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Soft physics observables in heavy ion collisions

First day. Soft physics observables in heavy ion collisions. in view of the LHC. Francesco Prino INFN – Sezione di Torino. Disclaimers:  experimentalist’s point of view  perspectives for the LHC. XIII Mexican school on particles and fields, San Carlos, Mexico, Oct 7th 008.

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Soft physics observables in heavy ion collisions

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  1. First day Soft physics observables in heavy ion collisions in view of the LHC Francesco Prino INFN – Sezione di Torino Disclaimers:  experimentalist’s point of view  perspectives for the LHC XIII Mexican school on particles and fields, San Carlos, Mexico, Oct 7th 008

  2. GOAL(s) of relativistic heavy ion collisions: Study nuclear matter at extreme conditions of temperature and density AND collect evidence for a state where quark and gluons are deconfined (Quark Gluon Plasma) AND study its properties Reminder: phase diagram

  3. Thermal freeze-out Elastic interactions cease Particle dynamics (“momentum spectra”) fixed Tfo (RHIC) ~ 110-130 MeV Chemical freeze-out Inelastic interactions cease Particle abundances (“chemical composition”) are fixed (except maybe resonances) Tch (RHIC) ~ 170 MeV Thermalization time System reaches local equilibrium teq (RHIC) ~ 0.6 fm/c Reminder: space time evolution

  4. Results published in the first year after RHIC startup: Multiplicity of unidentified particles at midrapidity  PHOBOS, sent to PRL on July 19th 2000  PHENIX, sent to PRL on Dec 21th 2000 Elliptic flow of unidentified particles  STAR, sent to PRL on Sept 13th 2000 Particle to anti-particle ratios  STAR, sent to PRL on Apr 13th 2001  PHOBOS, sent to PRL on Apr 17th 2001  BRAHMS, sent to PRL on Apr 28th 2001 Transverse energy distributions  PHENIX, sent to PRL on April 18th 2001 Pseudorapidity distributions of charged particles  PHOBOS, sent to PRL on June 6th 2001  BRAHMS, sent to Phys Lett B on Aug 6th 2001 Elliptic flow of identified particles  STAR, sent to PRL July 5th 2000 … then came the high pT particle suppression from PHENIX (sent to PRL on Sept 9th 2008) Heavy ion results vs. time First 10k-20k events, fast analysis statistics<≈100k events, longer analysis time due to the need of PID, detector calibration, combination of different detectors

  5. Pseudorapidity density of unidentified particles

  6. Particle production in heavy ion collisions • Multiplicity = number of particles produced in a collision • Multiplicity contains information about: • Entropy of the system created in the collision • How the initial energy is redistributed to produce particles in the final state • Energy density of the system (via Bjorken formula) • Mechanisms of particle production (hard vs. soft) • Geometry (centrality of the collision) • NOTE: In hadronic and nuclear collisions particle production is dominated by (non-perturbative) processes with small momentum transfer • Many models, but understanding of multiplicities based on first principles is missing

  7. Particles produced in PbPb at SPS • In central PbPb collisions at SPS (s=17 GeV) more than 1000 particles are created

  8. Particles produced in AuAu at RHIC • In central AuAu collisions at RHIC (s=200 GeV) about 5000 particles are created

  9. Multiplicity and centrality • The number of produced particles is related to the centrality (impact parameter) of the collision • Heavy ion collisions are described as superposition of elementary nucleon-nucleon collisions (e.g. Glauber model) • The number of nucleon-nucleon collisions ( Ncoll ) and the number of participant nucleons ( Npart ) depend on the impact parameter • Each collision/participant contributes to particle production and consequently to multiplicity

  10. Evaluation of Npart and Ncoll r0 (Pb)= 0.16 fm-3 • Glauber model calculations: • Physical inputs: • Woods-Saxon density for colliding nuclei • Nucleon-nucleon inelastic cross-section inel • Numerical calculation of Npart , Ncoll ... vs. impact parameter b C (Pb)= 0.549 fm r0 (Pb)= 6.624 fm

  11. Particle production - Hard • Hard processes = large momentum transfer small distance scales • Interactions at partonic level • Particles produced on a short time scale • Small coupling constant  calculable within perturbative QCD • In A-A collisions: • Modeled as superposition of independent nucleon-nucleon collisions • BINARY SCALING: hard particle production scale with the number of elementary nucleon-nucleon collisions (Ncoll)

  12. 99.5% soft Particle production - Soft • Soft processes = small momentum transfer  large scales • Can not resolve the partonic structure of the nucleons • Large coupling constant  perturbative approach not applicable  need to use phenomenological (non-perturbative) models • In A-A collisions: • WOUNDED NUCLEON MODEL: each nucleon participating in the interaction (wounded) contributes to particle production with a constant amount, no matter how many collisions it suffered • Soft particle production scale with the number of participant nucleons (Npart)

  13. Wounded nucleon model • Based on experimental observation (about 1970s) that multiplicites measured in protno-nucleus collisions scale as: • v = average number of collisions between nucleons (=Ncoll) • So: • since in p-p: Npart = 2 and in p-A: Npart= Ncoll+1

  14. Measuring the multiplicity • Experimentally we count the multiplicity of: • charged (ionizing) particles • particles in a given window covered by the detector (acceptance) • Difficult to compare results between experiments with different acceptances • For this reason, multiplicities are commonly expressed as charged particle densities in a given range of polar angle • Commonly used: number of charged particles in 1 unit of (pseudo)rapidity around midrapidity: Nch(|h|<0.5) o Nch(|y|<0,5) • NOTE: pseudorapidity is easier to access experimentally because it requires to measure just one variable (the polar angle q) and does not require particle identification and measurements of momenta • dN/dh (dN/dy) distributions contain also other information on the dynamics of the interaction

  15. Rapidity at RHIC (collider) • Before collision: • pBEAM=100 GeV/c per nucleon • EBEAM=(mp2+pBEAM2)=100.0044 per nucleon • b=0.999956, gBEAM≈100 • After collision: • Projectile and target nucleons (green) are slowed down and they are located at lower y (and b) values with respect to initial ones • Produced particles (red) are distributed in the kinematical region between the initial projectile and target rapidities • The maximum particle density is in the central rapidity region (midrapidity) :

  16. Rapidity at SPS (fixed target) • Before collision: • pBEAM=158 GeV/c , bBEAM=0.999982 • pTARGET=0 , bTARGET=0 • Midrapidity: • The dN/dy in the center-of-mass reference system is obtained from the one measured in the lab with a translation y’ = y - yMID • The dN/dh distribution does not have this property

  17. pT = pL q = 45 (135) degrees h = ±0.88 pT>pL pL>>pT pL>>pT Pseudorapidity • Midrapidity region • Particles with pT>pL produced at q angles around 90° • Bjorken formula to estimate the energy density in case of a broad plateau at midrapidity invariant for Lorentz boosts: • Fragmentation regions: • Particles with pL>>pT produced in the fragmentation of the colliding nuclei at q angles around 0° e 180°

  18. central peripheral Peak position moves (midrapidity = ybeam/2 ) Particle density at the peak increases with s PbPb collisions at SPS Pb-Pb at 40 GeV/c (√s=8.77 GeV) Pb-Pb at 158 GeV/c (√s=17.2 GeV)

  19. AuAu collisions at RHIC central central peripheral peripheral energy s

  20. Multiplicity per participant pair • We introduce the variables: • which are the particle density at mid-rapidity and the total multiplicity normalized to the number of participant pairs • Motivation • Simple test of the scaling with Npart • If particle production scales with Npart , this variable should not depend on the centrality of the collisions • Simple comparison with pp collisions where Npart=2

  21. dN/dhmax vs. centrality • Yield per participant pair increases by ≈ 25% from peripheral to central Au-Au collisions • Contribution of the hard component of particle production ? • BUT: • The ratio 200 / 19.6 is independent of centrality • A two-component fit with dN/dh [ (1-x) Npart /2 + x Ncoll ] gives compatible values of x (≈ 0.13) at the two energies • Factorization of centrality (geometry) and s (energy) dependence

  22. increasing s – decreasing x dN/dhmax vs. centrality and s • Factorized dependence of dNch/dhmax on centrality and s reproduced by models based on gluon density saturation at small values of Bjorken x Pocket formula: • l and d from ep and eA data • N0 only free parameter • Armesto Salgado Wiedemann, PRL 94 (2005) 022002 • Kharzeev, Nardi, PLB 507 (2001) 121.

  23. dN/dhmax vs. s • The dN/dh per participant pair at midrapidity in central heavy ion collisions increases with ln s from AGS to RHIC energies • The s dependence is different for pp and AA collisions

  24. s = 130 GeV NA50 at 158 A GeV/c Warning • Npart is not a direct experimental observable and affects the scale of both axes of plot of yield per participant pair • Different methods of evaluating Npart give significantly different results!

  25. Total multiplicity (Nch ) vs. centrality • Total multiplicity: • Need to extrapolate in the h regions out of acceptance • Small extrapolation in the case of PHOBOS thanks to the wide h coverage • Nch scales with Npart • Nch per participant pair different from p-p, but compatible with e+e-, collisions at the same energy

  26. Total multiplicity (Nch ) vs. s • Multiplicity per participant pair in heavy ion collisions: • Lower than the one of pp and e+e- at AGS energies • Crosses pp data at SPS energies • Agrees with e+e- multiplicities above SPS energies (s >≈ 17 GeV)

  27. e- p p e+ pp vs. e+e- • The difference between pp and e+e- multiplicities is understood with the “leading particle effect” • The colliding protons exit from the collision carrying away a significant fraction of s • In pp collisions only the energy seff ( < s ) is available for particle production • In e+e- the full s is fully available for particle production • The effective energy seff available for particle production is defined as: • with this definition, multiplicities in e+e- and pp at the same seff result to be in agreement • M. Basile et al.,, Nuovo Cimento A66 N2 (1981) 129.

  28. Universality • The seff dependence of multiplicities in pp, e+e- e AA (for s>15 GeV) follow a universal curve with the trend predicted by Landau hydrodynamics (Nch s1/4) • No leading particle effect in AA (multiple interactions of projectiles) • Universality of hadronization

  29. 62.4 GeV 200 GeV Cu+Cu Preliminary 3-6%, Npart = 100 PHOBOS PHOBOS Cu+Cu Preliminary 3-6%, Npart = 96 Au+Au 35-40%, Npart = 99 Au+Au Preliminary 35-40%,Npart = 98 Gold vs. copper • Unscaled dN/dh very similar for Au-Au and Cu-Cu collisions with the same Npart • Compare central Cu-Cu with semi-peripheral Au-Au • For the same system size (Npart) Au-Au and Cu-Cu are very similar

  30. Limiting fragmentation (I) • Study particle production in the rest frame of one of the two nuclei • Introduce the variable y’ = y - ybeam (or h’ = h – ybeam ) • Limiting fragmentation • Benecke et al., Phys. Rev. 188 (1969) 2159. • At high enough collision energy both d2N/dpTdy and the particle mix reach a limiting value in a region around y’ = 0 • Also dN/dh’ reach a limiting value and become energy independent around h’=0 • Observed for p-p and p-A collisions • In nucleus-nucleus collisions • Particle production in fragmentation regions independent of energy, but NOT necessarily independent of centrality

  31. Limiting fragmentation (II) PHOBOS Phys. Rev. Lett. 91, 052303 (2003) • Particle production independent of energy in fragmentation regions • Extended limiting fragmentation (4 units of h at 200 GeV) • No evidence for boost invariant central plateau

  32. Conclusions • Charged particle multiplicities follow simple scaling laws • Factorization into energy and geometry/system dependent terms • Extended limited fragmentation, no boost-invariant central plateau • Resulting Bjorken energy density in AuAu @ s=200 GeV: Peak energy density Thermalized energy density eBJ well above the predicted critical energy for phase transition to deconfined quarks and glouns

  33. Towards the LHC (I) • Extrapolation of dNch/dhmax vs s • Fit to dN/dh  ln s • Saturation model (dN/dh  sl with l=0.288) • Clearly distinguishable with the first 10k events at the LHC Saturation model Armesto Salgado Wiedemann, PRL 94 (2005) 022002 Central collisions Models prior to RHIC Extrapolation of dN/dhln s 5500

  34. Towards the LHC (II) • Extrapolation of limiting fragmentation behavior • Persistence of extended longitudinal scaling implies that dN/dh grows at most logarithmically with s  difficult to reconcile with saturation models Saturation model dN/dh≈ 1600 Log extrapolation dN/dh≈ 1100 • Borghini Wiedemann, J. Phys G35 (2008) 023001

  35. Multiplicity of identified particles

  36. Hadrochemistry • Measurement of the multiplicity of the various hadronic species (= how many pions, kaons, protons …), i.e. of the chemical composition of the system • Experimental data from SIS to RHIC energies can be described using “thermal” models based on the assumption that hadronization occurs following purely statistical (thermodynamical) laws • This allows to answer some questions about the characteristics of the system: • Was the fireball in thermal and chemical equilibrium at freeze-out time ? • What was the temperature Tch at the instant of chemical freeze-out ? • What was the baryonic content of the fireball ?

  37. Multiplicity of identified particles (I) • Pions vsprotons • At low energies (s<5 GeV) the fireball is dominated by nucleons stopped from the colliding nuclei (high stopping power) • Pions (produced in the interaction) dominate at high energies (s>5 GeV) • The decrease of proton abundance with increasing s indicates an increased transparency of the colliding nuclei

  38. Multiplicity of identified particles (II) • Pions • More abundant among the produced hadrons • due to lower mass and production threshold • Difference between abundances of p+ and p- at low energies due to isospin conservation • Large stopping power at low energies  Fireball dominated by the nucleons of the colliding nuclei  Negative total isospin due to neutron excess (N > Z for heavy nuclei)

  39. Multiplicity of identified particles (III) • Antiprotons • They are produced in the collision • Different from proton case: in the fireball there are both produced and stopped “protons” • Strong s dependence at SPS energies (onset of production) • At RHIC energies number of antiprotons ≈ number of protons • Net-protons ≈ 0 • Small number of protons stopped from the colliding nuclei

  40. Multiplicity of identified particles (IV) • Kaonsand L hyperons • The larger number of K+ and L with respect to their antiparticles (K- and Lbar) at low energies due to quark content of these hadrons • K+ (us) and L (uds) require to newly produce only the strange quark, while light quarks are present in the stopped nucleons • K- (us) and Lbar require the production of 2 or 3 new quarks • Associated production of K+ and L (ss pairs) - - -

  41. Multiplicity of identified particles (V) • Kaonsand Lhyperons • The difference between K+ and K- (and between L e Lbar) decreases with increasing s because the lower stopping power reduces the weight of “stopped” with respect to “produced” quarks • Very similar abundances of Lbar and antiprotons • They are both composed of 3 “produced” quarks and they have similar masses

  42. Multiplicity of identified particles (VI) • Conclusions • Small s (< 5 GeV): • fireball dominated by stopped particles • High baryonic content • Importance of isospin and quarks “stopped” from colliding nuclei • Large s (> 20 GeV): • Fireball dominated by produces particles • Low baryonic content • Mass hierarchy ( Np > NK > Np )

  43. Statistical hadronization models BASIC ASSUMPTIONS • The system (fireball) created in a heavy ion collision is in thermaland chemical equilibrium at the time of chemical freeze-out • The system can be described by a (grand-canonical) partition function and statistical mechanics can be used • Hadronization occurs following a purely statistical (entropy maximization) law • Original idea: Fermi (1950s), Hagedorn (1960s) • The hadronic system is described as an ideal gas of hadrons and resonances • Effective model for a strongly interacting system, consistent with Equation of State resulting from Lattice QCD below the critical temperature for quark and gluon deconfinement • Include all known mesons with mass<≈1.8 GeV and baryons with mass<≈2 GeV

  44. Statistical hadronization models NOTES • Chemical equilibrium is ASSUMED • With this assumption it is possible to calculate the multiplicity of the various hadronic species (how many pions, kaons, protons…) • By comparing the measured multiplicities with the ones predicted by the model it is possible to validate the hypothesis of chemical and thermal equilibrium • Statistical models don’t say nothing about HOW and WHEN the system reaches the chemical and thermal equilibrium • No assumption is made on the presence or not of a partonic phase in the system evolution • The higher hadron mass cut-off in the H&R gas limits the applicability of the model at temperatures T<190 MeV • Not a real limitation: above the critical temperature for parton deconfinement (Tc≈160-200 MeV) hadron gas can no longer be assumed

  45. Grand canonical partition function (I) • Starting point: partition function for a gas of identical particles (Bose or Fermi) of a given hadronic specie i: • a are the eigen-states (with energy Ea) of the single particle hamiltonian (= energy states with spin degeneracy) • mi is the chemical potential which ensures charge conservation • In an hadronic gas (=governed by strong interaction) limited to masses <1.8 GeV (= no charm, bottom and top) there 3 conserved charges (I3 = 3rd isospin component, B= baryon number, S=strangeness) • mI3,mB and mS are the potentials corresponding to each conserved charge • mi = energy needed to add to the system a particle of specie i with quantum numbers I3i, Bi, Si

  46. Grand canonical partition function (II) • Transforming into logarithm: • Continuum limit: • where we have introduced the fugacity:

  47. Particle densities • By performing the integral in the expression of the grand canonical partition function (see backup slides): • The density ni of particles (hadrons) of specie i is: • where Ni is the total number of particles of specie i in the system

  48. Other points • DECAY CHAINS • The total number of measured particles of specie i (e.g. pions) is given by “thermal” production (Ni) + contribution from decays of short-lived particles that are not measured (e.g. r decaying into pions) • EXCLUDED VOLUME CORRECTION • A repulsive term should be introduced in the partition function to account for the repulsive force between hadrons at short distances, • e.g. by assigning a eigen-volume to each hadron (Van Der Waals like) • STRANGENESS SUPPRESSION FACTOR (gS) • Accounts for the fact that the s quark, due to its larger mass may not be completely equilibrated • gS ≈ 1 in heavy ion collisions at SPS and RHIC (= no strangeness suppression)

  49. Free parameters of the model • Particle multiplicities given by: • There are 5 free parameters: T, mB, mS, mI3 and V • There are 3 charge conservation laws which allow to constrain 3 parameters starting from the knowledge of electric charge (=third isospin component), baryonic number and strangeness of the initial state (= protons ZS and neutrons NS “stopped” from colliding nuclei) • Fireball volume V and chemical potentials mS e mI3 are constrained • So, we remain with 2 free parameters: T e mB • plus (possibly) gS

  50. Fit to measured particle ratios • Why use particle ratios ? • Some systematic errors in experimental data cancel in the ratio • The dependence on volume V is removed in model calculations • The determination of V is affected by the uncertainty on the stopping power and on the “excluded volume” corrections • GOAL: find the values of T and mB that minimize the difference between model predicted and measured particle ratios • Done by minimizing a c2 defined as: • Riexp and Rimodel are the measured and predicted paerticle ratios • si is the (statistical + systematic) error on experimental points

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