Strong interactions and multiparticle production in heavy ion collisions

1
Strong interactions and multiparticle production
in heavy ion collisions

• ltNchgt, dNch/dy, particle ratios, dN/dpT
• Centrality dependence
• Energy (?s) dependence

2
From hadron to ion collisions

• Heavy Ion research field driven by search of
  Quark-Gluon Plasma (QGP)
• Specific signatures of QGP (like J/? suppression,
  multi-strange particle enhancement, jet
  quenching) have to be studied vs. global features
  like centrality, system size and center of mass
  energy
• It is essential to understand if multiparticle
  production in ion-ion collisions implies
  additional mechanisms as compared to
  hadron-hadron ones, in particular p-p and p-A
  collisions

3
Which are the basic observables ?

• Centrality (experimental) charged multiplicity
  Nch, transverse energy ET, forward energy EF,
  centrality (theoretical) impact parameter b,
  number of participants Npart, number of
  collisions Ncoll
• Charged multiplicity total yield, dNch/dy
  (dNch/d?), midrapidity yield dNch/dymax
• Identified particles (p,K,p) total yields and
  ratios of yields, transverse momentum (pT)
  distributions

4
Plan of the lecture

• Theoretical background some ideas from QCD, an
  example the Dual Parton Model
• Centrality determination experimental
  observables, Glauber model calculations
• Experimental results (mainly from SPS and RHIC)
  on charged particles yields (total and per
  species), rapidity and pT distributions
• Current interpretations of the results vs.
  centrality and ?s

5
Theory (1) from Parton Model to QCD

• Simplest case ee-?qq hadronization of quark
  jets (4?s10 GeV) explained by Field-Feynman
  model
• Independent emission of final hadrons
• Fixed distribution in longitudinal momentum,
  exponential pT spectrum
• For higher energy, pT broadening observed
  explained with QCD gluon emission ? parton
  shower, according to DGLAP evolution equations
  (see Calucci, Dremin)

6
Theory (2) QCD parton shower
Field Wolfram, 1983

• Free parton emission in first stages of shower
  development
• Hadron formation is
• local depends only on local parton system
• universal is independent of process (ee-, pp,
  DIS, )
• Example of hadronization rule each minimal
  colour singlet group (cluster) evolves
  independently when invariant mass drops below µc,
  decaying to hadronic resonances and then to final
  hadrons according to phase space

7
Theory (3) hadron-hadron collisions
Capella et al., Phys. Rep. 236 (1994) 225

• In ee- collisions, color separation leads to one
  string the same happens in some h-h collisions
  (e.g. pp) but not in pp, so this cannot be the
  dominant contribution at high energy flavor
  exchange implies ss-½
• To prevent flavor exchange a second string must
  be stretched (Dual Parton Model)

8
Theory (4) the central rapidity region

• In the DPM, the dN/dy distribution of produced
  hadrons comes from the overlap of q-qq and q-qbar
  chains
• pp two q-qq chains centered at y?
• pbar-p one short and one long chain, both
  centered at y0 ? highest dN/dy
• pp in between pbar-p and pp
• ?s dependence of plateau height in DPM its due
  to increasing importance of q-qbar chains at y0

9
Intermezzo rapidity and pseudorapidity

• For ultrarelativistic produced particles, instead
  of rapidity y½ln(EpL)/(E-pL), it is more
  convenient to measure its approximation, i.e.
  pseudorapidity (?)
• y ½ln(p(1cos?))/(p(1-cos?)) -ln
  tg(?/2) ?
• Changing variables from (y,pT) to (?,pT) we find
  
• dN/d?dpT (p/E)dN/dydpT
• (1-m2/(mT2cosh2y))½dN/dy
  dpT
• In the center of mass frame, at high energies,
  while dN/dy presents a plateau at y0, dN/d?
  presents a dip
• dN/d?cms,MAX (1-m2/(ltmT2gt))½ dN/dyMAX
• In the laboratory frame, both dN/d? and dN/dy
  present a maximum of approx. the same value at
  y?ybeam/2
• dN/d?lab,MAX dN/dyMAX ? dN/d? is not
  boost invariant !

10
Theory (5) DPM vs. hadron-hadron data
Charged particle densities vs. ? (left),
inclusive p and p- densities vs. x (right)
11
Theory (6) DPM vs. hadron-hadron data
Inclusive Ks in pp collisions (left), inclusive
ps in Kp collisions (right)
12
Theory (7) from h-h to nucleus-nucleus

• dN/dypp(y) Nkqq-q(y)Nkq-qq(y)(2k-2)Nkqsqs(y),
  where k is the average number of inelastic
  collisions
• k (?n?n)/??n

Nkqq-q(y), Nkq-qq(y), Nkqsqs(y) represent the
rapidity distributions of particles produced
respectively from diquark-quark, quark-diquark
and sea quark-antiquark chains
13
Theory (8) from h-h to nucleus-nucleus

• Moving on from hadron-hadron to nucleus-nucleus
  collisions, a similar formula holds for the
  rapidity density (at midrapidity) generated in
  the collision of two identical nuclei (AA) at
  any fixed impact parameter b

dN/dyAA(y,b) NA(b)Nµqq-q(y)Nµq-qq(y)(2k-2)N
µqsqs(y) (?(b)-NA(b))2kNµqsqs(y)
where NA(b) is the number of participants
from one nucleus, ?(b) is the average number of
N-N collisions and µ(b)k?(b)/NA(b) is the
average number of inelastic collisions per
nucleon at impact parameter b the average number
of string pairs per collision is k (as before).
14
Theory (9) what do we expect for A-A ?

• Assuming that the height of the plateau from a
  given type of string is energy independent, the
  experimental data on dN/dypp vs. ?s fix the
  energy dependence of k
• In ion-ion collisions we may expect two limiting
  cases for the charged particle rapidity density
• in absence of external multiple scattering
  (where a projectile nucleon interacts with two -
  or more - different target nucleons) we obtain
  the Wounded Nucleon Model limit ?(b)NA(b)
• when kgtgt1 multiple scattering dominates
• The difference dN/dyAA - NA(b)dN/dypp ,
  particularly for central collisions b0,
  NA(b)A, is the interesting term, and various
  mechanisms to describe its possible deviation
  from this simple model have been proposed, like
  string fusion (see Ugoccioni), shadowing (A.
  Capella et al. reduction factor from 0.65 b0
  to 0.84 b12 fm in Au-Au collisions at s130
  GeV), and so on.

15
Centrality (1) impact parameter

• In heavy ion collisions the volume and energy of
  the fireball is determined (at given beam
  energy) mostly by the number of participating
  nucleons Npart, which in turn depends on the
  impact parameter b

x beam axis
(y,z) transverse plane
16
Centrality (2) notation and caveats
Computing Npart is not completely trivial, there
are some differences between the Glauber model
calculations and some Monte Carlo codes like
FRITIOF, HIJING, VENUS, etc.
17
Centrality (3) experimental observables
NA50 experiment at CERN SPS
Transverse Energy ET
Multiplicity Nch
Forward energy EF
18
Centrality (4) measured distributions
NA50 has used both forward energy EZDC and
transverse energy ET (1.1lt?lt2.3) as centrality
variables, defining in this example 6 classes of
decreasing centrality
158 GeV
158 GeV
40 GeV
19
Centrality (5) measured distributions
NA57 experiment at SPS charged multiplicity Nch
in the pseudorapidity range 2lt?lt4 measured with
silicon microstrip detectors
Events have been classified in five centrality
classes, corresponding to given fractions of the
total inelastic Pb-Pb cross-section at 158 A GeV
20
Centrality (6) Glauber model

• Goal determine NA(b), NB(b), ?(b) for a given
  system and relate them to the measured centrality
  variables
• Model assumptions and approximations
• Nucleons inside each nucleus are independent
• Optical limit (nucleon size ltlt nucleus size)
• Small angle, very high energy scattering
• p-A and A-B collisions are a superposition of N-N
  collisions
• Physical inputs to the model
• Nucleon-nucleon inelastic cross section at the
  N-N center of mass energy (s030 mb at ?s17.3
  GeV, top SPS energy)
• Density distributions of nucleons inside nucleus
  for Pb it is ?(r)?0/(1exp(r-r0)/c) with
  r06.62 fm, c0.546 fm (measured in
  electron-nucleus scattering)

R.J. Glauber, High energy collision theory in
Lectures in theoretical physics, vol. I,
Interscience Publishers, New York 1959, pages
315-414
21
Centrality (7) Glauber model

• Within the models approximations, only
  transverse coordinates (y,z) are relevant
• The nuclear thickness function TA(s) is the
  probability density for finding a nucleon in
  nucleus A at transverse coordinate s with respect
  to its center
• TA(s) ??A(s,x)dx
• and is normalized ?d2sTA(s) 1
• The nuclear overlap function TAB(b) is given in
  terms of the nuclear thickness functions TA(s)
  and TB(b-s) of the two nuclei
• TAB(b) ?d2sTA(s)TB(b-s)
• and is needed to compute probabilities of 0,1,2,
  inelastic N-N interactions

Marzia Nardi, CERN Heavy Ion Physics School
CHIPS99, June 1999
22
Centrality (8) Glauber model
Probability of one inelastic collision between
two randomly chosen nucleons P1(b) TAB(b)s0

• Probability of exactly ? nucleon-nucleon
  collisions for impact parameter b
• P(?,b) (AB)!/?!(AB-?)!TAB(b)s0?1-TAB(b)
  s0AB-?

23
Centrality (9) Glauber model
The probability of inelastic interaction between
nucleus A and B is then ?AB(b) d?AB/d2b
??1ABP(?,b) 1 - P(0,b) 1 - 1-TAB(b)?0AB
The probability of inelastic interaction between
a proton and nucleus A is ?A(b) d?pA/d2b 1 -
1-TA(b)?0A
24
Centrality (10) number of collisions
The average number of N-N collisions at impact
parameter b is given by lt?(b)gt ?k1ABkP(k,b)
AB?0TAB(b)
Under the assumption of an inelastic A-B
collision, the average number Ncoll(b) of N-N
collisions is the same as lt?(b)gt except for very
large b Ncoll(b) ?k1ABkP(k,b) / ?k1ABP(k,b)
AB?0TAB(b) / ?AB(b)
25
Centrality (11) number of participants

• The number of participants (wounded) nucleons
  from both nuclei A and B is on average
• NW(b) NA(b)NB(b)
• A/?AB(b)?TA(s)?B(b-s)d2s
• B/?AB(b)?TB(b-s)?A(s)d2s
• A?TA(s)1-1-TB(b-s)s0Bd2s
  B?TB(b-s)1-1-TA(s)s0Ad2s
• NW is defined here as the number of nucleons
  having suffered at least one in elastic
  collision there are other ways to count
  participants, which can lead to different
  numbers
• Npart A B N(spectators), e.g. Npartpro
  A(1-EF/Ebeam)
• Npart from a dynamical simulation may (or may
  not) include rescattering with produced particles

26
Centrality (12) experimental resolution

• To connect Npart to the experimental observables
  (for example, assuming Nch q Npart, a good
  guess at SPS) we must consider several sources
  of fluctuations
• the fluctuation of Npart around its average value
  at given impact parameter b, evaluated via a
  Glauber MonteCarlo simulation
• the dispersion ?q of the number of charged
  particles per participant,
• ?q aq with a ? 1 at SPS energy in 2lt?lt4
• the experimental resolution on the measurement of
  the observable, ?expNch
• The differential cross-section can be written
  (taking Npart NW) as
• d?/dNch ?db1-P(0,b)G(Nch-qNW(b)?Nch)
• where G(µ?) is a Gaussian function and the
  overall dispersion is given by ?2Nch q2?2(NW)
  NW2?q2 (?expNch)2

27
Glauber MonteCarlo results (1)
Here are two examples of Glauber MonteCarlo
results for Pb-Pb collisions at the top SPS
energy of 158 A GeV (laboratory system)
The width (RMS) of the Npart distributions
depends on the chosen centrality variable and
also on the experimental resolution (more
examples later)
28
Glauber MonteCarlo results (2)
2Ncoll/Npart increases vs. ?s
Glauber calculation by the STAR experiment at
RHIC
29
Centrality and Nch

• The simplest assumption on particle production is
  that of proportionality between Nch (number of
  charged particles integrated over some rapidity
  interval) and the number of participants Npart
  (NW)
• ltNchgt q NW
• At high enough energies (RHIC), a term
  proportional to Ncoll is expected to become
  measurable, also because the ratio Ncoll/Npart is
  higher
• In order to test whether Nch, or the density
  dNch/d?max, scale like Npart or like Ncoll (or
  maybe as a combination of the two), it may be
  useful to define Npart and Ncoll using another
  experimental variable, like transverse energy ET
  or forward energy EF

30
Centrality and Nch data at SPS (1)
NW spectra computed for the 5 centrality classes
at fixed fractions of sinelastic (NA57)
NA57 has found at 158 GeV approximate agreement
with the Wounded Nucleon Model assumption ltNchgtN
Wa gives 1.02 lt a lt 1.09
WA98 finds a slightly stronger centrality
dependence ltNchgtNWa with a 1.08 0.05
31
Centrality and Nch data at SPS (2)
NA50 finds that the charged particle production
is in agreement with the Wounded Nucleon Model
both at 158 GeV and at 40 GeV a158 1.00
0.01 0.04 and a40 1.02 0.02 0.06
32
dNch/d? distributions at SPS (1)
NA50 at CERN SPS

• The pseudorapidity distributions
• at top SPS energy of 158 A GeV
• are well described by gaussian
• distributions
• the peak position ?MAX ranges
• from 3.08 to 3.12, in line with the
• value 3.10 extracted from VENUS
• (while yMAX is 2.91)
• the gaussian width decreases with
• increasing centrality, ranging from
• 1.620.05 for the most peripheral
• class to 1.500.03 for the most
• central one
• Similar considerations apply at the
• lower energy of 40 A GeV

33
dNch/d? distributions at SPS (2)
The gaussian width of dN/d? or dN/dy distributions
at AGS and SPS energies (central
collisions) follows an empirical scaling law ?
a b ln?s both for all charged and for
identified particles
Relation between widths ??(charged) ?y(p) gt
?y(p-) gt ?y(K) gt ?y(K-)
34
dNch/d? distributions at RHIC
35
From stopping to transparency
How much of the central plateau height comes from
net protons ?
Net protons distributions indicate high degree of
stopping at AGS energies, less stopping at top
SPS energy and almost full transparency at RHIC
36
Energy dependence of dN/d?MAX (1)
NA50 Phys. Lett. B 530 (2002) 33 and 43
NA50 (5 most central), yield translated from
lab. system to c.m.s. at ?s8.77 GeV yield
compatible with pp at ?s17.3 GeV yield is
gt50 higher than UA5 fits and 20 higher than
UA5CDF NSD fit (see Rimondi) not an ordinary
superposition of pp
Fit to UA5 CDF, Phys. Rev. D41 (1990) 2330

• ?
• UA5 fits (inelastic), Z. Phys. C33 (1986) 1
• ?

37
Energy dependence of dN/d?MAX (2)

• The PHOBOS experiment at RHIC
• has measured dNch/d? for central
• Au-Au collisions at 4 different energies,
• including s 19.6 GeV which is very
• close to the top SPS energy
• When the 3 published dNch/d?lab Pb-Pb
• values from the SPS experiments are
• translated into dNch/d?CMS, they show
• good agreement with PHOBOS
• The dNch/d?CMS values measured by
• the four RHIC experiments at 130 GeV
• and (respectively) at 200 GeV are quite
  consistent

G. Roland, INT/RHIC workshop, Dec. 2002
38
Energy dependence of dN/d?MAX (3)
P. Steinberg (PHOBOS Collab.), Quark Matter 2002
39
Similarity between AA and ee- ?
40
Total multiplicity vs. beam energy
41
Approach to universality ?
pp?pX
P. Steinberg (PHOBOS Collab.), Quark Matter 2002
42
Limiting fragmentation at RHIC
Gunther Roland / MIT at INT Workshop, 13 Dec.
2002 see Rimondi, UA5 data
43
Centrality dependence at SPS
At top SPS energy (158 A GeV), approximate
scaling with Nparta is observed NA50 a
1.00 0.01 0.04 NA57 a 1.05 0.05 WA98
a 1.08 0.03 Npart evaluated with VENUS
A second term scaling with Ncollß is not
needed to explain SPS data
NA50 at SPS
44
Centrality dependence at RHIC (1)
At RHIC, the increase of dNch/d? measured by
PHENIX at 130 GeV is a factor 1.6 for
central collisions, with respect to UA5 pbar-p
collisions A simple two-component model
indicates a sizeable contribution of a
term scaling like Ncoll
see Ugoccioni for more on this subject
45
Centrality dependence at RHIC (2)
46
What can we learn from identified particles ?

• Integrated particle yields, and ratios like
  K/p, tell us about the chemical freeze-out
  stage of the collision (see Becattini), when
  inelastic interactions cease
• Transverse spectra (pT, mT) of different particle
  species tell us about the kinetic freeze-out
  stage, when even elastic interactions cease
• Statistical and hydrodynamical models, implying
  local thermal equilibration, have been employed
  successfully to describe yields and transverse
  spectra (starting from the early models of Fermi
  and Landau)
• The main parameters that can be extracted from
  data are
• Temperature
• Baryochemical potential at chemical freeze-out
• Collective flow velocity at kinetic freeze-out

47
Identified particles at SPS (1) rapidity
NA49 at SPS has measured identified particles
spectra for central collisions at several
energies The p spectra were not analyzed
directly, due possible contamination from
protons p yields were instead deduced from the
ratios p/p- (0.97 at 158 GeV)
Data at 40, 80, 160 A GeV Phys. Rev. C 66 (2002)
054902 Data at 30 A GeV Volker Friese,
Strangeness in Quark Matter 2003
48
Transverse momentum spectra

• Single particle spectra can be interpreted in the
  context of models of the source using
  hydrodynamic expansion
• For a stationary fireball the distribution takes
  the forms
• EdN/dp3 dN/(mTdmTdydf) ? mTexp(-mT/T)
• for a narrow rapidity slice near
  y(fireball), and
• dN/(mTdmT) ? mTK1(mT/T) ?mTexp(-mT/T) mTgtgtT
• for rapidity-integrated distributions
• Experimentally it is found (NA49, WA98) that the
  simple form EdN/dp3 ? exp(-mT/T) often fits data
  better
• A collective flow velocity is introduced as a
  second parameter (the first is temperature) in
  the blast wave model by Schnedermann and Heinz
  Phys. Rev. C 50 (1994)1675

49
Identified particles at SPS (2) mT
NA49 Blast wave fit indicates temperature of
122-127 MeV and average flow velocity of
0.48 Pions were not included in the blast wave
fit due to significant resonance contribution at
low mT
V. Friese, NA49, Strange Quark Matter 2003
50
Identified particle yields at RHIC
p/p-
pbar/p
BRAHMS experiment
51
Particle ratios vs. energy (1) at midrapidity
Volker Friese (NA49), Strange Quark Matter 2003,
Atlantic City, March 2003
52
Particle ratios vs. energy (2) in 4 p
Data at 30 AGeV support phase transition
scenario (Statistical Model of the Early Stage)
Volker Friese (NA49), Strange Quark Matter 2003,
Atlantic City, March 2003
53
Particle ratios vs. energy (3)
BRAHMS results at y0 seem to indicate saturation
of K/p reached at top SPS energy
54
Chemical freezeout and phase diagram
A thermal analysis of hadron multiplicities in
central Pb-Pb Au-Au collisions (but see also
Becattini) shows that hadron yields are
equilibrated (two-parameter fit temperature and
baryochemical potential) for SPS top energy and
above, hadron yields are frozen at the phase
boundary Fodor, Katz Lattice QCD PBM, JS
Bag model EOS in this case equilibrium can
hardly be achieved within hadron gas
PBM and JS, J. Phys. G 28 (2002) 1971
55
Conclusion

• Charged particles measurements are essential in
  heavy ion collisions
• Centrality determination
• Particle production mechanism
• Chemical equilibration (yield ratios)
• Collective behaviour (temperature, radial flow)
• The evolution of charged particle production vs.
  energy presents very interesting features
• Charged particle data could well be relevant to
  establish the onset of deconfinement