# Presentation: 933175

## Event-by-Event Fluctuationsin 40, 80, and 158AGeV/c Pb+Au CollisionsHiroyuki Sako and H. Appelshäuserfor the CERES/NA45 CollaborationQuark Matter 2004Oakland, Jan 11-17, 2004

- Goals
- Mean pT fluctuations
- Net-charge fluctuations
- Conclusions

**Notes:**

We present in this talk, event-by-event mean pt fluctuations and net-charge fluctuations in 40, 80, and 158 AGeV/c Pb+Au
Collisions from CERES experiment. 

## Goals of mean pT fluctuations

- Search for the critical point and the phase transition
- Non-monotonic variation and enhancement as a function of collision energy
*M. Stephanov et al, PRD60 (1999)14028*
*A. Dumitru et al, PLB 504 (2001) 282*
- How does thermalization/rescattering modify the fluctuations with respect to the superposition of N+N collisions?
-  Comparison with p+p extrapolation as a function of centrality

**Notes:**
We discuss here the goals of fluctuation studies;
With mean pt fluctuations, we can search for the QCD critical point and phase transition, via non-monotonic variations and enhancement as a function of collision energy.
To study how the thermalization and rescattering modifies the fluctuations with respect to the pp superposition,
we compare the data with the pp scaling as a function of centrality.

With net-charge fluctuations, we search for deconfined phase transition, via suppressed fluctuations due to smaller change units of quarks than hadrons.
To study if the observed fluctuations are described by the resonance gas models, we compare the data with RQMD and UrQMD.

## Goals of net charge fluctuations

- Search for the deconfined phase transition
- Suppressed fluctuations due to small charge unit of (anti-) quarks
*Jeon, Koch, PRL 85 (2000) 2076*
*Asakawa, Heinz, Muller, PRL 85 (2000) 2072** *
- Are observed fluctuations described by the resonance gas models?
-  Comparison with RQMD/UrQMD

- Primary vertex
- SIDC1+SIDC2
- Track/momentum
- TPC
- Centrality
- SIDCs
- Multiplicity Counter
- Acceptance
- =2(80/158GeV)
- ~1.3(40 GeV)
- 2.0<<2.9
- (near mid-rapidity)

- CERES Experiment

- Multiplicity Counter

- Hadron measurement near mid-rapidity in Pb+Au collisions

**Notes:**
For fluctuation analysis, CERES measures hadrons near mid-rapidity in Pb+Au collisions.
Here is the setup of CERES experiment. In this analysis, we use 2 silicon drift detectors, sidc1 and sidc2 to reconstruct
The primary vertex. And reconstruct charged particle tracks and calculate momentum with TPC. Centrality is defined by SIDCs and Multiplicity counter, MC. The Accept in phi is 2pi at 80 and 158 AGeV/c, but about 1.3 pi at 40 GeV/c. pseudo-rapidity range is from 2.0 to 2.9 which covers mid-rapidity.

## Mean pT Fluctuations

- (D. Adamova*, et al,* CERES collaboration,
*Nucl. Phys. A727(2003)97-119*)

## Event-by-event mean pT distributions

- Event-by-event mean pT distributions

-    Event-by-event *M**pT* distributions in real events are slightly wider than those in mixed events
- Evidence for the non-statistical (dynamical) mean pT fluctuations

- Real
- /mixed

- 6.5% central, 2.2<<2.7, 0.1<pT<1.5GeV/c

- Real
- mixed

**Notes:**
From now, we show results of mean pt fluctuations.
Here are distributions of Mpt, namely, mean of pt of all particles per event
From real events, in red, and from mixed events in blue at the 3 beam energies.
By taking the ratio of real to mixed events distributions, you see deviation above 1.

Therefore, The real distributions are slightly wider than mixed events, because the ratio between the real
 and mixed distributions is larger than 1 in low and high Mpt.
This shows the evidence for the non-statistical mean pt fluctuations.

## Measures of mean pT fluctuations

- CERES
- Proportional to mean covariance
- of all particle pairs / event
- PHENIX (S.Adler, nucl-ex/0310005)
- Statistical distribution
- The 2 measures 0
- Multiplicity dependence

**Notes:**
In this talk We use the two measures for pt fluctuations.
We CERES define Sigma pt given by this formula, where Sigma_Mpt is the r.m.s of the Mpt distribution,
and Sigma_Mpt stat is that for the statistical distribution defined as r.m.s of inclusive pt distribution divided by the square-root of
Mean multiplicity, N, and this is normalized by the mean pt.
 Note that Sigma pt is proportional to mean covariance of all particle pairs /event.
Fpt is defined by PHENIX, given by this simple equation.
For statistical distributions, sigma_Mpt is equal to sigma_Mpt stat and thus the two measures approaches 0.
The multiplicity dependence is different between the two measures. Sigma_pt squared is proportional
To Fpt divided by N and also commonly used measure, Phipt has the same dependence as Fpt.

## Dependence of mean pT fluctuations on pseudo-rapidity interval ()

- Dependence of mean pT fluctuations on pseudo-rapidity interval ()

* ****pT* decreases only 30% with and saturates at 
*F**pT *increases by factor of 3~5 in -
-  ***pT* at each is similar at 3 energies
*F**pT* has large difference due to multiplicity difference

- 0.1<pT<1.5GeV/c, 6.5% central
- ||< at each bin

* ****pT * is robust under change of multiplicity and 
- Use ***pT *to compare our data to RHIC data with wider 

**Notes:**
Here we show dependence of mean pt fluctuations on pseudo-rapidity acceptance size (delta eta).
The left plot shows Fpt in % as a function of delta eta ,and the right plot shows Sigma pt in % as
A function of delta eta.
 Sigmapt decreases only by 30% and saturates at delta eta larger than 0.5, while Fpt increases by factor of 2-5 in delta eta from lowest to highest delta eta bin. 
Sigma at each delta eta is similar among 3 beam energies,
While Fpt has large difference,due to multiplicity difference. 
Thus, Sigma pt is less sensitive to change of multiplicity and delta eta
And therefore we use sigma pt to compare our data to RHIC data
With wider delta eta.

## Collision energy dependence

- Fluctuations of  ~1% similar at SPS and RHIC
- No indication for non-monotonic dependence or enhanced fluctuations at the critical point
- (~2% at SPS,
-      Stephanov, PRD60 (1999) 14028)

- S.Voloshin (STAR), nucl-ex/0109006

- S.Adler (PHENIX), nucl-ex/0310005

- Central, pT<2GeV/c,
- Uncorrected for short
- range correlations

- J.Adams (STAR), nucl-ex/0308033

- Refs.

**Notes:**
Here we show collision energy dependence of Sigma pt.
Sigma_pt in central events near mid-rapidity is plotted as a function of sqrt(s) of nucleon pair. 
These 3 red points show our CERES data. The blue and cyan points
show STAR data at different centralities at 130GeV. 
These non-statistical fluctuations are about 1%,
Similar between SPS and RHIC. Therefore, no indication for non-monotonic
dependence or enhanced fluctuations in the critical point of about 2% at SPS is observed.

## Centrality dependence at 158 AGeV/c

- Baseline:extrapolation from p+p measurement
- 12% measured in p+p at ISR
- (*Braune, PLB123(1983)467*)
- Non-monotonic dependence and enhancement of *F**pT* in semi-central events
- Maximum of 2.8 % at *N**part*~100 (30-40% central)
- Consistent with the baseline in central and peripheral

- Corrected for short range correlations

- 

*F**pT* = 1.4% (const)

**Notes:**
Here we show centrality dependence of mean pt fluctuations at 158 GeV.
We first define the baseline as the extrapolation from pp fluctuations measured at ISR.
This is given by this formula for Sigma pt, with the scaling with No. of participants,
And The baseline for Fpt is given by constant of 1.4%.
Comparing our data with the baseline, we see enhancement of fluctuations
in semi-central events, with maximum of Fpt of 3% at Npart around 100
No enhancement in central and peripheral events are observed.
Note that this dependence of Fpt on Npart is similar to PHENIX observation.

## Comparison with PHENIX data

- Similar dependence of *F**pT*  to PHENIX data
- Non-monotonic dependence of *F**pT* as a function of Npart
- Increase in *F**pT** *as a function of upper pT cut
- Indication of same production mechanism?

-    PHENIX
- (s1/2=200GeV)
- nucl-ex/031005

- CERES

- Centrality dependence

- Upper pT cut dependence

- 20-30% central

- 20-25% central

- pTmin=0.1GeV/c

- pTmin=
- 0.2GeV/c

## Comparison with RQMD and UrQMD

- Without rescattering
- Fluctuations agree with p+p
- RQMD w/ rescattering
- Enhanced fluctuations in semi-central
- Increase of mean pT
- Qualitatively reproduces data
- UrQMD w/ rescattering
- Reduced fluctuations
- Flat mean pT

- CERES data

- Strong connection between centrality dependence of fluctuations and <pT>?
- (c.f. S. Gavin, talk in this session, nucl-th/0308067)

**Notes:**
Now we compare centrality dependence of Fpt with RQMD and UrQMD.
RQMD and URQMD withou the rescattering , shown by dashed lines, we see the fluctuations agree with the pp baseline. 
When including the rescattering, fluctuations
Increase in RQMD in semi-central events with maximum around Npart=200.
RQMD slightly overestimate central events.
On the other hand, in URQMD with rescattering, fluctuations decreases
And underestimates the observed fluctuations in all centrality class.
From these comparisons, we found rescattering modifies fluctuations
From the pp baseline. Only RQMD with rescattering has enhancement in semi-central
Events as the observed fluctuations.

## Net Charge Fluctuations

## Measure  dyn (C. Pruneau et al, PRC66 (2002) 044904)

= Dynamical fluctuations of difference between normalized multiplicity of positive particles and that of negative particles
= 0 for statistical distribution
Neutral resonance decay into a positive and a negative particles decreases dyn
Advantages of dyn
Correction for the global charge conservation is constant and additive

Insensitive to detector inefficiency

- = Dynamical fluctuations of difference between normalized multiplicity of positive particles and that of negative particles
- = 0 for statistical distribution
- Neutral resonance decay into a positive and a negative particles decreases dyn
- Advantages of dyn
- Correction for the global charge conservation is constant and additive
- Insensitive to detector inefficiency

- Measures of net charge fluctuations

**Notes:**
Now, we move to the fluctuations of net-charge, Q, which is the difference between
Positive and negative particle multiplicities.
We use the measure nu-dynamical, defined by this formula, where the bracket shows the event-wise average.
Nu-dynamical is 0 for the statistical distribution and neutral resonance decays into a positive an a negative particles decreases fluctuations.

Nu_dynamical has the following advantages over other measures.
The correction for the global charge conservation is constant with the 4pi multiplicity
Of charged particles, and the correction is additive. 
Also, No efficiency correction is necessary.

## Centrality dependence of net charge fluctuations

- Fluctuations lower than charge conservation limit
- Fluctuations far above the QGP models of      ~ 3.5
- No indication for   phase transition
- (Jeon, PRL85 (2000) 2076,
- Asakawa, PRL85 (2000) 2072)
- Slight decrease with  centrality
- Deviation from constant with superposition of sub-collisions
- Rescattering and resonance effects ?

- 
- 0.1<pT<2.5GeV/c

*Preliminary*

- Charge conservation limit
- NA49 collaboration,
- PRC66(2002)054902

**Notes:**
Here, we show centrality dependence of nu-dynamical.
This plot shows mean charged particle multiplicity N times nu-dynamical, as a function of number of participants
Npart.
In case of superposition of elementary sources, N nu-dynamical is expected to be constant. The data show weak dependence on centrality which is close to superposition of elementary sources, but slightly decrease in centrality. This may be indication of increase of resonance fraction.
The observed fluctuations are smaller than charge conservation limit shown by dashed lines. The fluctuations are much larger than the QGP model predictions of –3.5 

## Collision energy dependence of net charge fluctuations

-  dyn corrected for charge conservation
- Decrease at SPS
- Little decrease from SPS top energy to RHIC
- UrQMD and RQMD are consistent with the observed fluctuations

- STAR 130GeV: J.Adams, PRC68(2003)044905

- STAR 200GeV:C.Pruneau, nucl-ex/0304021

- PHENIX: K.Adcox, PRL89(2002)082301

- Central events

- Refs.

**Notes:**
In the end, we show collision energy dependence of nu-dynamical.
These 3 red points are CERES data, and 2 blue points are STAR data at sqrts of 130 and 200 GeV.
Nu-dymamical decreases at SPS energies. But there is almost no change from SPS top energy to the RHIC energies.
Both URQMD and RQMD reproduce the fluctuations and decreasing tendency at SPS.

## Conclusions

- Mean pT fluctuations
- Dynamical fluctuations of ~ 1 % are observed at SPS, which are similar to RHIC data. No indication for the critical point or phase transition.
- Fluctuations show non-monotonic dependence on centrality with enhancement over p+p extrapolation in semi-central
- Dependence on the centrality and upper pT cut is similar to PHENIX data
- Net-charge fluctuations
- Dynamical fluctuations smaller than charge conservation limit are observed at SPS
- No indication for suppressed fluctuations in QGP
* ****dyn* corrected for charge conservation decreases at SPS energies but changes little from the SPS top energy to RHIC. At SPS UrQMD and RQMD reproduce the data.

## CERES/NA45 Collaboration

- D. Adamova1, G. Agakichiev2, H. Appelshaeuser3, V. Belaga4, P. Braun-Munzinger2,
- R. Campagnolo3, A. Castillo2, A. Cherlin5, S. Damjanovic3, T. Dietel3, L. Dietrich3,
- A. Drees6, S. I. Esumi3, K. Filimonov3, K. Fomenko4, Z. Fraenkel5, C. Garabatos2,
-  P. Glaessel3, G. Hering2, J. Holeczek2, V. Kushpil1, B. Lenkeit7, W. Ludolphs3, A. Maas2,
- A. Marin2, J. Milosevic3, A. Milov5, D. Miskowiec2, L. Musa7, Yu. Panebrattsev4,
- O. Petchenova4, V. Petracek3, A. Pfeiffer7, J. Rak8, I. Ravinovich5, P. Rehak8, M. Richter3,
- H. Sako2, W. Schmitz3, J. Schukraft7, S. Sedykh2, W. Seipp3, A. Sharma2, S. Shimansky4,
- J. Slivova3, H. J. Specht3, J. Stachel3, M. Sumbera1, H. Tilsner3, I. Tserruya5, J. P. Wessels2,
- T. Wienold3, B. Windelband3, J. P. Wurm8, W. Xie5, S. Yurevich3, V. Yurevich4
*NPI ASCR, Rez, Czech Republic*
*GSI Darmstadt, Germany*
*Heidelberg University, Germany*
*JINR Dubna, Russia*
*Weizmann Institute, Rehovot, Israel*
*SUNY at Stony Brook, U.S.A.*
*CERN, Geneva, Switzerland*
*BNL, Upton, U.S.A.*
*MPI, Heidelberg, Germany*

## Comparison to other SPS and RHIC experiments

- Fluctuations at SPS and RHIC show similar non-monotonic dependence

- PHENIX (s1/2=200GeV)
- nucl-ex/031005

- STAR (s1/2=130GeV)
- nucl-ex/0308033

- NA49 (158AGeV/c)
- hep-ex/0311009

- CERES (158AGeV/c)

## Dependence of mean pT fluctuations on upper pT cut

- Dependence of mean pT fluctuations on upper pT cut

- PHENIX (s1/2=200GeV) nucl-ex/031005

## Pseudo-rapidity dependence of net-charge fluctuations

-  dyn corrected for charge conservation increases as a function of 
- To compare energy dependence, we need to use similar  acceptance

##  acceptance dependence of net-charge fluctuations

-  acceptance dependence of net-charge fluctuations

- Use 80 and 158 AGeV/c data to extrapolate 40 AGeV data to 

## Centrality cut

- Multiplicity Counter vs BC3 (measurement of beam spectator)

## Uncorrected centrality dependence 

- Uncorrected centrality dependence

## pT vs Npart

- pT vs Npart

## Centrality bin dependence

- Sys error due to finite centrality bin-size
- Maximum of ~ -0.4% at 30-50% central
- From dp/p slope
- Estimated contribution ~ -0.4%

## Sys error of Npart

## Centrality dependence of net charge fluctuations with RQMD/UrQMD

## Uncorrected dyn vs sqrt(s)

## Multiplicity dependence of pT fluctuations

- Multiplicity dependence of pT fluctuations

- Superposition of elementary sources whose number is proportional to the multiplicity
-  ***pT**2* is proportional to probability *p *to select a correlated pair
- Centrality dependence
- Change *N**s*, fix *n*, ***pT**2* ~N-1*,F**pT* ~ const
- Long range correlations, with  cut
- Fix *N**s*, change* n*, ***pT**2* ~const, *F**pT* ~ *N*
* ****pTis *is good to compare data with different y acceptance

- 0.1<pT<2.0GeV/c
- Corrected for SRC

## Multiplicity dependence of net-charge fluctuations

- Similar discussions with mean pT fluctuations apply
- Just replace ***pT**2* -> ***dyn*
- Centrality dependence
* ****dyn* ~*N**-1*
- Long range correlations, with  cut, random removal of tracks
* ****dyn*  ~const
- Deviation from constant for  range dependence may be due to correlations of daughters from a resonance

## Comparison to p+p collisions

- Consistent with p+p superposition with Npart scaling in 20% central events
- Rescattering effect is weak.

*NPA727(2003)97*

**Notes:**
次にISRで測定された陽子・陽子衝突での揺らぎとの比較をおこないます。

この図は、Sigma_ptを反応核子数(Npart)の関数としてプロットしたものです。この反応核子数が大きいほど中心衝突、あるいは衝突径数が小さいことを示します。

 重ね合わせる陽子・陽子衝突の数をNpartと仮定すると、原子核・原子核衝突における揺らぎはISRで測定された陽子・陽子衝突のゆらぎ、12%によってこの式のように表され、Npartの-1/2乗のスケーリングが成り立ちます。この重ね合わせ模型はデータによく一致することがわかります。この結果もまた、rescattering等の原子核衝突特有の効果が弱いことを示します。

## Effect of rescattering

- Rescattering effect is opposite between RQMD and UrQMD
- Measured fluctuations are consistent with both models without rescattering

- 158 AGeV/c

*NPA727(2003)97*

**Notes:**
ここで、二つの模型について、二次粒子の散乱、すなわちrescatteringをスイッチオン、オフして揺らぎを比較したのがこのプロットです。これらの模型では通常Rescatteringオンですが、RQMDはデータより高く、URQMDはデータより低くなります。ところがrescatteringをオフにすると、両者ともデータと一致することがわかります。この結果は、rescatteringが実際には非常に弱く、またrescatteringはハドロン相で起こるため、ハドロン相の寿命が非常に短いことを示唆するものです。

##  range dependence of net-charge fluctuations

-  range dependence of net-charge fluctuations

- Consistent with NA49 data at 40 and 158 AGeV/c
- Small difference of vdyn in collision energies after correction for the charge conservation
- Decrease of |vdyn| as a function of 
- Rapidity correlations of daughters from a resonance decay?

## Pseudo-rapidity range dependence

- Enhanced fluctuations at <=0.4
- Similar trend in RQMD/UrQMD without rescattering
- Enhancement disappears in RQMD/UrQMD with rescattering

- 158 AGeV/c

**Notes:**
最後にゆらぎのpseudo-rapidityの幅への依存性を調べます。黒い点がデータで、青い三角がrescatteringなしのURQMD、これがrescatteringをオンにしたURQMDです。データはpseudo-rapidityの幅が0.4以下の範囲で、増加していますが、この傾向はrescatteringなしのURQMDでよく再現されています。ところがrescatteringをオンにするとこの増加は消えてしまいます。この結果も再び、rescatteringが弱いことを示します。

## Net Charge Fluctuations

- Net-charge:*Q=N**+**-N**-*
- Measure
- Fluctuations decrease 1 ~ 0.85 as a function of s1/2
- Increasing fraction of resonances?
- RQMD/UrQMD models reproduce SPS data
- No indication for QGP fluctuations
- Hadron diffusion in y larger than the yacc?

**Notes:**
Collision energy dependence of net-charge fluctuations

 Collision energy dependence of net-charge fluctuations is shown here.

 Net charge is defined as difference between positive and negative particle multiplicities.

 We define a measure as this formula, where sigma_real is the sigma of Q distribution in real events, and sigma_stat is that in the statistical distribution.

 Red points show CERES data again as a function of sqrt(s), compared to PHENIX data at RHIC. They show smooth decrease from 1 to 0.85. 1 corresponds to uncorrelated pion gas limit and 0.75 corresponds to resonance gas limit, therefore the data seem to suggest increasing fraction of resonances.

 Two hadronic models, RQMD and UrQMD, reproduce the SPS data very well.

 We found no indication of suppressed QGP fluctuations of about 0.3. One possible reason is hadron diffusion in rapidity is larger than the rapidity acceptance.

## Pseudo-rapidity dependence of pT fluctuations

- Pseudo-rapidity dependence of pT fluctuations

- Data show higher fluctuations in mid-rapidity
- RQMD reproduces this tendency
- UrQMD has no  dependence

## Corrections for HBT/Coulomb correlations and two-track resolution

- Method
- Remove tracks with small q to another track with a probability
- Add tracks from another event with close opening angles to a real track to correct for lost tracks due to two-track resolution
- Repeat 1. and 2. until the resulting correlation function is flat as a function of q

## PT fluctuation after corrections for HBT and two-track resolutions

- After SRC removal, fluctuations reduce by ~ 30%
- Weak  dependence from /2 to 2.

## Gamma fit

## Statistics and centrality selection

-                                              No. of Pb+Au events
-      Pbeam             #event
-   40 AGeV/c               1.4M
-     80 AGeV/c              0.5M
-    158 AGeV/c              0.5M
- Centrality selection
- Multiplicity in SDDs (40 GeV) Multiplicity Counter (80/158 GeV)
- Number of participant nucleons is estimated with a geometric nuclear overlap (Glauber) model
- /geo             b           <Npart>
-           0-5%          0-3.3 fm       358
- 	   5-10%        3.3-4.7 fm     289
-         10-15%       4.7-5.8 fm     240
-         15-20%       5.8-6.6 fm     200

## Centrality determination

- Determination of centrality
- 0%-100% of the total Pb+Au inelastic cross section
- 0% -> impact parameter=0
- Multiplicity Counter gain distribution

## Systematic errors (6.5% most central)

- PT fluctuation
-                                    40GeV   80GeV    158GeV
- Tracking efficiency +-0.11%  +-0.11%  +-0.06%
- Pile-up events          +-0.03%  +-0.03%  +-0.03%
- Momentum scale     +0.08-0.03% +0.05-0.07% +0.02-0.07%
- Fiducial cut              +-0.01%       -                -
- SDD-TPC assoc.      +-0.02% +-0.02%   +-0.02%
-  2,vertex cut           +0.39-0.04% +0.13-0.01%   <+- 0.01%
**Total                        ****+0.41****-0.23****%**** ****+0.18****-0.13****%**** ****+0.12****-0.13****%**
- Net-charge fluctuation
-                                   40GeV   80GeV   158GeV
- Pile-up events          +-0.0001  +-0.0001  +-0.0001
-  extrapolation         +-0.0003          -             -
- SDD-TPC assoc.      +0.0000-0.0005   +0.0000-0.0004  +0.0000-0.0004
- 2,vertex cut             +0.0001-0.0001   +0.0000-0.0003 +0.0001-0.0002
**Total                        ****+0.0006****-0.0006  ****+0.0001****-0.0005   ****+0.0004****-0.0005**

## Flow toy model

- Pt and multiplicity distributions from the real data (158AGeV)
- Flow input
- Reaction plane angle changes randomly
- No pt fluctuations produced (track efficiency 80-100%, ebe v2 fluctuations 0-50%),
-  pt <0.3% in and Fpt <0.2%

## Tracking selection and parameters

- Track Selection
- TPC tracks (no. of hits >= 11-14 out of 20)
- Target cut (projection of TPC track on the primary vertex < 4cm)
- Momentum resolution
-  p/p =**(0.024****2****+(0.036p)****2****)****1/2** at 40 AGeV
- =**(0.015****2****+(0.016p)****2****)****1/ 2** at 80, 158 AGeV
- Acceptance
- ~ 60% of TPC at 40 AGeV
-  >90% at 80, 158 AGeV
- Tracking efficiency
- Better than 85% at pT>0.05GeV/c
- 2-particle resolution
- ~5 mrad in TPC

## Target area