Refine
Year of publication
Document Type
- Preprint (32)
- Article (8)
- Conference Proceeding (1)
- Report (1)
Language
- English (42)
Has Fulltext
- yes (42)
Is part of the Bibliography
- no (42)
Keywords
- Kollisionen schwerer Ionen (11)
- Quark-Gluon-Plasma (6)
- heavy ion collisions (5)
- heavy-ion collisions (5)
- QGP (4)
- SPS (4)
- quark-gluon plasma (4)
- equation of state (3)
- hydrodynamisches Modell (3)
- quark-gluon-plasma (3)
Institute
We discuss that hadron-induced atmospheric air showers from ultra-high energy cosmic rays are sensitive to QCD interactions at very small momentum fractions x where nonlinear effects should become important. The leading partons from the projectile acquire large random transverse momenta as they pass through the strong field of the target nucleus, which breaks up their coherence. This leads to a steeper x_F-distribution of leading hadrons as compared to low energy collisions, which in turn reduces the position of the shower maximum Xmax. We argue that high-energy hadronic interaction models should account for this effect, caused by the approach to the black-body limit, which may shift fits of the composition of the cosmic ray spectrum near the GZK cutoff towards lighter elements. We further show that present data on Xmax(E) exclude that the rapid ~ 1/x^0.3 growth of the saturation boundary (which is compatible with RHIC and HERA data) persists up to GZK cutoff energies. Measurements of pA collisions at LHC could further test the small-x regime and advance our understanding of high density QCD significantly.
We calculate prompt photon production in high-energy nuclear collisions. We focus on the broadening of the intrinsic transverse momenta of the partons in the initial state from nuclear e ects, and their influence on the prompt photon pt distribution. Comparing to WA98 data from Pb+Pb collisions at s = 17.4A GeV we find evidence for the presence of nuclear broadening at high pt in this hard process. Below pt < 2.7 GeV the photon distribution is due to small momentum transfer processes. At RHIC energy, s = 200A GeV, the e ect of intrinsic transverse momentum on the spectrum of prompt photons is less prominent. The region pt = 3 4 GeV would be the most promising for studying the nuclear broadening effects at that energy. Below pt = 2 3 GeV the contribution from large momentum transfers flattens out, and we expect that region to be dominated by soft contributions.
We calculate prompt photon production in high-energy nuclear collisions. We focus on the broadening of the intrinsic transverse momenta of the partons in the initial state from nuclear effects, and their influence on the prompt photon pt distribution. Comparing to WA98 data from Pb+Pb collisions at s = 17.4A GeV we find evidence for the presence of nuclear broadening at high pt in this hard process. Below pt < 2.7 GeV the photon distribution is due to small momentum transfer processes. At RHIC energy, s = 200A GeV, the e ect of intrinsic transverse momentum on the spectrum of prompt photons is less prominent. The region pt = 3 4 GeV would be the most promising for studying the nuclear broadening e ects at that energy. Below pt = 2 3 GeV the contribution from large momentum transfers flattens out, and we expect that region to be dominated by soft contributions.
We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that there is stronger attraction on distance scales on the order of the inverse Debye mass for quark pairs aligned along the direction of anisotropy than for transverse alignment.
We study the production of transversely polarized Λ hyperons in high-energy collisions of protons with large nuclei. The large gluon density of the target at saturation provides an intrinsic semi-hard scale which should naturally allow for a weak-coupling QCD description of the process in terms of a convolution of the quark distribution of the proton with the elementary quark–nucleus scattering cross section (resummed to all twists) and a fragmentation function. In this case of transversely polarized Λ production we employ a so-called polarizing fragmentation function, which is an odd function of the transverse momentum of the Λ relative to the fragmenting quark. Due to this kt-odd nature, the resulting Λ polarization is essentially proportional to the derivative of the quark–nucleus cross section with respect to transverse momentum, which peaks near the saturation momentum scale. Such processes might therefore provide generic signatures for high parton density effects and for the approach to the “black-body” (unitarity) limit of hadronic scattering.
We solve the coupled Wong Yang–Mills equations for both U(1) and SU(2) gauge groups and anisotropic particle momentum distributions numerically on a lattice. For weak fields with initial energy density much smaller than that of the particles we confirm the existence of plasma instabilities and of exponential growth of the fields which has been discussed previously. Also, the SU(2) case is qualitatively similar to U(1), and we do find significant “abelianization” of the non-Abelian fields during the period of exponential growth. However, the effect nearly disappears when the fields are strong. This is because of the very rapid isotropization of the particle momenta by deflection in a strong field on time scales comparable to that for the development of Yang–Mills instabilities. This mechanism for isotropization may lead to smaller entropy increase than collisions and multiplication of hard gluons, which is interesting for the phenomenology of high-energy heavy-ion collisions.
We introduce a model for the real-time evolution of a relativistic fluid of quarks coupled to non-equilibrium dynamics of the long wavelength (classical) modes of the chiral condensate. We solve the equations of motion numerically in 3+1 spacetime dimensions. Starting the evolution at high temperature in the symmetric phase, we study dynamical trajectories that either cross the line of first-order phase transitions or evolve through its critical endpoint. For those cases, we predict the behavior of the azimuthal momentum asymmetry for highenergy heavy-ion collisions at nonzero impact parameter.
To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for nonequilibrium e ects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time teq CM H 5 fm/c C 2RAu/³CM. Observables which are sensitive to the early stage of the collision (like e.g. nucleon flow) therefore di er considerably from those calculated in the one-fluid model.
We discuss the early evolution of ultrarelativistic heavy-ion collisions within a multi- fluid dynamical model. In particular, we show that due to the finite mean-free path of the particles compression shock waves are smeared out considerably as compared to the one-fluid limit. Also, the maximal energy density of the baryons is much lower. We discuss the time scale of kinetic equilibration of the baryons in the central region and its relevance for directed flow. Finally, thermal emission of direct photons from the fluid of produced particles is calculated within the three-fluid model and two other simple expansion models. It is shown that the transverse momentum and rapidity spectra of photons give clue to the cooling law and the early rapidity distribution of the photon source.
Abstract: We study transverse expansion and directed flow in Au(11AGeV)Au reactions within a multi-fluid dynamical model. Although we do not employ an equation of state (EoS) with a first order phase transition, we find a slow increase of the transverse velocities of the nucleons with time. A similar behaviour can be observed for the directed nucleon flow. This is due to non-equilibrium e ects which also lead to less and slower conversion of longitudinal into transverse momentum. We also show that the proton rapidity distribution at CERN energies, as calculated within this model, agrees well with the preliminary NA44-data.
We investigate the excitation function of quark-gluon plasma formation and of directed in-plane flow of nucleons in the energy range of the BNLAGS and for the Ekin Lab = 40A GeV Pb+Pb collisions performed recently at the CERN-SPS. We employ the three-fluid model with dynamical unification of kinetically equilibrated fluid elements. Within our model with first-order phase transition at high density, droplets of QGP coexisting with hadronic matter are produced already at BNL-AGS energies, Ekin Lab C 10A GeV. A substantial decrease of the isentropic velocity of sound, however, requires higher energies, Ekin Lab C 40A GeV. We show the e ect on the flow of nucleons in the reaction plane. According to our model calculations, kinematic requirements and EoS effects work hand-in-hand at Ekin Lab = 40A GeV to allow the observation of the dropping velocity of sound via an increase of the directed flow around midrapidity as compared to top BNL-AGS energy.
Noneequilibrium models (three-fluid hydrodynamics and UrQMD) use to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions. It is demonstrated that these two models - although they do treat the most interesting early phase of the collisions quite differently(thermalizing QGP vs. coherent color fields with virtual particles) - both yields a reasonable agreement with a large variety of the available heavy ion data.
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Dilepton spectra are calculated with and without shifting the rho pole. Except for S+Au collisions our calculations reproduce the CERES data.
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Effects of a density dependent pole of the rho-meson propagator on dilepton spectra are studied for different systems and centralities at CERN energies.
We calculate the yields of a variety of hadrons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities di ering strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
We investigate the excitation function of directed flow, which can provide a clear signature of the creation of the QGP and demonstrate that the minimum of the directed flow does not correspond to the softest point of the EoS for isentropic expansion. A novel technique measuring the compactness is introduced to determine the QGP transition in relativistic-heavy ion collisions: The QGP transition will lead to higher compression and therefore to higher compactness of the source in coordinate space. This e ect can be observed by pion interferometry. We propose to measure the compactness of the source in the appropriate principal axis frame of the compactness tensor in coordinate space.
Compactness is introduced as a new method to search for the onset of the quark matter transition in relativistic heavy ion collisions. That transition supposedly leads to stronger compression and higher compactness of the source in coordinate space. That effect could be observed via pion interferometry. We propose to measure the compactness of the source in the appropriate principal axis frame of the compactness tensor in coordinate space.
Hadron and hadron cluster production in a hydrodynamical model including particle evaporation
(1997)
We discuss the evolution of the mixed phase at RHIC and SPS within boostinvariant hydrodynamics. In addition to the hydrodynamical expansion, we also consider evaporation of particles o the surface of the fluid. The back-reaction of this evaporation process on the dynamics of the fluid shortens the lifetime of the mixed phase. In our model this lifetime of the mixed phase is d 12 fm/c in Au + Au at RHIC and d 6.5 fm/c in Pb + Pb at SPS, even in the limit of vanishing transverse expansion velocity. Strong separation of strangeness occurs, especially in events (or at rapidities) with relatively high initial net baryon and strangeness number, enhancing the multiplicity of MEMOs (multiply strange nuclear clusters). If antiquarks and antibaryons reach saturation in the course of the pure QGP or mixed phase, we find that at RHIC the ratio of antideuterons to deuterons may exceed 0.3 and even 4He/4He > 0.1. In S + Au at SPS we find only N/N H 0.1. Due to fluctuations, at RHIC even negative baryon number at midrapidity is possible in individual events, so that the antibaryon and antibaryon-cluster yields exceed those of the corresponding baryons and clusters.
We analyze the hadronic freeze-out in ultra-relativistic heavy ion collisions at RHIC in a transport approach which combines hydrodynamics for the early, dense, deconfined stage of the reaction with a microscopic non-equilibrium model for the later hadronic stage at which the hydrodynamic equilibrium assumptions are not valid. With this ansatz we are able to self-consistently calculate the freeze-out of the system and determine space-time hypersurfaces for individual hadron species. The space-time domains of the freeze-out for several hadron species are found to be actually four-dimensional, and di er drastically for the individual hadrons species. Freeze-out radii distributions are similar in width for most hadron species, even though the is found to be emitted rather close to the phase boundary and shows the smallest freeze- out radii and times among all baryon species. The total lifetime of the system does not change by more than 10% when going from SPS to RHIC energies.
We discuss a model for the space-time evolution of ultrarelativistic heavy-ion collisions which employs relativistic hydrodynamics within one region of the forward light-cone, and microscopic transport theory (i.e. UrQMD) in the complement. Our initial condition consists of a quark-gluon plasma which expands hydrodynamically and hadronizes. After hadronization the solution eventually changes from expansion in local equilibrium to free streaming, as determined selfconsistently by the interaction rates between the hadrons and the local expansion rate. We show that in such a scenario the inverse slopes of the mT -spectra of multiple strange baryons ( Xi,Omega) are practically una ected by the purely hadronic stage of the reaction, while the flow of p's and Lambda's increases. Moreover, we find that the rather soft transverse expansion at RHIC energies (due to a first-order phase transition) is not washed out by strong rescattering in the hadronic stage. The earlier kinetic freeze-out as compared to SPS-energies results in similar inverse slopes (of the mT -spectra of the hadrons in the final state) at RHIC and SPS energies.
We calculate the yields of pions, kaons, and Æ-mesons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities differing strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
We study the time scale for pressure equilibration in heavy ion collisions at AGS energies within the three-fluid hydrodynamical model and a microscopic cascade model (UrQMD). We find that kinetic equilibrium is reached in both models after a time of 5 fm/c (center-of-mass time). Thus, observables which are sensitive to the early stage of the reaction differ considerably from the expectations within the instant thermalization scenario (one-fluid hydrodynamical model).
We investigate hadron production and transverse hadron spectra in nucleus-nucleus collisions from 2 A·GeV to 21.3 A·TeV within two independent transport approaches (UrQMD and HSD) based on quark, diquark, string and hadronic degrees of freedom. The enhancement of pion production in central Au+Au (Pb+Pb) collisions relative to scaled pp collisions (the ’kink’) is described well by both approaches without involving a phase transition. However, the maximum in the K+ p+ ratio at 20 to 30 A·GeV (the ’horn’) is missed by ~ 40%. Also, at energies above ~5 A·GeV, the measured K± mT-spectra have a larger inverse slope than expected from the models. Thus the pressure generated by hadronic interactions in the transport models at high energies is too low. This finding suggests that the additional pressure - as expected from lattice QCD at finite quark chemical potential and temperature - might be generated by strong interactions in the early pre-hadronic/partonic phase of central heavy-ion collisions. Finally, we discuss the emergence of density perturbations in a first-order phase transition and why they might affect relative hadron multiplicities, collective flow, and hadron mean-free paths at decoupling. A minimum in the collective flow v2 excitation function was discovered experimentally at 40 A·GeV - such a behavior has been predicted long ago as signature for a first order phase transition.
Entropy production in the compression stage of heavy ion collisions is discussed within three distinct macroscopic models (i.e. generalized RHTA, geometrical overlap model and three-fluid hydrodynamics). We find that within these models \sim 80% or more of the experimentally observed final-state entropy is created in the early stage. It is thus likely followed by a nearly isentropic expansion. We employ an equation of state with a first-order phase transition. For low net baryon density, the entropy density exhibits a jump at the phase boundary. However, the excitation function of the specific entropy per net baryon, S/A, does not reflect this jump. This is due to the fact that for final states (of the compression) in the mixed phase, the baryon density \rho_B increases with \sqrt{s}, but not the temperature T. Calculations within the three-fluid model show that a large fraction of the entropy is produced by nuclear shockwaves in the projectile and target. With increasing beam energy, this fraction of S/A decreases. At \sqrt{s}=20 AGeV it is on the order of the entropy of the newly produced particles around midrapidity. Hadron ratios are calculated for the entropy values produced initially at beam energies from 2 to 200 AGeV.
We calculate the Gaussian radius parameters of the pion-emitting source in high energy heavy ion collisions, assuming a first order phase transition from a thermalized Quark-Gluon-Plasma (QGP) to a gas of hadrons. Such a model leads to a very long-lived dissipative hadronic rescattering phase which dominates the properties of the two-pion correlation functions. The radii are found to depend only weakly on the thermalization time tau i, the critical temperature T c (and thus the latent heat), and the specific entropy of the QGP. The dissipative hadronic stage enforces large variations of the pion emission times around the mean. Therefore, the model calculations suggest a rapid increase of R out/R side as a function of K T if a thermalized QGP were formed.
We study the thermodynamic properties of infinite nuclear matter with the Ultrarelativistic Quantum Molecular Dynamics (URQMD), a semiclassical transport model, running in a box with periodic boundary conditions. It appears that the energy density rises faster than T4 at high temperatures of T approx. 200 - 300 MeV. This indicates an increase in the number of degrees of freedom. Moreover, We have calculated direct photon production in Pb+Pb collisions at 160 GeV/u within this model. The direct photon slope from the microscopic calculation equals that from a hydrodynamical calculation without a phase transition in the equation of state of the photon source.
Impact parameter dependencies in Pb(160 AGeV)+Pb reactions : hydrodynamical vs. cascade calculations
(1999)
We investigate the impact parameter dependence of the specific entropy S/A in relativistic heavy ion collisions. Especially the anti-Lambda/anti-proton ratio is found to be a useful tool to distinguish between chemical equilibrium assumptions assumed in hydrodynamics (here: the 3-fluid model) and the chemical non-equilibrium scenario like in microscopic models as the UrQMD model.
Entropy production in the initial compression stage of relativistic heavy-ion collisions from AGS to SPS energies is calculated within a three-fluid hydrodynamical model. The entropy per participating net baryon is found to increase smoothly and does not exhibit a jump or a plateau as in the 1-dimensional one-fluid shock model. Therefore, the excess of pions per participating net baryon in nucleus-nucleus collisions as compared to proton-proton reactions also increases smoothly with beam energy.
Nonequilibrium models (three-fluid hydrodynamics, UrQMD, and quark molecular dynamics) are used to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions from the SPS via RHIC to LHC. It is demonstrated that these models - although they do treat the most interesting early phase of the collisions quite differently (thermalizing QGP vs. coherent color fields with virtual particles) -- all yield a reasonable agreement with a large variety of the available heavy ion data. Hadron/hyperon yields, including J/Psi meson production/suppression, strange matter formation, dileptons, and directed flow (bounce-off and squeeze-out) are investigated. Observations of interesting phenomena in dense matter are reported. However, we emphasize the need for systematic future measurements to search for simultaneous irregularities in the excitation functions of several observables in order to come close to pinning the properties of hot, dense QCD matter from data. The role of future experiments with the STAR and ALICE detectors is pointed out.
The transverse momentum distribution of prompt photons coming from the very early phase of ultrarelativistic heavy ion collisions for the RHIC and LHC energies is calculated by means of perturbative QCD. We calculate the single photon cross section (A + B -> gamma + X) by taking into account the partonic sub processes q + q -> gamma + g and q + g -> gamma + q as well as the Bremsstrahlung corrections to those processes. We choose a lower momentum cut-off k0 = 2 GeV separating the soft physics from perturbative QCD. We compare the results for those primary collisions with the photons produced in reactions of the thermalized secondary particles, which are calculated within scaling hydrodynamics. The QCD processes are taken in leading order. Nuclear shadowing corrections, which alter the involved nuclear structure functions are explicitly taken into account and compared to unshadowed results. Employing the GRV parton distribution parametrizations we find that at RHIC prompt QCD-photons dominate over the thermal radiation down to transverse momenta kT ≈ 2 GeV. At LHC, however, thermal radiation from the QGP dominates for photon transverse momenta kT ≤ 5 GeV, if nuclear shadowing effects on prompt photon production are taken into account.
Direct photon production in central Pb+Pb collisions at CERN-SPS energy is calculated within the relativistic microscopic transport model UrQMD, and within distinctly di erent versions of relativistic hydrodynamics. We find that in UrQMD the local momentum distributions of the secondaries are strongly elongated along the beam axis initially. Therefore, the preequilibrium contribution dominates the photon spectrum at transverse momenta above H 1.5 GeV. The hydrodynamics prediction of a strong correlation between the temperature and radial expansion velocities on the one hand and the slope of the transverse momentum distribution of direct photons on the other hand thus is not recovered in UrQMD. The rapidity distribution of direct photons in UrQMD reveals that the initial conditions for the longitudinal expansion of the photon source (the meson fluid ) resemble rather boostinvariance than Landau-like flow.
Report-no: UFTP-492/1999 Journal-ref: Phys.Rev. C61 (2000) 024909 We investigate flow in semi-peripheral nuclear collisions at AGS and SPS energies within macroscopic as well as microscopic transport models. The hot and dense zone assumes the shape of an ellipsoid which is tilted by an angle Theta with respect to the beam axis. If matter is close to the softest point of the equation of state, this ellipsoid expands predominantly orthogonal to the direction given by Theta. This antiflow component is responsible for the previously predicted reduction of the directed transverse momentum around the softest point of the equation of state.
A generic property of a first-order phase transition in equilibrium, and in the limit of large entropy per unit of conserved charge, is the smallness of the isentropic speed of sound in the mixed phase . A specific prediction is that this should lead to a non-isotropic momentum distribution of nucleons in the reaction plane (for energies < 40A GeV in our model calculation). On the other hand, we show that from present effective theories for low-energy QCD one does not expect the thermal transition rate between various states of the effective potential to be much larger than the expansion rate, questioning the applicability of the idealized Maxwell/Gibbs construction. Experimental data could soon provide essential information on the dynamics of the phase transition.
The microscopic phasespace approach URQMD is used to investigate the stopping power and particle production in heavy systems at SPS and RHIC energies. We find no gap in the baryon rapidity distribution even at RHIC. For CERN energies URQMD shows a pile up of baryons and a supression of multi-nucleon clusters at midrapidity.
The extension of the Periodic System into hitherto unexplored domains - anti- matter and hypermatter - is discussed. Starting from an analysis of hyperon and single hypernuclear properties we investigate the structure of multi-hyperon objects (MEMOs) using an extended relativistic meson field theory. These are contrasted with multi-strange quark states (strangelets). Their production mechanism is stud- ied for relativistic collisions of heavy ions from present day experiments at AGS and SPS to future opportunities at RHIC and LHC. It is pointed out that abso- lutely stable hypermatter is unlikely to be produced in heavy ion collisions. New attention should be focused on short lived metastable hyperclusters ( / 10 10s) and on intensity interferometry of multi-strange-baryon correlations.
The rapidity distribution of thermal photons produced in Pb+Pb collisions at CERN-SPS energies is calculated within scaling and three- fluid hydrodynamics. It is shown that these scenarios lead to very different rapidity spectra. A measurement of the rapidity dependence of photon radiation can give cleaner insight into the reaction dynamics than pion spectra, especially into the rapidity dependence of the temperature.
We calculate thermal photon and neutral pion spectra in ultrarelativistic heavy-ion collisions in the framework of three-fluid hydrodynamics. Both spectra are quite sensitive to the equation of state used. In particular, within our model, recent data for S + Au at 200 AGeV can only be understood if a scenario with a phase transition (possibly to a quark-gluon plasma) is assumed. Results for Au+Au at 11 AGeV and Pb + Pb at 160 AGeV are also presented.
We study dilepton production from a quark-gluon plasma of given energy density at finite quark chemical potential μ and find that the dilepton production rate is a strongly decreasing function of μ. Therefore, the signal to background ratio of dileptons from a plasma created in a heavy-ion collision may decrease significantly.
The ALICE experiment at the LHC has studied J/psi production at mid-rapidity in pp collisions at sqrt{s}=7 TeV through its electron pair decay on a data sample corresponding to an integrated luminosity L_int = 5.6nb-1. The fraction of J/psi from the decay of long-lived beauty hadrons was determined for J/psi candidates with transverse momentum p_t>1.3 GeV/c and rapidity |y|<0.9. The cross section for prompt J/psi mesons, i.e. directly produced J/psi and prompt decays of heavier charmonium states such as the Psi(2S) and Csi_c resonances, is sigma_prompt-J/psi(pt > 1.3 GeV/c, |y| < 0.9) = 8.3 +- 0.8(stat.) +- 1.1(syst.) + 1.5 - 1.4(syst. pol.) micro barn. The cross section for the production of b-hadrons decaying to J/psi with p_t>1.3 GeV/c and |y|<0.9 is sigma_{J/psi<-h_B} = 1.46 +- 0.38(stat.) + 0.26 -0.32(syst.) micro barn. The results are compared to QCD model predictions. The shape of the p_t and y distributions of b-quarks predicted by perturbative QCD model calculations are used to extrapolate the measured cross section to derive the b-bbar pair total cross section and dsigma/dy at mid-rapidity.