STUDY OF CHARGE CORRELATIONS

1
STUDY OF CHARGE CORRELATIONS USING THE BALANCE
FUNCTION Panos Christakoglou, Angelos Petridis,
Maria Vassiliou University of Athens for the NA49
and ALICE Collaborations
2
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

3
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

4
MOTIVATION

• Oppositely charged particles are created at the
  same location of space-time.
• Charge - anticharge particles that were created
  earlier (early stage hadronization) are
  separated further in rapidity.
• Particles pairs that were created later (late
  stage hadronization) are correlated at small ?y.
• The Balance Function quantifies the degree of
  this separation and relates it with the time of
  hadronization.

5
DEFINITION

• The Balance function is defined as a
  correlation in y of oppositely charge particles,
  minus the correlation of same charged particles,
  normalized to the total number of particles.

P1 any rapidity interval in the detector P2
relative rapidity difference
6
BALANCE FUNCTIONS HOW DO THEY WORK

• The Balance Function is constructed in such way
  that can identify correlated pairs of oppositely
  charged particles on a statistical basis.

The numerator counts the pairs that satisfy both
criteria within an event and then is summed over
all events. The denominator counts particles that
were used for the creation of pairs within an
event and then summed over all events.
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THE WIDTH OF THE BALANCE FUNCTION

• The overall width of the Balance Function (BF) in
  relative rapidity is a combination of the thermal
  spread and the effect of diffusion.
• Due to cooling the width falls with time
  (stherm).
• The effect of diffusion stretches the BF (sdn).
• If the hadronization occurred at early times then
  the effect of collisions is to broaden the BF.
• On the other hand late stage hadronization would
  result into narrower BF.

8
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

9
SYSTEM SIZE DEPENDENCE - vsNN 17.3 GeV

• The width takes its maximum value for pp
  interactions.
• Data show a strong system size and centrality
  dependence.
• Neither HIJING nor shuffled data show any sign of
  system size or centrality dependence.

C. Alt et al. NA49 collaboration, Phys.Rev.
C71, 034903 (2005).
10
COMPARISON NA49 STAR

• NA49 data show a decrease of the width of the
  order of (17 3) from the most peripheral to
  the most central PbPb collisions.
• STAR data show also a strong centrality
  dependence of the order of (14 2).

STAR ? lt 1.3 NA49 -0.4lt?lt2.0
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RAPIDITY DEPENDENCE _at_ SPS
The narrowing of the BF with centrality is
observed only in the mid-rapidity region.
P. Christakoglou et al. NA49 collaboration, AIP
Conf.Proc. 828, 107-112 (2006)
12
ENERGY DEPENDENCE _at_ SPS

• First indication of an energy dependence for real
  data.
• This dependence is not apparent in microscopic
  models such as UrQMD and HSD.

13
COMPARISON NA49 STAR
The results are not directly comparable yet,
since STAR studies the BF in a different phase
space window!!!
P. Christakoglou et al. NA49 collaboration, AIP
Conf.Proc. 828, 107-112 (2006)
14
ENERGY DEPENDENCE _at_ SPS FORWARD RAPIDITY

• Motivated by the previous study, we have also
  analyzed the BF in the forward rapidity regions
  for each SPS energy.
• Results show no energy dependence in the forward
  rapidity regions.
• Interesting and important results for
  interpretations of the energy dependence.

15
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

16
SYSTEM SIZE DEPENDENCE PIONS

• Width is extracted by calculating the weighted
  average in all the analyzed interval except the
  first bin (0.1-gt1.4).
• This was done in order to exclude short range
  correlation effects, such as HBT or Coulomb, that
  are reflected in the first bin of the BF's
  distributions.
• Width decreases with increasing system size and
  centrality for real data but not for the UrQMD
  points.

17
SYSTEM SIZE DEPENDENCE KAONS

• Width is extracted by calculating the weighted
  average in all the analyzed interval exept the
  first bin (0.1-gt1.4).
• No apparent sign of any centrality dependence in
  neither data nor UrQMD points.
• Width decreases when going from CC to the most
  peripheral PbPb interactions.

18
RAPIDITY CORRELATIONS STAR

• According to G. Westfall et. Al, J.Phys.G30,
  S345-S349 (2004), STAR studied the BF for pp and
  AuAu collisions at vs 200 GeV for different
  particle species.
• Width for pion pairs decreases with increasing
  centrality.
• No such dependence for kaon pairs and HIJING.

19
INVARIANT MOMENTUM STUDY

• According to Scott Pratt and Sen Cheng,
  Phys.Rev.C68, 014907 (2003), if one studies the
  BF in terms of the invariant relative momentum,
  one could get a clearer insight about the
  possible physics interpretation.
• In terms of laboratory momenta P and q the
  different components are defined as follows

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MOMENTUM CORRELATIONS - CENTRALITY

• Width is extracted by the fitting function.
• Width decreases with centrality for pion pairs.
• Results are inconclusive for kaon pairs.
• Results are still preliminary.

sGeV/c
sGeV/c
21
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

22
AMPT v-1.11

• AMPT is a multi-phase transport model which
  contains a quark-parton phase before
  hadronization.
• It consists of four main components
• Spatial and momentum distributions of hard
  partons and soft string excitations are obtained
  from HIJING.
• The parton cascade follow the ZPC model.
• When parton interactions cease, they are
  recombined with their parent strings to form
  hadrons according to LUND string fragmentation
  mechanism.
• The scatterings among resulting hadrons are
  described by the relativistic transport model
  ART.
• I used this model to generate PbPb events _at_ vsNN
  17.3 GeV for different centrality classes.

Zi-Wei Lin et al., Phys.Rev.C72, 064901 (2005 )
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DEPENDENCE ON THE FREEZE-OUT TIME

• In order to study the relation between the BF and
  the time of hadronization, we use the event mean
  of particle freeze-out time.

PRELIMINARY
There is a clear dependence of the width on the
hadronization time. The decrease is of the order
of (12 3).
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DEPENDENCE ON THE MULTIPLICITY

• I also studied whether this is just a trivial
  multiplicity dependence effect.
• Within the same centrality class, I divided the
  sample into several sub-samples according to the
  number of generated particles for each event.
• The outcome is that the narrowing of the width
  can not be attributed to the increasing
  multiplicity.

PRELIMINARY
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DATA MODELS COMPARISON

• We have already reported the narrowing of the
  width of the BF with increasing centrality for
  experimental data.
• This decrease is of the order of (17 3).

PRELIMINARY

• Microscopic models such as UrQMD and HIJING cant
  reproduce this narrowing.
• On the other hand, the multi-phase trasport model
  AMPT with the time evolution of the partons can
  qualititivelly reproduce this behavior.
• The decrease is of the order of (12 3).

26
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

27
PSEUDORAPIDITY STUDY SYSTEMATIC ERRORS

• The cuts on three parameters were varied and the
  corresponding width was calculated.
• The parameters were chosen to be Vz, br, bz.
• The pseudorapidity phase space analyzed was
  -1.0,1.0.

PYTHIA events
ALICE Collaboration, Physics Performance Report
vII, CERN/LHCC/2005-030
28
PSEUDORAPIDITY STUDY INTERVAL STUDY

• The analyzed interval was varied starting from
  1.0 (-0.5,0.5) up to 2.0 (-1.0,1.0) with a
  step 0.2.

PYTHIA events
ALICE Collaboration, Physics Performance Report
vII, CERN/LHCC/2005-030
29
RAPIDITY STUDY

• Interval analyzed ALICE central barrel
  acceptance.

PYTHIA events
According to S.A. Bass, P. Danielewicz, S. Pratt,
Phys. Rev. Lett. 85, 2689 (2000), heavier
particles are characterized by narrower BF
distributions
ALICE Collaboration, Physics Performance Report
vII, CERN/LHCC/2005-030
30
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Energy dependence study for all the SPS energies.
• BF for identified particles
• Preliminary results on the rapidity correlations.
• Comparison with STAR.
• Preliminary results on the momentum
  correlations.
• Model calculations and predictions.
• Extension of the method to LHC energies.
• Summary.

31
SUMMARY

• The BF might give insight about the time of
  hadronization.
• The BF has been studied for all charged
  particles
• Results from both SPS and RHIC show a strong
  system size and centrality dependence which is
  not seen in microscopic models and shuffled
  events.
• Results from SPS show that the narrowing of the
  BF is only observed around mid-rapidity.
• The scan throughout all SPS energies show a first
  indication of an energy dependence of the
  normalized parameter W.
• The BF has also been studied for identified pion
  and kaon pairs
• Preliminary results on the study of rapidity
  correlations show that there is a system size
  dependence of the width for pion pairs but not
  for kaon pairs.
• Similar behaviour has been reported by STAR.
• Preliminary results on the study of momentum
  correlations show that there is a system size
  dependence of the width for pion pairs but not
  for kaon pairs.
• The study of a multi-phase model which
  incorporates the time evolution of partons before
  their hadronization revealed a clear relation of
  the width of the BF with the time of
  hadronization.
• Method has been extended to LHC energies and the
  corresponding results have been included in the
  PPR vII. Work is still ongoing.