STUDY OF THE CHARGE CORRELATIONS WITH THE BALANCE FUNCTION Panos Christakoglou, Angelos Petridis, Ma

1
STUDY OF THE CHARGE CORRELATIONS WITH THE
BALANCE FUNCTION Panos Christakoglou, Angelos
Petridis, Maria Vassiliou University of Athens
2
OUTLINE

• Introduction
• Motivation.
• BF definition and basic properties.
• NA49 experimental setup.
• BF for all charged particles
• System size dependence for two SPS energies.
• Comparison with STAR.
• Rapidity dependence.
• Possible explanations.
• 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 predictions.
• Extension of the method to LHC energies.
• Summary.

3
BALANCE FUNCTION INTRODUCTION
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.
7
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
  suggests narrower BF.

8
THE NA49 EXPERIMENT
Large acceptance hadron spectrometer at the
CERN-SPS
9
SYSTEM SIZE DEPENDENCE ALL CHARGED PARTICLES
10
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).
11
COMPARISON NA49 STAR

• NA49 data show a strong centrality dependence of
  the order of (17 3).
• STAR data show also a strong centrality
  dependence of the order of (14 2).

12
RAPIDITY DEPENDENCE _at_ SPS
The narrowing of the BF with centrality is
located at the mid-rapidity region.
13
SUGGESTED INTERPRETATIONS

• Delayed hadronization scenario of an initially
  deconfined phase.
• S.A. Bass, P. Danielewicz, S. Pratt, Phys. Rev.
  Lett. 85, 2689 (2000).
• J. Adams et al. (STAR collaboration), Phys. Rev.
  Lett. 90, 172301 (2003).
• C. Alt et al. (NA49 collaboration), Phys. Rev. C
  71, 034903 (2005).
• Part of the decrease could be attributed to the
  presence of the resonances decay products.
• P. Bozek, W. Broniowski, W. Florkowski,
  nucl-th/0310062.
• P. Bozek, W. Broniowski, W. Florkowski,
  nucl-th/0402028.
• Statistical hadronization model with the addition
  of hydrodynamic expansion. Several smaller
  fireballs with individual charge conservation
  blast wave model.
• S. Cheng et al., Phys. Rev. C 69, 054906 (2004).
• Quark coalescence model of an initially
  deconfined phase reproduced the values of the
  width from STAR.
• A. Bialas, Phys. Lett. B31, 579 (2004).
• A. Bialas and J. Rafelski, Phys. Lett. B633,
  488-491 (2006).

14
ENERGY DEPENDENCE ALL CHARGED PARTICLES
15
ENERGY DEPENDENCE _at_ SPS
16
COMPARISON NA49 STAR
The results are not directly comparable yet,
since STAR studies the BF in a different phase
space window!!!
17
ENERGY DEPENDENCE _at_ SPS FORWARD RAPIDITY

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

18
RAPIDITY CORRELATIONS IDENTIFIED CHARGED
PARTICLES
19
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.

20
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.

21
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.

22
MOMENTUM CORRELATIONS IDENTIFIED CHARGED
PARTICLES
23
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,
  he 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

24
MOMENTUM CORRELATIONS - CENTRALITY

• Width is extracted by the fitting fuction of the
  form f(x)x2exp(-x2/s2).
• Width decreases with centrality for pion pairs.
• No sign for centrality dependence in kaon pairs.
• Still, the results are considered to be
  preliminary
• Detailed studies especially on the kaon
  contamination will be reported soon.

25
PRELIMINARY RESULTS FROM THERMAL MODEL
26
THERMAL MODEL GENERAL DESCRIPTION

• Input parameters
• TCHEMICAL Temperature that determines
  abundances.
• TKINETIC Temperature of the kinetic freeze-out.
• VCHEMICAL Canonical volume determined by
  distance sampled before chemical freeze-out.
• yt(max) Maximum collective radial transverse
  rapidity for blast-wave-consistent boosting
• etamax Maximum collective longitudinal rapidity
  for blast-wave-consistent boosting
• Main procedures
• The code makes canonical partition functions as a
  function of the chemical equilibration
  temperature TCHEMICAL and the ensemble volume
  VCHEMICAL.
• Then it makes a list of phase space points
  consistent with the partition function.
• The results are read and then the produced
  particles are statistically decayed.
• Each ensemble is boosted with a collective
  velocity chosen randomly to be consistent with
  the blast wave parameters yt(max) and eta(max).
  All the particles in a given ensemble are boosted
  by the same velocity and then used to calculate
  balance functions.

27
RAPIDITY STUDY THERMAL MODEL

• According to S.A. Bass, P. Danielewicz, S. Pratt,
  Phys. Rev. Lett. 85, 2689 (2000), the width
  depends on the break-up temperature and on the
  mass of each particle.
• The BF was calculated for different particle
  species for 3 kinetic temperatures (T 150, 120
  and 90 MeV).
• Narrower distributions for lower temperature.

28
INVARIANT MOMENTUM STUDY THERMAL MODEL

• The BF was calculated for different particle
  species for 3 kinetic temperatures (T 150, 120
  and 90 MeV).
• Narrower distributions for lower temperature.

29
EXTENSION OF THE METHOD TO LHC ENERGIES
30
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.

31
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.

According to S. Jeon et al., Phys. Rev C65,
044902 (2002).
32
RAPIDITY STUDY

• Analysis interval -1.0,1.0.
• PID was assigned using AliESDtrackGetESDPid(Doub
  le_t p) method according to the highest
  probability value.

According to S.A. Bass, P. Danielewicz, S. Pratt,
Phys. Rev. Lett. 85, 2689 (2000), heavier
particles are characterized by narrower BF
distributions
33
SUMMARY
34
SUMMARY

• The BF could 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 simulated and shuffled points.
• Results from SPS show that the previous effect is
  located 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.
• Method has been extended to LHC energies and the
  corresponding results have been included in the
  PPR vII. Still there is an ongoing attempt on
  this part.

35
BACKUP
36
SYSTEM SIZE DEPENDENCE _at_ vsNN17.3 GeV
37
EVENT AND TRACK SELECTION

• EVENT SELECTION
• Cut on the vertex position in x,y and z
  direction.

• TRACK SELECTION
• Cut on the extrapolated distance of the closest
  approach of the particle at the vertex plane (dx
  and dy).
• Azimuthal acceptance.

• PHASE SPACE
• 2.6 ? 5.0 (vs 17.2 GeV)
• 0.005 Pt 1.5 GeV/c
• Acceptance filter

38
RAPIDITY DEPENDENCE
39
vsNN 17.2 GeV FORWARD REGION
40
vsNN 8.8 GeV FORWARD REGION
41
RAPIDITY AND MOMENTUM CORRELATIONS
42
EVENT TRACK SELECTION

• Standard event and track cuts were used.
• I used 4 centrality classes by merging Veto3 and
  Veto4 as well as Veto5 and Veto6.
• PID was performed by using the dE/dx information
  of the DSTs as well as the corresponding class
  T49TrackCut.

43
MOMENTUM CORRELATIONS
44
MOMENTUM CORRELATIONS BF DISTRIBUTIONS - PIONS

• Distributions were fitted with a function of the
  form f(x)x2exp(-x2/s2)
• The width was extracted by the fitting function
  that's why I tried to fit where I had the best
  x2.
• The negative values of B(Qinv) for low Qinv have
  also been reported in the original paper as
  coming from distorting effects (culombHBT).

45
MOMENTUM CORRELATIONS BF DISTRIBUTIONS - KAONS

• Distributions were fitted with a function of the
  form f(x)x2exp(-x2/s2)
• The width was extracted by the fitting function
  that's why I tried to fit where I had the best
  x2.
• The resulting distributions have large errors and
  are not really suitable for fitting.

46
RESULTS FROM MODEL
47
RAPIDITY STUDY THERMAL MODEL (3)

• Narrower distributions for heavier particles.

48
INVARIANT MOMENTUM STUDY THERMAL MODEL (2)

• Narrower distributions for lighter particles.