Countrate estimates. Particle production in heavy ion collisions

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Transcript of Countrate estimates. Particle production in heavy ion collisions

  • Countrate estimates

  • Particle production in heavy ion collisions

  • Particle multiplicities for central Au+Au collisionsfrom UrQMD calculations Au+Au 6 AGeV central minimum bias 0.00072 0.00018Example production

    Direct production:NN + - NN (Ethr = 12.7 GeV)

    Production via multiple collisions:

    NN K+N, NN K+K-NN, K- - 0, -K- - -

  • R = reactions/secNB = beam particles/sec = cross section [barn = 10-24cm2]NT /F = target atoms/cm2 = NA d/A with Avogadros Number NA = 6.021023 mol-1, material density [g/cm3], target thickness d [cm] atomic number A Reaction rate: R = NB NT/F

  • Reaction cross section and target thicknessReaction cross section: R = (2 R)2 = 4 (r0A1/3)2 with r0=1.2 fmAu+Au collisions: A=197 R = 6.1 barn, 1 barn = 10-24 cm2Reaction probability for Au+Au collisions: R/NB = R NT/F = 6.1 b 6.021023d/A = 6.1 10-24 cm2 6.02102319.3 g/cm3d/197 = 1%

    target thickness d = 0.027 cm

  • Production cross sections for min. bias Au+Au collisions at 6 AGeV:

    () = M() x R = 1.810-4 x 6.1 b = 1.110-3 bParticle production probabilities for min. bias Au+Au at 6 AGeV:R()/NB =()NAd/A = () [b]1.610-3 = 1.810-6recorded particles: R()/NB = ?Experimental efficiencies?

  • Acceptances and Efficiencies

    = p Det Trigg DAQ analysiswith = angular acceptance p = momentum acceptanceDet = detector efficienciesTrigg = trigger efficienciesDAQ = deadtime correction of DAQanalysis = efficiency of analysis (track finding, cuts for background suppression , ...)Typical values: 0.5, p 0.8, Det 0.9, Trigg 0.9, DAQ 0.5, analysis 0.3,

    0.05

  • Typical detection probabilities in Au+Au at 5 AGeV:R()/NB = 1.810-60.05 = 910-8

    Recorded rates for a Au-beam intensity of 108/sec:R() = 108/sec x 910-8 = 9/sec

    Recorded yield after 1 week beam on target: Y = 9 x 3600 x 24 x 7 = 5.4106

    These numbers refers to one collision system and one beam energy only. Systematic studies require excitation functions (several beam energies) with different collision systems !

  • Observables

    U+U 23 AGeV

  • Pion multiplicities per participating nucleons

  • meson-baryon interaction

  • SIS: KaoS AGS: E802,E866 SPS: NA49Production of K+ und K- mesons in central AuAu/PbPb collisionsNN K+LN: Elab 1.6 GeVNN K+K-NN: Elab 2.5 GeV RHICRHIC

  • Meson production in central Au+Au collisionsW. Cassing, E. Bratkovskaya, A. Sibirtsev, Nucl. Phys. A 691 (2001) 745

  • Rapidity distributions Rapidity: y(0) = y-ym with y =0.5 ln [(E+pz)/(E-pz)] Central Pb+Pb collisions at SPS energies C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

  • Particle yields in midrapidity from central A+A collisions

  • Partition functionParticle densitygi = (2Ji+1) spin degeneracy factor, temperature T, and Ei = (p2 + m2)i the total energy. net baryon density: B 4 ( mT/2)3/2 x [exp((B-m)/T) - exp((-B-m)/T)] baryons - antibaryons

  • Central Au+Au collisions (midrapidity): statistical model results E = 2 AGeVE = 4 AGeVE = 6 AGeVE = 8 AGeVA. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

  • E = 10.7 AGeVE = 40 AGeVE = 80 AGeVCentral Au+Au collisions (midrapidity): statistical model results

  • E = 158 AGeVCentral Au+Au collisions (midrapidity): Statistical model results

  • Central Au+Au collisions (midrapidity): Statistical model results

  • Central Au+Au collisions (midrapidity): Statistical model results

  • Central Au+Au collisions (midrapidity): Statistical model results

  • Central Au+Au collisions (midrapidity): Statistical model results

  • Central Au+Au collisions (midrapidity): Statistical model results

  • Strangeness/pion ratios Decrease of baryon-chemicalpotential: transition frombaryon-dominatedto meson-dominatedmatter ?C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

  • Strangeness = 2 (K+ + K) + 1.54 ( + )Entropy = 1.5 (+ + ) + 2 p

  • The freeze-out curve in the QCD phase diagramA. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

  • J. Randrup and J. Cleymans, hep-ph/0607065

  • Particle yields

  • Pion production in Au + Au collisions at 1.5 AGeVData: T. Schuck, Dipl. Thesis 2003, GSI/Uni Frankfurt

  • "Boltzmann" parameterisation:

    d3/dp3 = C1 exp(-E/T1) + C2 exp(-E/T2)

  • Kinetic energy of a particle:Ek = Eth + Eflow = 3/2 kT + m/2flow2The explosion of the fireball Blast wave model: isotropically expanding System with temperature T P.J. Siemens and J.O. Rasmussen, Phys. Rev. Lett. 42 (1979) 880

    dotted line: f = const. solid line: Hubble expansion f = rH

  • N. Xu, Int. J. Mod. Phys. E16 (2007) 715

  • Determination of collision centralityNumber of participating nucleons in A+A collisions : Apart = 2 x A/Z x (Z Zspec) or Zero Degree Calorimeter: EZDC= Ebeam APro-Spec and Apart = 2 ( A - EZDC/Ebeam)

  • Determination of the reaction planeTransverse Momentum Method: P. Danielewicz & G. Odyniec, Phys. Lett. 157 B (1985) 146Q = p = 1 fr y>ycmR = arctan(Qy/Qx)

    Dispersion of the reaction plane:Sub-Event-Method: = 1 - 2

  • The pion clock: in-plane emission in Au+Au collisions at 1.0 AGeVA. Wagner et al., Phys. Rev. Lett. 85 (2000) 18

  • Expect Large Pressure Gradients Hydro FlowThe Flow Probe

  • Dense baryonic matter up to 3 0:

    Probing the nuclear equation-of-state with heavy ions

  • Observable in HI collisions: collective flow (driven by pressure)The equation-of-state of (symmetric) nuclear matter

    E/A(ro) = -16 MeV d(E/A)(ro)/dr = 0 Compressibility:k = 9r2 d2 (E/A)/ dr2 k = 200 MeV: "soft" EOSk = 380 MeV: "stiff" EOSC. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1Equation of state:

    PV T E P E/V E/A

  • Definition of the potentials in transport codesBethe Weizsaecker mass formula:Volume term(with eos)+Surface term+Coulomb term+symmetry term(+pairing term not included)2 and 3 body interactions (no equilibrium required)

  • The eos in IQMDafter the convolution of the Skyrme type potentials supplemented by momentum dependent interactions (mdi) for infinite nuclear matter at equilibriumhardsoft

  • Energy per nucleon in nuclear matter (Skyrme potential):E/A = 3kF2/(10M) + ra/2 + brg /(1 + g) The nuclear matter equation of state Conditions: E/A(ro) = -16 MeV d(E/A)(ro)/dr = 0 Compressibility:k = 9r2 d2 (E/A)/ dr2 = 200 - 400 MeV

  • Baryon/energy density in central cell (Au+Au, b=0 fm):Transport code HSD: mean field, hadrons + resonances + strings

    E. Bratkovskaya, W. Cassing Baryon and energy densities at FAIR energies

  • Dynamics of a semi-central Au+Au collision at 2 AGeV(BUU calculation, P. Danielewicz, MSU)

  • Azimuthal angle distribution:dN/dF (1 + 2v1 cosF + 2v2 cos2F)C.Pinkenburg et al., (E895), Phys. Rev. Lett. 83 (1999) 1295Azimuthal angular distribution of protons measured in Au+Au collisions at 1.15, 2, 4, 6, 8 AGeVRapidity: y(0) = y-ym with y = 0.5 ln [(E+pz)/(E-pz)] AGeV

  • dN/dF (1 + 2v1 cosF + 2v2 cos2F)P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 Probing the nuclear equation-of-state: proton collective flow Transverse in-plane flow: Elliptic flow: F = d(px/A)/d(y/ycm) K = 170 210 MeV K = 170 380 MeV

  • New data: Au + Au collisions at SIS energies A. Andronic et al. (FOPI Collaboration) Phys. Lett. B612 (2005) 173

  • P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 pressure P = 2 ( (/) / )with nuclear density and energy density Pressure as function of density

    Independent observable ? particle production

    Within microscopic transport models the collective flow is sensitive to:

    The nuclear matter equation of state

    In-medium nucleon-nucleon cross sections

    Momentum dependent interactions

  • Probing the equation-of-state of symmetric nuclear matter:Kaon production in Au+Au collisions at 1 AGeV pp K+p (Ethres= 1.6 GeV)K+ reabsorption negligible

  • NN K+LN reduced (Ebeam = 1.6 GeV)pN K+L, DN K+LN enhanced MK+ (Apart) 1.8

    Mp+ Apart

    Kaon production in Au+Au collisions at subthreshold beam energies

  • The creation of strange mesons

  • Probing the nuclear equation-of-state ( = 1 3 0) by K+ meson production in C+C and Au+Au collisionsTransport model (RBUU)Au+Au at 1 AGeV: = 200 MeV max 2.9 0 K+ = 380 MeV max 2.4 0 K+Reference system C+C: K+ yield not sensitive to EOSIdea: K+ yield baryon density compressibility Experiment: C. Sturm et al., (KaoS Collaboration), Phys. Rev. Lett. 86 (2001) 39Theory: Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

  • The compressibility of nuclear matterExperiment: C. Sturm et al., (KaoS Collaboration) Phys. Rev. Lett. 86 (2001) 39Theory: QMD Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 IQMD Ch. Hartnack, J. Aichelin, J. Phys. G 28 (2002) 1649soft equation-of-state: k 200 MeVAu/C ratio: cancellation of systematic errors both in experiment and theory

  • Exploring the "nuclear" EOS at 30 < < 70

    Measure excitation function of (multi-strange) hyperon production in heavy-ion collisions from 2 - 15 AGeV (no data yet):

    Direct produc