Collective flow model for the pion transverse momentum spectra from relativistic nuclear collisions at CERN

The transverse momentum spectra for pions observed by WA80 and NA35 collaborations are analysed within a fireball model with collective isentropic expansion and a realistic freeze-out criterion. By varing the initial state of the fireball, an excellent fit to the data is achieved for the whole measured range ofP _T . Slight differences in the data for the spectral slopes from central and pheripheral collisions originate in our model from the difference in the size of the fireball and in the number of participating nucleons in central and peripheral collisions. Using additional information from two-pion correlations, we can extrapolate our model back from the freeze-out point (determined from the spectra) to the initial state; we find that an initial energy density of 1.5–2GGeV/fm³ is sufficient to explain the data from central O+Au collisions at 200A GeV.     

Hadron spectra from nuclear collisions

We describe high energy nuclear collisions by a superposition of isotropically decaying thermal sources (“fireballs”) of freeze-out temperature T = 0.15 GeV. The longitudinal fireball superposition is taken as boost-invariant, in a rapidity range determined by the average energy loss of nucleons in p?p collisions. The transverse fireball motion is assumed to be due to random walk initial state collisions; it is determined by p?A data and then extrapolated to central A?B interactions. We thus obtain parameter-free predictions for the rapidity and transverse momentum spectra of hadrons produced in high energy nucleus-nucleus collisions. The results account fully for the observed broadening of transverse momentum distributions, so that single-particle spectra require neither collective flow nor temperature increase.     

Reconstructing the freeze-out state in Pb+Pb collisions at 158 <Emphasis Type="Italic">A</Emphasis>GeV/<Emphasis Type="Italic">c</Emphasis><Superscript>a</Superscript>

For a class of analytical parametrizations of the freeze-out state of relativistic heavy ion collisions, we perform a simultaneous analysis of the single-particle m _⊥-spectra and two-particle Bose-Einstein correlations measured in central Pb+Pb collisions at the CERN SPS. The analysis includes a full model parameter scan with χ² confidence levels. A comparison of different transverse density profiles for the particle emission region allows for a quantitative discussion of possible model dependencies of the results. Our fit results suggest a low thermal freeze-out temperature T≈95±15 MeV and a large average transverse flow velocity \(\bar v_ \bot \approx 0.55 \pm 0.07\). Moreover, the fit favours a box-shaped transverse density profile over a Gaussian one. We discuss the origins and the consequences of these results in detail. In order to reproduce the measured pion multiplicity our model requires a positive pion chemical potential. A study of the pion phase-space density indicates μ_π≈60 MeV for T=100 MeV.     

Thermal dileptons from quark and hadron phases of an expanding fireball

A fireball model with time evolution based on transport calculations is used to examine the dilepton emission rate of an ultra-relativistic heavy-ion collision. A transition from hadronic matter to a quark-gluon plasma at a critical temperature T _C between 130-170 MeV is assumed. We also consider a possible mixed phase scenario. We include thermal corrections to the hadronic spectra below T _C and use perturbation theory above T _C. The sensitivity of the spectra with respect to the freeze-out temperature, the initial fireball temperature and the critical temperature is investigated. Received: 4 August 2000 / Accepted: 14 November 2000     

The reconstructed final state of Au+AU collisions from PHENIX and STAR data at √s=130 AgeV— Indication for quark deconfinement at RHIC

The final state of Au+Au collisions at √s=130 AGeV at RHIC has been reconstructed within the framework of the Buda-Lund hydrodynamical model, by performing a simultaneous fit to final data on twoparticle Bose-Einstein correlations of the STAR and PHENIX Collaboration, and final identified single-particle spectra as measured by the PHENIX Collaboration. The results indicate a strongly three dimensional expansion, with a four-velocity field that is almost a spherically symmetric Hubble flow. We find large transverse geometrical source sizes, R _G=9.8±1.2 fm, relatively short mean freeze-out time, τ₀=6.1±0.3 fm/c and a short duration of particle emission, Δτ=0.02±1.5 fm/c. Most strikingsly, we find an indication for a hot central part of the hydrodynamically evolving core, characterized by a central temperature T ₀=202±13 MeV that is close to (or even above) the deconfinement temperature of the quark-hadron phase transition. The best fit indicates a cold surface temperature T _s=110±16 MeV. When the possibility of the hot center is excluded, the confidence level of the fit decreases from 28.9% to 1.0%. Predictions are made for the rapidity dependence of the slope parameters and for the transverse mass depedence of the rapidity width of the single-particle spectra, and the transverse mass dependence of the non-identical particle correlations.     

Freeze-out conditions in ultrarelativistic heavy-ion collisions

We present recent results on single particle transverse momentum distributions of pions, kaons and protons, measured in CERN Experiment NA44, of 200 AGeV/c S+S and 158 AGeV/c Pb+Pb central collisions. By comparing these data with thermal and transport models, freeze-out parameters like the temperatureT _fo and the chemical potentials (μ _q ,μ _s ) are extracted and discussed.     

Inflation of fireballs, the gluon wind and the homogeneity of the HBT radii at RHIC

We solve analytically the ellipsoidally expanding fireball hydrodynamics with source terms in the momentum and energy equations, using the non-relativistic approximation. We find that energy transport for high-p _tjets of gluons to the medium leads to a transient, exponential inflation of the fireballs created in high energy heavy ion collisions. In this transient, inflatory period, the slopes of the single particle spectra are exponentially increasing, while the HBT radius parameters are exponentially decreasing with time. This effect is shown to be similar to the development of the homogeneity of our Universe due to an inflatory period. Independently of the initial conditions, and the exact value of freeze-out time and temperature, the measurables (single particle spectra, the correlation functions, slope parameters, elliptic flow, HBT radii and cross terms) become time-independent during the late, non-inflatory stages of the expansion, and they satisfy a new kind of scaling laws. If the expansion starts with a transient inflation caused by the gluon wind, it leads naturally to large transverse flows as well as to the simultaneous equality, and scaling behaviour of the HBT radius parameters, R _side≈R _out≈R _long≈t _f √T _f /m. With certain relativistic corrections, the scaling limit is 281-2, where m _tis the mean transverse mass of the pair.     

Is there a low-p T “anomaly” in the pion momentum spectra from relativistic nuclear collisions?

The influence of resonance production in relativistic hadron-hadron and nucleus-nucleus collisions, and their role in explaining the so-called “anomalous” behaviour of the hadronic transverse momentum spectra at lowp _T is studied qualitatively and quantitatively in the framework of a simple thermodynamical model. In the discussion effects from the different kinematics in 2- and 3-body decays and from the finite width of the resonances are included. We compare our results with data from the NA35 collaboration for pion, kaon, proton and Λp _T -spectra from 200 A GeV S+S collisions and withpp data at similar energies. The model can successfully describe both S+S andpp data withT=200 MeV, μ _b =250 MeV andT=180 MeV, μ _b =250 MeV, respectively. We discuss the consistency of these parameters by comparing with measured particle ratios and checking the freeze-out conditions. We conclude that the low-p _T part of the pion spectra is dominated by resonance decays, and that there is no low-p _T “anomaly”. We also find, that the flattening of the high-p _T tail in central nuclear collisions compared topp data is probably not of thermal origin but caused by other effects, e.g. collective transverse flow.     

Charged particle production and correlations at high transverse momentum at the CERN intersecting storage rings

We study the production of identified charged particles in pp collisions at a c.m. energy of 63 GeV in events with an identified high-p_T trigger particle. The measurements were performed at the CERN Intersecting Storage Rings using the Axial Field Spectrometer.Production ratios are presented as a function of p_T in the range 2.5 to 8 GeV/c.     

High transverse momentum identified particle spectra in 200 GeV collisions from STAR

Significant baryon over meson enhancement was measured at RHIC in the intermediate transverse momentum range of p _T =2?4 GeV/c (“baryon-meson puzzle”). With STAR detector we were able to extend particle identification towards higher transverse momentum offering further insights into the particle production mechanisms at intermediate to high p _T . In this paper we present results on charged pion, proton and anti-proton spectra and ratios at intermediate to high p _T exploiting the relativistic rise of the specific ionization energy loss measured in the STAR Time Projection Chamber. These measurements provide valuable information about the production mechanisms of particles at intermediate p _T in relativistic heavy ion collisions, e.g. coalescence/recombination versus jet fragmentation.     

The transverse momentum of partons in large pT processes

An approximate method is used to investigate the effects of parton transverse momentum in large p_T particle production within the framework of hard scattering models. We derive an approximate expression for the mean bias towards the trigger of each of the two participating partons and find that event one of the partons is biased more than the other, even with a 90° trigger. We treat the transverse momentum of partons and their closely related off-mass-shell behaviour as a perturbation in the equation for the single-particle inclusive cross section, and then expand in a Taylor series. We calculate the first non-zero correction term and find that to this order, the cross section is increased by parton transverse momentum effects by typically a factor of 1.7 for p_T = 3 GeV/c with 〈k_T〉 = 500 MeV/c, or 1.25 for p_T = 3 GeV/c with 〈k_T〉 = 300 MeV/c, and that the correction decreases rapidly with increasing p_T.     

The transverse energy distribution in hadron-lead collisions

The transverse energy cross-sectiondσ/dE _T has been measured in the pseudorapidity region 0.6<η<2.4 for hadron-lead collisions at 200 GeV/c incident hadron momentum. TheE _T distribution extends to 40 GeV, which is twice the kinematic limit forp-p collisions at the same incident beam momentum. The distribution ofE _T is found to shift towards low pseudorapidities with increasing total transverse energy.     

Thermal hadron production in Si-Au collisions

The most abundantly produced hadron species in Si - Au collisions at the BNL-AGS (nucleons, pions, kaons, antikaons and hyperons) are shown to be in accord with emission from a thermal resonance gas source. Within the uncertainties of the present data, two freeze-out points are possible. The best agreement is obtained for a temperature T ? 110 MeV and a baryochemical potential μ_B ? 540 MeV, corresponding to about 1/3 standard nuclear density. Another possible point lies at about twice nuclear density, with T ? 160 MeV and μ_B ? 620 MeV. Our analysis takes the isopin asymmetry of the initial state fully into account.     

Transverse energy and charged-particle multiplicity at various centralities at RHIC: Statistical model estimates⋆

The transverse energy and the charged-particle multiplicity at midrapidity are evaluated in a single-freeze-out model for different centrality bins at RHIC at = 130 and 200GeV. The predictions of the model are done at the freeze-out parameters determined earlier from measured particle yields and p_T spectra. The results agree qualitatively well with the experimental data.     

High transverse momentum prompt photon production by π− and π+ on protons at 280 GeV/c

The inclusive cross sections for prompt photon production by π^? and π⁺ on protons have been measured with a beam momentum of 280 GeV/c using a fine grained electromagnetic calorimeter and the CERN Omega spectrometer. The transverse momentum and Feynmanx _F ranges covered are 4.0<p _T <7.0GeV/c and ?0.45<x _F <0.55 respectively. A quantitative comparison of the prompt photon cross section with next-to-leading order QCD predictions using Duke and Owens structure functions is performed.     

High transverse momentum π0 production by π− and π+ on protons at 280 GeV/c

The inclusive cross sections for π⁰ production by π^? and π⁺ on protons have been measured with a beam momentum of 280 GeV/c using a fine grained electromagnetic calorimeter and the CERN Omega spectrometer. The transverse momentum and Feynmanx _F ranges covered are 4.0<p _T <7.0 GeV/c and ?0.45<x _F <0.6 respectively. The data are compared with leading order QCD calculations.     

Universal pion freeze-out phase-space density

Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb–Pb and π–p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose–Einstein distribution f=[exp(E/T)−1]⁻¹ at T∼ 120 MeV, modified for radial expansion. π–p data are also consistent with f, but at T∼ 180 MeV and without radial flow.     

Highlights of the beam energy scan from STAR

The first part of the beam energy scan (BES) program at RHIC was successfully completed in the years 2010 and 2011. First STAR results from particle yield measurements are in good agreement with previously published data from SPS and AGS experiments whereas other results like azimuthal HBT and K/?? event-by-event fluctuations differ at some energies. In addition, new observations like the centrality dependence of chemical freeze-out parameters (T _ch and ?? _B ) or the smoothly increasing difference with decreasing energy in the elliptic flow v ₂ between particles and corresponding anti-particles, are discussed.     

A measurement of the transverse momenta of partons,and of jet fragmentation as a function of √s in p-p collisions

A large solid-angle apparatus consisting of a superconducting solenoid magnet, cylindrical drift chambers and two arrays of lead-glass counters was used to examine particles associated with a high transverse momentum trigger in p-p collisions with three √s values at the CERN ISR. The trigger was given by energy deposition in lead-glass arrays centred at 90°. The trigger transverse momentum range covered was 3 < $\text{p}{}_{\mathrm{<mtext>T\; trig</mtext>}}\text{< 11}\text{GeV}\text{c}$. Results are given for p_out for both individual charged particles, and also for the sum of charged particle momenta in the hemisphere opposite to the trigger. Mean values are then deduced for the parton transverse momentum k_T, and for the jet fragmentation momentum j_T.