1. Francesco Prino INFN – Sezione di Torino
Charged particle pseudorapidity distributions in nucleus-nucleus collisions from SPS to LHC
Francesco Prino
INFN – Sezione di Torino
XLIV International Winter Meeting on Nuclear Physics
Bormio, January 31st, 2006
OUTLINE:
Physics motivation
Experimental requirements and techniques
Experimental results from SPS and RHIC
Perspectives for ALICE at the LHC

2. Introduction: Physics motivation

3. Particle production in nuclear collisions
Particle multiplicity in nucleus-nucleus collisions (= number of particles produced in the collision) = global observable carrying important information about:
How initial energy available is redistributed for producing particles in the final state
Entropy of the system created in the collision
Initial energy density, parton density in the initial state
Centrality of the collision
Nucleus-nucleus collisions described in multicollision models as a superposition of elementary (nucleon-nucleon) collisions
Underlying dynamics of the particle production mechanism
Hard processes
Large momentum transfer
Small distance
Interactions at partonic level
Governed by perturbative QCD
Scale like the number of elementary collisions (Ncoll)
Soft processes
Small momentum transfer
Large distance
Described by phenomenological non-perturbative models
Scale like the number of participant nucleons (Npart)

4. Evaluation of Npart and Ncoll
Glauber model calculations:
Physical inputs:
Woods-Saxon density for colliding nuclei
Nucleon-nucleon inelastic cross-section inel
Numerical calculation of:
Interaction probability, Npart , Nspect, Ncoll vs. impact parameter b
r0 (Pb)= 0.16 fm-3
C (Pb)= fm
r0 (Pb)= fm
Accel.
AGS
SPS
RHIC
LHC
√s (GeV)
3-5 17
200
5500
sinel 21 33 42 60

5. Key measurements Scaling of particle multiplicity vs. energy
Change the energy available for particle production
Change the number of collision per participant
Handle for changing the balance of particle production between soft and hard processes
Scaling of particle multiplicity vs. centrality of the collision
Change the volume of particle production region ( Npart)
Handle for changing the system size
Second handle for changing the balance between soft and hard processes
Scaling of particle multiplicity for different colliding nuclei
Second handle to change the system size

6. Particle momentum distributions
Particle momenta decomposed
Longitudinal momentum (pL)
Transverse momentum (pT)
Rapidity variable
Lorentz invariant
Pseudorapidity variable
h≈y for large momenta
h more easily accessed experimentally

7. dN/dh – basics pT = pL q = 45 (135) degrees h = ±0.88 pT>pL
Midrapidity peak / plateau
Sensitive to hadroproduction details
Related to energy density
Bjorken formula (requires a “central-plateau structure” in the y distribution of produced particles)
Boost-invariant central plateau?
Width of the distribution
Information on longitudinal expansion and stopping power (stopping vs. transparency)
Fragmentation regions
Investigate effects connected with target and projectile fragmentation
pT = pL
q = 45 (135) degrees
h = ±0.88
pT>pL
pL>>pT

8. Experimental requirements and techniques

9. Experimental issues Acceptance: Analysis techniques
Large h coverage to measure particles at mid-rapidity and in fragmentation regions
Low pT cut-off if a magnetic field is present
Analysis techniques
Count fired channels (hits) on detectors NA50, PHOBOS
In general 1 hit NOT EQUAL to 1 particle because of:
PHYSICAL PROCESSES in the detector volume (multiple occupancy, charge sharing…)
INSTRUMENTAL PROBLEMS (electronic noise, cross-talk …)
What is done is to count CLUSTERS (i.e. groups of contiguous strips firing together) and apply a correction to go from clusters to crossing particles
Measure energy deposition in detector channels NA57, BRAHMS, PHOBOS
Correction for Landau distribution of energy deposition required
Match hits between 2 detectors (TRACKLETS) PHOBOS
More precise alignment and knowledge of primary vertex required
Correction for tracking efficiency to be applied
Full tracking NA49, STAR

10. Example: NA50 analysis Silicon microstrip detector measuring
the number and the angular distribution
of charged particles produced in the collision
2 Planes (MD1, MD2)
each plane made of 2 layers (up/down)
36 azimuthal sectors (=10o)
192 radial strips (=0.02)
6912 strips in each plane
Only 128 innermost strips used

11. NA50 analysis method
High multiplicity bin
Extract number of particles from number of clusters in bins of h (=0.15) and centrality
Cluster size distribution not reproduced by a VENUS+GEANT simulation (only physical clusters)
Dedicated MC, aimed at reproducing cluster size distribution observed in data
Calculate primary dNch/d.
Subtract the delta electron contribution (GEANT)
Max. 5% of the occupancy in the most peripheral bin
Divide by secondary/primary ratio (extracted from VENUS+GEANT simulation)
VENUS+GEANT data reconstructed with
the same method as experimental data.
1.2 –1.8 correction factor.
Does not depend on centrality.
Depends on target thickness, target position,
particular MD plane.
Large corrections due to thick (3 mm) target

12. Cross checks (I) Compare results from different detector planes
Average between detector planes
Wide  coverage
Compare results from runs with two different target thicknesses and positions
Average between different thicknesses
Wider  coverage

13. Cross checks (II)
Compare results from 2 independent centrality estimators
dN/dh values obtained with ET and EZDC centrality selections agree within 1.5%
Both centrality estimators independent of MD
ET centrality selection
EZDC centrality selection
 Abreu et al. (NA50 collaboration) Phys. Lett. B530 (2002) 43

14. Experimental results: width of the distribution

15. Width of dN/dh distribution (I)
Information on longitudinal expansion and degree of stopping
How would an isotropic source emitting at rest look like?
FWHM = 1.8

16. Width vs. centrality at SPS and RHIC
NA50 at 158 GeV/c (√s=17.2 GeV)
√s= 200 GeV
√s= 130 GeV
Gaussian width (FWHM) decreases with increasing centrality
Observed also by NA35, WA80, Helios/Emulsion, E802
Stopping power effect
Decreasing contribution of protons from target and projectile fragmentation

17. Width vs. energy NA50 most central Pb-Pb E877 central Au-Au
Available phase space in rapidity increases with √s
Fit with the simple scaling law sh = a + b · ln s
At SPS energies dN /dh (dN/dy) are twice as large as the one expected from a thermal fireball (Senger and Strobele, nucl-ex/ )

18. Experimental results: particle density at midrapidity

19. Midrapidity peak / plateau
The maximum of pseuorapidity distribution (dNch/dh | max ) at hcm=0:
Most frequently used variable to characterize the multiplicity of the interaction
Independent of phase space acceptance  allows comparison between different experiments
Increases with collision energy (√s) and centrality
central
central
peripheral
peripheral

20. Scaling with centrality at the SPS (I)
Agreement within 10% among experiments at 158 GeV/c
Fit with the power law
Values of exponent a between (NA50) and 1.08 (WA98)
Depends on the model to calculate Npart (NA50 finds a=1.00 with a Glauber estimation of Npart and with a VENUS estimation)
Two-component fit:
Values of B compatible with 0

21. Scaling with centrality at the SPS (II)
Npart describes the centrality dependence of particle production at midrapidity at SPS energies
Soft processes dominate particle production at such energies
No important contribution from hard processes (as expected)
Introduce yield per participant pair:
A flat behaviour reflects the linear dependence of dN/dhmax on Npart
NA50

22. Scaling with centrality at RHIC
PHOBOS PRC 2004, nucl-ex/
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-compoment fit with dN/dh  [ (1-x) Npart /2 + x Ncoll ] gives compatible values of x (≈ 0.13) at the two energies.

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

24. Density at midrapidity vs. energy
WARNING when comparing dN/dhmax between collider and fixed target experiments: pseudo-rapidity h is not boost invariant
Conversion from dN/dh|lab to dN/dy (Lorentz invariant) and then to dN/dh|cm
dN/dhmax in central heavy ion collisions increases as ln(s) from AGS to top RHIC energies
Different √s dependence in pp and heavy ion collisions

25. Experimental results: total charged multiplicity

26. Multiplicity vs. density at midrapidity
central
peripheral
√s= 200 GeV
The shape of pseudorapidity distributions is not independent of centrality (Npart)
Height increases more than linearly with Npart
Width decreases with increasing centrality
BUT Height  Width ≈ constant

27. Total multiplicity vs. Npart
Total multiplicity obtained integrating dN/dh distributions
Small extrapolation thanks to the wide h coverage of PHOBOS
Total charged-particle multiplicity proportional to Npart
Total yield per participant is the same as in e+e- collisions at the same energy

28. Gold vs. copper
Cu+Cu
Preliminary
3-6%, Npart = 100
PHOBOS
62.4 GeV
200 GeV
Au+Au
35-40%,Npart = 98
3-6%, Npart = 96
35-40%, Npart = 99
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

29. Integrated yield vs. energy
Multiplicity in pp collisions lower than in e+e-
Understood as due to leading particle effect
The outgoing proton takes away a substantial amount of energy 1
Multiplicity in AA collisions
Below pp and e+e- at AGS energies
Cross through pp at SPS energies
Joins e+e- data above top SPS energy
No leading particle effect AA collisions at RHIC energies
Due to multiple collisions per participant ?

30. Experimental results: fragmentation regions

31. Limiting fragmentation
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 the fragmentation region
independent of energy, but NOT necessarily
independent of centrality

32. Limiting fragmentation (I)
PHOBOS Phys. Rev. Lett. 91, (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
Spectator emission ?

33. Limiting fragmentation (II)
Different limiting curves for central and peripheral data
Particle production in the fragmentation region changes significantly with centrality
The hypothesis of limiting fragmentation does not imply that the limiting curve is independent of centrality
BUT both (central and peripheral) energy independent

34. What have we learned so far ?
Charged particle multiplicities follow simple scaling behaviours
Total yield at RHIC energies ≈ Npart  multiplicity in e+e- at the same energy
Extended (up to 4 h units) fragmentation regions where particle production is independent of energy (BUT not of centrality)
No evidence for a boost invariant central plateau also at top RHIC energy
From STAR White paper:
“Most bulk properties measured appear to fall on quite SMOOTH CURVES with similar results from lower energy collisions…Similarly the centrality dependences observed at RHIC are generally smooth… These experimental results contrast with theoretical speculations and predictions… which often suggested strong energy dependences accompanying the hadron-to-QGP phase transition”
Energy density from Bjorken formula and measured dN/dy (dN/dh) at top RHIC energy gives values of ~ 5 GeV/fm3 “well above the critical density (1 GeV/fm3) predicted by Lattice QCD for a transition to the QGP

35. Perspectives for ALICE at the LHC

36. Energy dependence and the LHC
Detectors planned for
dN/dh > 5000
Saturation model
Armesto, Salgado, Wiedemann hep-ph/
dN/dη ~ 1800
dN/dη ~ 1100
Models prior to RHIC
Log extrapolation

37. Limiting fragmentation and the LHC
dN/dη ~ 1800
dN/dη ~ 1100
W. Busza, Zakopane ’04
Limiting fragmentation

38. Inner Tracking System (ITS) Time Projection Chamber (TPC)
ALICE at the LHC
Forward Multiplicity Detector (FMD)
Inner Tracking System (ITS)
Time Projection Chamber (TPC)

39. ALICE pseudorapidity coverage
p-p collisions at LHC:
s = 14 TeV
ybeam = 9.6
Different measurement techniques
CLUSTERS on innermost ITS layers (Silicon Pixels)
TRACKLETS with 2 innemost layers of ITS (Silicon Pixels)
FULL TRACKING (ITS+TPC)
ENERGY DEPOSITION in the pads of Forward Multiplicity Detector (FMD)

40. dN/dh measurement with ITS
Multiplicity from:
2 innermost layers of Silicon Pixel Detectors:
Wider h coverage
No energy loss information
Analysis techniques:
Count “clusters” on the 2 layers
Count “Tracklets” (associations between 2 layers)
L= 97.6 cm
Silicon Pixel Detectors (2D)
Silicon Drift Detectors (2D)
Silicon Strip Detectors (1D)
R= 43.6 cm
 ALICE collab. - Pysics Performance Report - Vol II

41. dN/dh at mid-rapidity with ITS
dN/dh in |h|<0.5 for:
100 HIJING events
Standard noise level
No magnetic field
zVERTEX = 0
Hits = number of primary particles crossing a layer
Number of clusters
Lower than generated multiplicity in layer 1
due cluster merging at high multiplicity
Enhanced in layer 2
due to secondary particles produced in the inner layer
Tracklets
Association efficiency decreases with increasing multiplicity

42. Systematic effects Magnetic field effect Noise level effect
Clusters in layer 1 insensitive to the field
low pT tracks do not reach layer 2
Field = 0 best condition to measure multiplicities
(looser cut)
(tighter cut)
Generated mult.
Standard noise level
Noise level effect
Tracklet method more stable against noise level
Noise effect almost completely removed at the price of a decrease of efficiency (larger MonteCarlo correction needed)

43. dN/dh reconstruction in ITS (I)
dN/dh distribution for:
1 central HIJING event (dN/dh = 6000)
Standard noise level
No magnetic field
zVERTEX = 0
With zVERTEX smearing an acceptance correction has to be included

44. dN/dh reconstruction in ITS (II)
dN/dh distribution for:
300 semi-central HIJING events (dNch/dh ≈ 3000)
Standard noise level
No magnetic field
zVERTEX spread = ± 5 cm
+ acceptance correction
zVERTEX spread allows to increase the h coverage

45. Thanks to… …and to… …and to…
Tiziano Virgili (NA57), Gunther Roland (PHOBOS) for giving me plots and material
…and to…
Marek Idzik, Marco Monteno, Marzia Nardi, Luciano Ramello for discussions and clarifications
…and to…
NA50 and ALICE collaborations

46. Backup slides

47. Multiplicity and collision centrality
The impact parameter (b) determines the “centrality” of the event
SMALL IMPACT PARAMETER (Central events)
Many participant nucleons (large Npart ) and few spectators
Many nucleon-nucleon collisions ( large Ncoll )
Big system
Many produced particles (~ 5000 at top RHIC energy )
LARGE IMPACT PARAMETER (Peripheral events)
Few participant nucleons (small Npart ) and many spectators
Few nucleon-nucleon collisions (small Ncoll )
Small system
Few produced particles

48. “Glauber” calculations
Optical approximation
 Czyz and Maximon, Annals Phys. 52 (1969) 59.
Nucleus thickness functions
Nucleus-nucleus thickness function
Nucleon-nucleon collision probability

49. PHOBOS Apparatus

50. Centrality determination in NA50
Two detectors independent from MD to measure event-by-event centrality related observables
Electromagnetic calorimeter  transverse energy of neutral particles (ET)
Zero Degree Calorimeter  energy of spectator nucleons (EZDC)
Centrality intervals for dN/dh analysis defined in terms of fraction of total inelastic cross section

51. NA50 analysis method (I) Data selection
Beam cleaning cuts, pile-up rejection, interaction in-target identification
Calculation of raw number of particles in each h bin (=0.15) and centrality class
Cluster (group of contiguous strips firing together) correction
Cluster size distribution not reproduced by a VENUS+GEANT simulation
Dedicated MC, aimed at reproducing cluster size distribution observed in data
High multiplicity bin
Low multiplicity bin

52. NA50 analysis method (II)
Calculation of primary dNch/d.
Subtraction of the delta electron contribution (from GEANT).
Max. 5% of the occupancy in the most peripheral bin.
Correction with secondary/primary ratio from VENUS+GEANT simulation
VENUS+GEANT data reconstructed with
the same method as experimental data.
1.2 –1.8 correction factor.
Do not depend on centrality.
Depend on target thickness, target position,
particular MD plane.
Large corrections due to thick target
Systematic error estimation
8% systematic error on primary charged multiplicity
 Abreu et al. (NA50 collaboration) Phys. Lett. B530 (2002) 33

53. Changing the beam energy
ET centrality selection
ET centrality selection
Pb-Pb at 40 GeV/c (√s=8.77 GeV)
Pb-Pb at 158 GeV/c (√s=17.2 GeV)
Particle density at the peak increases with available energy
Peak position changes (midrapidity = ybeam/2 )

54. Width of dN/dh distribution (II)
E917 at AGS
PHOBOS at RHIC
At RHIC energies only 22% of the particles emitted with pT>pL ( |h| < 0.88 )
Incomplete stopping already at AGS energies

55. Width vs. centrality at RHIC
√s= 200 GeV
√s= 130 GeV
√s= 19.6 GeV
Gaussian width decreases with increasing centrality
Same feature observed at SPS energies

56. Scaling with centrality at the SPS (II)
Factor 1.7 between NA50 and NA57 measurements
Quite different experimental conditions and analysis techniques for the different experiments
EZDC not available for NA50 at this energy, so not all the cleaning cuts were applied to this data sample
NA57 uses the multiplicity to define centrality classes (autocorrelations?)
Fit with the power law
Values of exponent a between (NA50) and 1.09 (NA57)

57. Npart GLAUBER vs. VENUS

58. Boost invariant central plateau?
Pseudorapidity distorts the distributions for production angles near 0° and 90°
Rapidity distributions from BRAHMS at RHIC very similar to data at lower energies and well represented by gaussian fits
No evidence of a plateau at midrapidity

59. dNch/dh in p-p
LHC
C. Jorgensen

60. Predictions before RHIC startup Predictions before LHC startup
2000
4000
6000
8000
dNch / dy
10000
Predictions before RHIC startup
Predictions before LHC startup