# Presentation: 450277

## NEW Fluctuation and Low-pT Correlation Results from PHENIX

- Workshop on Correlations and Fluctuations in Relativistic Nuclear Collisions – 7/8/06
- Jeffery T. Mitchell
*(Brookhaven National Laboratory)*

_**Outline**_
** ****Multiplicity Fluctuations**
** ****Correlation Lengths **
**	****(using multiplicity fluctuations)**
** ****Low-p****T**** Correlations**

## The PHENIX Detector

**Although the PHENIX acceptance is traditionally considered small for event-by-event measurements, the acceptance is large enough to provide a competitive sensitivity to most observables.**

**Acceptance:**
**|********| ~ 0.35, |********|~ ******

**Two “central arm” spectrometers anchored by drift chambers and pad chambers for 3-D track reconstruction within a focusing magnetic field.**

## Measuring Multiplicity Fluctuations with Negative Binomial Distributions

**Multiplicity distributions in hadronic and nuclear collisions can be described by the Negative Binomial Distribution. The magnitude of the parameter k describes the deviation from a Poisson distribution ******** higher k means more Poissonian. **

**Central 62 GeV Au+Au**

***UA5: sqrt(s)=546 GeV p-pbar, Phys. Rep. 154 (1987) 247.***
***E802: 14.6A GeV/c O+Cu, Phys. Rev. C52 (1995) 2663. ***

**UA5**

**E802**

**PHENIX Preliminary, 62 GeV Au+Au**

**5-10% Central**

**25-30% Central**

## Impact Parameter Fluctuations: Data

***A major source of non-dynamical fluctuations are contributions due to geometry (N******part******) fluctuations due to the finite width of the centrality bin. This can be demonstrated directly with data...***

**Geometry fluctuations drive ********2****/******** down and N.B.D. k up.**

**PHENIX Preliminary**

## Impact Parameter Fluctuations:Estimation Using HIJING 1.37

- Impact Parameter Fluctuations:Estimation Using HIJING 1.37

**Corrections for geometry fluctuations are estimated using HIJING 1.37 run a) with a fixed impact parameter, and b) with an impact parameter covering the range of the 5% centrality bin. Estimations match the 1% centrality data. Estimated systematic errors are 12-15% (included in all further data points.**

## A Survey of Scaled Variance, 

- A Survey of Scaled Variance, 

** ****Inclusive charged hadron fluctuations. **
** ****0.2 < p****T**** < p****T,max ****GeV/c**
**These values are corrected to remove the contribution due to impact parameter (geometrical) fluctuations and projected to 2******** in azimuth for direct comparisons to NA49 and other experiments.**
** ****The Poissonian (random) limit is 1.0.**
** ****Large non-random fluctuations are observed that increase with p****T**** and decrease with centrality, although the p****T****-dependence is relatively weak, unlike <p****T****> fluctuations.**

**PHENIX Preliminary**

**PHENIX Preliminary**

## Fluctuations over the entire pT range

- Fluctuations over the entire pT range

**Inclusive charged hadron fluctuations. All points are projected to 2******** azimuthal acceptance, corrected for detector occupancy and efficiency. All points are corrected for non-dynamical geometry fluctuations due to the finite width of the centrality bins. Errors include time-dependent systematic errors, azimuthal extrapolation systematic errors, and impact parameter correction systematic errors. p+p fluctuations are consistent with projections of UA5 results to sqrt(s)=200 GeV.**

**0.2 < p****T**** < 3.0 GeV/c**

**0.2 < p****T**** < 3.0 GeV/c**

**PHENIX Preliminary**

**PHENIX Preliminary**

## Thermodynamically Motivated Observables: Relating distributions to compressibility

- In the Grand Canonical Ensemble, the variance in particle number N (with =<N>) is related to the compressibility, kT, via
- The N.B.D. k parameter is related to the scaled variance via
- N.B.D. k and the scaled variance can then be related to compressibility:

## Multiplicity Fluctuations: Universal Scaling

**All species scaled to the 200 GeV dataset. The data appear to follow a universal curve.**

## Multiplicity Fluctuations: Universal Scaling

**NA49 data corrected for geometry fluctuations (10% centrality bins) also lie on the universal curve.**

## Multiplicity Fluctuations: Universal Scaling

**The universal curve can be described by a power law function of N****part****.**

## Multiplicity Fluctuations: Extracting a Correlation Length

** ****To extract  ********, the N.B.D. k parameter is extracted by fitting the multiplicity distribution in successive ranges of ******** or ********.**
** ****NBD k can be related to a correlation length as follows (see *****E802, Phys. Rev. C52 (1995) 2663*****  and K. Homma’s presentation):**
** **

**Here, ******** is fixed to 0.5 (based on PHENIX preliminary correlation function measurements). ******** and ******** are free parameters.**

## Example: N.B.D. k vs. d

**Example: N.B.D. k vs. d******

**PHENIX Preliminary**

## Correlation length () in centrality and pT,max

- Correlation length () in centrality and pT,max

**Measurements with the full PHENIX magnetic field.**
**All species show the same increasing trend as N****part**** and p****T,max**** decrease. Correlation length increases at low p****T****.**

**PHENIX Preliminary**

**PHENIX Preliminary**

## Correlation length () in centrality and pT,max

- Correlation length () in centrality and pT,max

**PHENIX Preliminary**

**PHENIX Preliminary**

**All species show the same increasing trend as N****part**** and p****T,max**** decrease. Correlation length increases at low p****T****.**

## Correlation Length vs. Centrality

**The correlation lengths are small, but cannot be explained by detector resolution effects.**
**Correlation lengths increase from 200 to 62 GeV.**

**0.2 < p****T**** < 3.0 GeV/c**

**0.2 < p****T**** < 3.0 GeV/c**

## Correlation Lengths: Universal Scaling

**The universal curves can be described by a power law function of N****part****.**

**These points have been scaled to match the 200 GeV data. Notice that the correlation lengths exhibit a universal behavior as a function of centrality.**

**0.2 < p****T**** < 3.0 GeV/c**

**0.2 < p****T**** < 3.0 GeV/c**

## Universal Scaling: pT-independent

- Universal Scaling: pT-independent

**The power law curves describing the data are independent of p****T**** range. The scaling appears to be driven by low p****T**** processes.**

**0.2 < p****T**** < 0.75 GeV/c**

**0.2 < p****T**** < 0.75 GeV/c**

## Correlation length  and static susceptibility 

- Correlation length  and static susceptibility 

**PHENIX Preliminary**

**PHENIX Preliminary **

- Np

- Np

- k=0 * T

- Divergence of susceptibility is the
- indication of 2nd order phase transition.

- Divergence of correlation length is an
- indicator of a critical temperature.

- Correlation length 

**No magnetic field**

**No magnetic field**

## Systematic check of the correlation length

****

****

****

**PHENIX Preliminary**

**PHENIX Preliminary**

**PHENIX Preliminary**

**10%**** ****cent. bin width**
**  ****5% cent. bin width**

-  can absorb finite centrality
- bin width effects, namely,
- finite initial temperature
- fluctuations, while physically
- important parameters are
- stable.

**Shift to smaller fluctuations**

**Np**

**No magnetic field**

## <pT> Fluctuations

**Red: Random Expectation           (******** distribution)**
**Blue: STAR acceptance fluctuation of:**
******pT****=52.6 MeV,**
** ****F****pT****=14%, **
******2****pT,dyn****=52.3 (MeV/c****2****),**
******pT****=9.8%**

- MpT = Event-by-Event Average pT

- Gamma distribution calculation for statistically independent particle emission with input parameters taken from the inclusive spectra. *See M. Tannenbaum, Phys. Lett. B498 (2001) 29.*

## PHENIX Event-by-Event <pT> Fluctuation Results

**0.2 < p****T**** < p****T****max**

**20-25% centrality**

***S. Adler et al., Phys. Rev. Lett. 93 (2004) 092301.***

**Highlights: Non-random fluctuations are observed. Non-monotonic centrality-dependence. Strong p****T****-dependence. p****T**** fluctuations appear to be driven by high p****T**** particles. The shape can be explained using a PYTHIA-based simulation by the contribution of correlations due to jets.**

## <pT> Fluctuations: Universal Scaling?

**The universal curves can be described by a power law function of N****part****.**

## Two-Particle Correlations at Low pT

** ****Most charged particle correlation results are performed in the interesting high-p****T**** region with a trigger particle.**
** ****The low-p****T**** region and its evolution to the high p****T**** region is interesting too!**
** ****This study will quote correlation amplitudes in a given centrality, p****T****, and ******** bin with no trigger particle determined using the mixed event method via:**
**  ****C(********) = (dN/d********data****/dN/d********mixed****)*(N****events,mixed****/N****events,data****)**
**Note: No reference subtraction here.**
** ****Correlations will be plotted in p****T**** and y****T**** (which serves to emphasize the low p****T**** region).**
** ****Shown are results for 200 GeV Au+Au, 62 GeV Au+Au, 200 GeV p+p, and 200 GeV d+Au collisions. y****T****-y****T**** correlations are integrated over azimuth.**

**p****T****=0.3 GeV ******** y****T****=1.5 **
**p****T****=0.5 GeV ******** y****T****=2.0**
**p****T****=1 GeV ******** y****T****=2.7**
**p****T****=1.5 GeV ******** y****T****= 3.1**

***Assuming the pion mass for y******T******.***

## Like-sign Near-side (<60o) Correlations in Transverse Rapidity

- Like-sign Near-side (<60o) Correlations in Transverse Rapidity

**200 GeV p+p**

**200 GeV d+Au**

**62 GeV Au+Au**

**200 GeV Au+Au**

**HBT-like component here**

**Jets**

**p****T****=0.3 GeV ******** y****T****=1.5 **
**p****T****=0.5 GeV ******** y****T****=2.0**
**p****T****=1 GeV ******** y****T****=2.7**
**p****T****=1.5 GeV ******** y****T****= 3.1**

**|********|<0.7**

**0-5% central**

**0-5% central**

**p****T****-p****T**** Correlations**

## Unlike-sign Near-side (<60o) yT Correlations

- Unlike-sign Near-side (<60o) yT Correlations

**200 GeV p+p**

**200 GeV d+Au**

**62 GeV Au+Au**

**200 GeV Au+Au**

**The jet structure persists, the broad peak with the HBT component on the near side does not.**

**p****T****-p****T**** Correlations**

## Correlations Comparisons along a yT,1=yT,2 bin slice

**p****T****=0.25 GeV ******** y****T****=1.34**
**p****T****=0.3 GeV ******** y****T****=1.5 **
**p****T****=0.5 GeV ******** y****T****=2.0**
**p****T****=0.9 GeV ******** y****T****=2.56**
**p****T****=1.5 GeV ******** y****T****= 3.1**

** ****The 62 GeV and 200 GeV Au+Au distributions are similar.**
** ****The behavior at low p****T**** between Au+Au and d+Au collisions is different in all 4 cases.**
** ****The influence of resonance and conversion contributions is under investigation.**

## Like-sign Near-side (<60o) yT Correlations

- Like-sign Near-side (<60o) yT Correlations

**0-5%**

**10-15%**

**20-25%**

**30-35%**

**40-50%**

**60-70%**

***The primary features persist from central to peripheral collisions. Correlations for the most peripheral collisions are similar to d+Au collisions. This statement is true for all 4 cases.***

**200 GeV Au+Au**

## Correlations Comparisons along a yT,1=yT,2 bin slice

- Correlations Comparisons along a yT,1=yT,2 bin slice

**The integrated correlation amplitudes vary little over  a wide range of centralities (and pair occupancies). Later, background and flow-subtracted peak amplitudes will be measured.**

**p****T****=0.25 GeV ******** y****T****=1.34**
**p****T****=0.3 GeV ******** y****T****=1.5 **
**p****T****=0.5 GeV ******** y****T****=2.0**
**p****T****=0.9 GeV ******** y****T****=2.56**
**p****T****=1.5 GeV ******** y****T****= 3.1**

## Charge Difference Correlations: C(LS)-C(US): Near Side

**Charge Difference Correlations: C(LS)-C(US): Near Side**

**200 GeV p+p**

**200 GeV d+Au**

**62 GeV Au+Au, 0-5% Central**

**200 GeV Au+Au, 0-5% Central**

**Calculated by subtracting the correlation amplitude of unlike-sign pairs from that of like-sign pairs. It is expected that  primarily HBT remains in this case at low y****T****. The remaining peak is much broader in Au+Au collisions and shifted in y****T**** compared to p+p and d+Au collisions. The location of the peaks in y****T**** agree with STAR results.**

## Charge Difference Correlations: C(LS)-C(US): Away Side

**Charge Difference Correlations: C(LS)-C(US): Away Side**

**200 GeV p+p**

**200 GeV d+Au**

**62 GeV Au+Au, 0-5% Central**

**200 GeV Au+Au, 0-5% Central**

**A similar peak with similar properties compared to the near-side is seen on the away-side, but with a lower integrated correlation amplitude.**

## Charge Difference Correlations Comparisons along a yT,1=yT,2 bin slice

- Charge Difference Correlations Comparisons along a yT,1=yT,2 bin slice

**The near and away side charge difference correlations are qualitatively similar. The p+p and d+Au charge difference correlations do not decrease significantly at low y****T****.**

## Near-Side Peak Amplitude vs. Centrality

**200<p****T,1****<500 MeV/c, 200<p****T,2****<500 MeV/c**

**|********|<0.1**

**Azimuthal correlation functions were measured for all like-sign pairs with both pairs in the p****T**** range from 200-500 MeV (y****T****<2). The near-side peak was fit to a Gaussian convoluted with a Background*cos(2********) flow term (Au+Au only). For |********|<0.1, the like-sign pairs are correlated in Q****invariant**** space, the unlike-sign pairs are not.**

- ||<60o

## Near-Side Peak Amplitude vs. Centrality

**200<p****T,1****<500 MeV/c, 200<p****T,2****<500 MeV/c**

**|********|<0.1**

**These 2 species lie on a universal curve. The universal curves can be described by a power law function of N****part****. Look for Cu+Cu data soon...**

- ||<60o

## Near-Side Peak Amplitude vs. pT

- Near-Side Peak Amplitude vs. pT

**|********|<0.1**

**p****T,min****<p****T,1****<p****T,max****, p****T,min****<p****T,2****<p****T,max**

**Central Au+Au flow- and background-subtracted amplitudes decrease exponentially with p****T**** while the p+p and d+Au amplitudes remain flat. The amplitude increase above 1 GeV is due to the contribution of hard processes. No evidence for excess contributions from hard processes is seen in Au+Au collisions in the p****T****=0.5-1.0 GeV/c range.**

**Points plotted in the center of each p****T**** bin.**

**p****T**** bin widths have been chosen such that the mean number of pairs per event is the same in each bin.**

- ||<60o

## Let’s assume that the increased fluctuations are indicative of critical behavior. Then, it is expected that a) the system can be described by critical exponents, and b) all systems can be described by the same set of critical exponents. Recall that

The critical exponent for compressibility is represented by the symbol  and is described by

Replacing and solving for 1/kNBD gives (A=constant, T=Temperature, V=volume)

- The critical exponent for compressibility is represented by the symbol  and is described by
- Replacing and solving for 1/kNBD gives (A=constant, T=Temperature, V=volume)

- Just for Fun: A Critical Exponent Analysis

## N.B.D. 1/k+1/

**All four systems exhibit a power law behavior with respect to N****part****. All systems appear to follow a universal curve within errors.**
**The fit assumes that N****part,c****~0**
**The value of the critical exponent is ********=1.24±0.13 (p=1/3) for all species.**
**This is consistent with ******** for common gas-liquid phase transitions, which are typically between 1.2 and 1.3.**

- N.B.D. 1/k+1/

**0.2 < p****T**** < 3.0 GeV/c**

** ********=1.24±0.13**

## Critical Exponents vs. p and Npart,c

## PHENIX has presented a survey of multiplicity fluctuations as a function of collision species, collision energy, centrality, and pT range. 
The fluctuations increase with a power law behavior as centrality decreases.
All species measured can be described by a universal power law curve.
 PHENIX has presented a survey of correlation length measurements using multiplicity fluctuations
Correlation lengths at low pT exhibit a maximum at Npart=100.
Correlation lengths are smaller than similar measurements at the AGS.
Correlation lengths increase with decreasing beam energy.
Correlation lengths increase at low pT.
Correlation lengths as a function of Npart (Npart>100) for all species can be described by a universal power law curve.
PHENIX has presented a survey of two-particle pT correlations at low pT in Au+Au, d+Au, and p+p.
Significant differences in like-sign near-side correlations are seen between p+p and d+Au at low pT.

- The fluctuations increase with a power law behavior as centrality decreases.
- All species measured can be described by a universal power law curve.
-  PHENIX has presented a survey of correlation length measurements using multiplicity fluctuations
- Correlation lengths at low pT exhibit a maximum at Npart=100.
- Correlation lengths are smaller than similar measurements at the AGS.
- Correlation lengths increase with decreasing beam energy.
- Correlation lengths increase at low pT.
- Correlation lengths as a function of Npart (Npart>100) for all species can be described by a universal power law curve.
- PHENIX has presented a survey of two-particle pT correlations at low pT in Au+Au, d+Au, and p+p.
- Significant differences in like-sign near-side correlations are seen between p+p and d+Au at low pT.

- Conclusions

## Good luck to our host country!

- Photos from Round 1:
- Italy 1, USA 1

## Auxiliary Slides

## <pT> Fluctuations: Universal Scaling?

**The universal curves can be described by a power law function of N****part****. Residual STAR vs. PHENIX differences may be attributed to acceptance.**

## Acceptance and Occupancy Corrections: Results Extrapolated to 2 Acceptance

**Multiplicity fluctuations are acceptance dependent. PHENIX results shown here are projected to 2p acceptance to facilitate direct comparisons to other measurements.**

## A Survey of N.B.D. 1/k

** ****Inclusive charged hadron fluctuations. **
** ****These values are corrected to remove the contribution due to impact parameter (geometrical) fluctuations and projected to 2******** in azimuth for direct comparisons to NA49.**
** ****Here, the Poissonian (random) limit is 1/k********0. **
** ****Large non-random fluctuations are observed that decrease with centrality.**

**Preliminary Request**

**PHENIX Preliminary**

**PHENIX Preliminary**

## Jet Simulation Results: PHENIX at sqrt(sNN) = 200 GeV

- The Sprob parameter is initially adjusted so that FpT from the simulation matches FpT from the data for 20-25% centrality (circled). It is then FIXED and finally scaled by RAA for all other centralities.

**20-25% centrality**

**PHENIX Data: nucl-ex/0310005**

**200 MeV/c < p****T**** < p****T****max**

**This decrease due to jet suppression?**

**This decrease is due to the signal competing with the M****pT**** width increase for low N.**

## Impact Parameter Fluctuations: HIJING 1.37

**Corrections for geometry fluctuations are estimated using HIJING 1.37 run a) with a fixed impact parameter, and b) with an impact parameter covering the range of the 5% centrality bin. Estimations match the 1% centrality data. Estimated systematic errors are 12-15% (included in all further data points.**

## Relations to the observable N.B.D k

**Fluctuation caused by**
**centrality bin width**

**Two point correlation function in one dimensional case in a fixed *****T***

**Two particle correlation function**

**Relation to N.B.D. k**

## Susceptibility

## Correlation Length Excitation Function

**The correlation lengths measured here are small. However, they are an order of magnitude larger than the two-track resolution (when projected to the detector radius).**

## Near-Side Peak Width vs. Centrality

**200<p****T,1****<500 MeV/c, 200<p****T,2****<500 MeV/c**

**|********|<0.1**

**The standard deviation of the Gaussian fit to the flow- and background-subtracted near-side peaks for all like-sign pairs within the p****T**** range 200-500 MeV/c. The 200 GeV Au+Au peaks broaden significantly towards the most central collisions. The d+Au peak is much more narrow than the p+p peak.**

## Correlation Lengths: Critical Exponent Analysis

**The data from other systems have been scaled to lie on top of the 200 GeV Au+Au points for emphasis. The fits yield ********=4.26 for pseudorapidity and ********=5.53 for azimuth. The typical value for ******** in common systems is 0.5.**

** ********=4.26±0.16**

** ********=5.53±0.18**

## Thermodynamically Motivated Observables: Relating pT Fluctuations to Heat Capacity

** ****Let’s switch p****T**** fluctuation measures to the commonly used ********pt**** = (event-by-event p****T**** variance) – (inclusive p****T**** variance)/(mean multiplicity per event) normalized by the inclusive mean p****T****. For random particle emission, this variable is 0.**
** ****From *****R. Korus et al., Phys. Rev. C64 (2001) 054908*****, this variable can be related to the heat capacity by:**
** ****The critical exponent for the heat capacity is given by:**
** ****Substituting gives:**

## <pT> Fluctuations: Critical Exponent Analysis

**The CERES data has been scaled to the match the PHENIX data. Within the (large) errors, the various species lie on a universal curve. The fit to the PHENIX data yields ********=-2.38. Typical values are ********=0.1.**

** ********=-2.38±0.04**

## <pT> Fluctuations: Critical Exponent Analysis

**The CERES and PHENIX data has been scaled to match the STAR 200 GeV Au+Au data. Within the smaller STAR errors, the various species lie on a universal curve. The fit to the STAR data yields ********=-3.77. Typical values are ********=0.1.**

** ********=-2.38±0.04**

** ********=-3.77±0.51**

## Power Law Fit Systematics

******~0.1**

******~0.5**

******~0.5**

******~0.4**

## Like-sign Away-side (>120o) yT Correlations

- Like-sign Away-side (>120o) yT Correlations

**200 GeV p+p**

**200 GeV d+Au**

**62 GeV Au+Au**

**200 GeV Au+Au**

**The jet structure persists, the peak with the  HBT component does not. A low p****T**** correlation  is observed in Au+Au collisions only for p****T****<300 MeV/c. It’s source is under investigation.**

**p****T****-p****T**** Correlations**

## Unlike-sign Away-side (>120o) yT Correlations

- Unlike-sign Away-side (>120o) yT Correlations

**200 GeV p+p**

**200 GeV d+Au**

**62 GeV Au+Au**

**200 GeV Au+Au**

**The jet structure persists, the broad peak with the HBT component from like-sign near-side pairs does not.**

**p****T****-p****T**** Correlations**