the same strength. However, the \Raa measured at forward rapidity shows significantly stronger rise towards peripheral collisions as compared to \Raa at mid-rapidity, that leads to the discrepancy on the level of $35 \%$ for $N_{part} = 100$. The trend is consistent with the model of parton energy loss in strongly absorbing medium \cite{deinese,drees}. In this picture, for $y = 0$, the jet emission is dominated by the emission from the surface which quenches the dependence of \Raa on the system size. On the other hand, for $y \approx 3$, the transition from surface to volume emission can occur, which leads to stronger dependency on \Npart. \section{SUMMARY} The results from BRAHMS and other RHIC experiments clearly show that studies of high energy nucleus - nucleus collisions have moved to a qualitatively new physics domain. It is characterized by a high degree of reaction transparency leading to the formation of a near baryon free central region with approximate balance between matter and antimatter. >From the measurement of charged particles multiplicieties in this region the lower limit for the energy density at $\tau_{o}$ = 1fm/c have been determined which is 5 GeV/fm$^3$ and 3.7 GeV/fm$^3$, for central Au + Au reactions at \rootsnn{200} and \rootsnn{62.4}, respectively. Therefore the conditions necessary for the formation of a deconfined system appear to be well fulfilled for the RHIC energies. Analysis within the statistical model of the relative abundances of $K^{-}$, $K^{+}$, $p$ and $\bar{p}$ suggests the equilibrium at chemical freeze-out at temperature of 170 MeV with the noticeably strong correlation between strange quarks and baryonic chemical potentials. The analysis of particle spectra within the blast-wave model indicates the kinetic freeze-out temperature of the order of 120 MeV and a large transverse expansion velocity which is consistent with the high initial energy density. The measurement of the elliptic flow parameter $v_2$ versus rapidity and $p_T$ shows weak dependence of the $v_{2}(p_T)$ on rapidity. The $p/\pi$ ratios measured within $0 < \eta < 3$ for Au + Au and Cu + Cu at \rootsnn{200} and \rootsnn{62.4} reveal strong enhancement of protons and anti-protons yields compared to pion yields. The models that incorporate interplay between soft and hard proceses can discribe the data at mid-rapidity. We compared \Raa for Au + Au at \rootsnn{200} and \rootsnn{62.4}, and for Au + Au and Cu + Cu at \rootsnn{200}. The general observed trend is that \Raa increases with: decreasing collision energy, system size, and collision centrality. For Au + Au central collisions at \rootsnn{200} the \Raa shows very weak dependence on rapidity (in $0 < y < 3.2$ interval), both for pions and protons. \section{ACKNOWLEDGMENTS} This work was supported by the division of Nuclear Physics of the Office of Science of the U.S. Department of Energy, the Danish Natural Science Research Council, the Research Council of Norway, the Polish Ministry of Science and Information Society Technologies grant number 0383/P03/2005/29 and the Romanian Ministry of Education and Research. \begin{thebibliography}{12} \bibitem{star_flow_papers} C. Adler {\it et al.} [STAR Collaboration], Phys.\ Rev.\ C{\bf 66} 034904 (2002). J. Adams {\it et al.} [STAR Collaboration], Phys.\ Rev.\ Lett.\ {\bf 92} 062301 (2004). \bibitem{phenix_flow_paper} S. S. Adler {\it et al.} [PHENIX Collaboration], Phys.\ Rev.\ Lett.\ {\bf 91} 182301 (2003). \bibitem{hydro1} P. F. Kolb and U. Heinz, nucl-th/0305084, and references therein. \bibitem{phobos_flow_paper} B. B. Back {\it et al.} [PHOBOS Collaboration], nucl-exp/0407012 (2004). \bibitem{br_PRL91} I. Arsene {\it et al.} [BRAHMS Collaboration], Phys.\ Rev.\ Lett.\ {\bf 91} (2003) 072305. %hep-ph/0405045 \bibitem{khar_CGC} D. Kharzeev, Y. V. Kovchegov, and K. Tuchin Phys. Lett. B599 (2004) 23, and references therein. \bibitem{star_Adler} C. Adler {\it et al.} [STAR Collaboration], Phys.\ Rev.\ Lett.\ {\bf 90} 082302 (2003). \bibitem{star_Hardtke} C. Adler {\it et al.} [STAR Collaboration], Nucl.\ Phys.\ A {\bf 715} 272 (2003). \bibitem{br_evordau} I. Arsene {\it et al.} [BRAHMS Collaboration], Phys.\ Rev.\ Lett.\ {\bf 93} 242303 (2004) \bibitem{marian} J. Jalilia-Marian, Nucl.\ Phys.\ A {\bf 748} 664 (2005). \bibitem{br_nim} M.~Adamczyk {\it et al.} [BRAHMS Collaboration], Nucl.\ Instr.\ and Meth.\ A {\bf 499} (2003) 437. \bibitem{khar_multi} D. Kharzeev and E. Levin, Phys. Lett. B {\bf 599} (2001) 79. %BRAHMS mult 130 reference PLB \bibitem{br_mult1} I. G. Bearden {\it et al.} [BRAHMS Collaboration], Phys. Lett. B523 (2001) 227. %BRAHMS mult 200 reference \bibitem{br_mult2} I. G. Bearden {\it et al.} [BRAHMS Collaboration], Phys.\ Rev.\ Lett.\ {\bf 88} (2002) 202301. \bibitem{alner} G. J. Alner {\it et al.}, Z. Phys. C{\bf 33}, 1 (1986). %``Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region,'' \bibitem{bjor} J.~D.~Bjorken, Phys.\ Rev.\ D {\bf 27} (1983) 140. \bibitem{br_meson} I. G. Bearden {\it et al.} [BRAHMS Collaboration], submitted to Phys. Rev. Lett. (nucl-ex/0403050) %``Lattice results on QCD thermodynamics,'' \bibitem{karsch} F.~Karsch, Nucl.\ Phys.\ A {\bf 698} (2002) 199. %BRAHMS stopping paper at 200 \bibitem{br_stopping} I. G. Bearden {\it et al.} [BRAHMS Collaboration], Phys.\ Rev.\ Lett.\ {\bf 93} (2004) 102301. %BRAHMS stopping paper at 200 \bibitem{br_ratios} I. G. Bearden {\it et al.} [BRAHMS Collaboration], Phys.\ Rev.\ Lett.\ {\bf 90} (2003) 102301. %therma model \bibitem{becatt} F. Becattini {\it et al.}, Phys.\ Rev.\ C{\bf 64} 024901 (2001). \bibitem{blast1} P. J. Siemens and J. O. Rasmussen, Phys.\ Rev.\ Lett.\ {\bf 42} (1979) 808. \bibitem{qm05_hiro} H. Ito [BRAHMS Collaboration], this volume. \bibitem{br_Claus} C. E. J\o{}rgensen {\it et al.} [BRAHMS Collaboration], Nucl.\ Phys.\ A {\bf 715} (2003) 741c. \bibitem{br_Yin} Z. Yin {\it et al.} [BRAHMS Collaboration], J. Phys. G {\bf 30} (2004) S983. \bibitem{eunjoo_Fries} R. J. Fries {\it et al.} Phys.\ Rev.\ C{\bf 68} 044902 (2003). \bibitem{eunjoo_Greco} V. Greco, C. M. Ko, and I. Vitev, {\it et al.} Phys.\ Rev.\ C{\bf 71} 041901R (2005). \bibitem{eunjoo_Hwa} R. C. Hwa and C. B. Yang, Phys. Rev. C{\bf 70} (2004) 024905. \bibitem{eunJoo_Vitev} I. Vitev and M. Gyulassy, Nucl. Phys. A{\bf 715} (2003) 779c. \bibitem{VTPop} V. T. Pop {\it et al.}, Phys. Rev. C{\bf 70} (2004) 064906. \bibitem{qm05_eunjoo} Eun Joo Kim [BRAHMS Collaboration], this volume. \bibitem{eunjoo_Hirano_Nara} T. Hirano, and Y. Nara Phys. Rev. C{\bf 68} (2003) 064902 \bibitem{wang} X. N. Wang, Phys.\ Rev.\ C{\bf 58} 2321(1998). \bibitem{qm05_truls} T. M. Larsen [BRAHMS Collaboration], this volume. \bibitem{qm05_radek} R. Karabowicz [BRAHMS Collaboration], this volume. \bibitem{gyulassy_quenching} M. Gyulassy, P. Levai, and I. Vitev, Nucl. Phys. B{\bf 594} (2001) 371. M. Gyulassy, P. Levai, and I. Vitev, Phys. Rev. D{\bf 66} (2002) 014005. \bibitem{deinese} A. Dainese, C. Loizides, and G. Pai{\'c}, Eur. Phys. J. C38 (2005) 461-474. \bibitem{drees} A. Drees, H. Feng, J. Jia, Phys. Rev. C{\bf 71} (2005) 034909. \end{thebibliography} \end{document} _______________________________________________ Brahms-l mailing list Brahms-l@lists.bnl.gov http://lists.bnl.gov/mailman/listinfo/brahms-l
This archive was generated by hypermail 2.1.8 : Wed Oct 05 2005 - 11:04:20 EDT