# Presentation: 261754

##               Rapporteur II:Global & Flow Observables

**Peter Steinberg**
- Brookhaven National Laboratory

## Global Flow

- Peter Steinberg
- BNL

## Outline

**Global Variables**
- Event shape
- dN/d
- Centrality dependence
- dN/d
- dET/d
- pT
- Initial Energy density

**“****Flow” **
- Event shape
- dN/d
- Centrality dependence
- dN/d
- Species
- v1,v2,
- Initial Pressure

-  In principle, we are looking at two important pieces of the equation of state...

## Centrality: Participants vs. Spectators

**Centrality: ****Participants vs. Spectators**

- “Spectators”

- Zero-degreeCalorimeter

- “Spectators”

- Many things **scale** with **N****part**:
-  Transverse Energy
-  Particle Multiplicity
-  Particle Spectra

**“****Participants”**

- Only ZDCs **measure N****part**** **

- The collision geometry (i.e. the impact parameter) determines the number of nucleons that **participate** in the collision

**Produced Particles**

## Measuring Centrality

- Fluctuations modify the response
- less central events fluctuate to central bins
- The final “measurement” of Npart is the best attempt to factor out the facts of life!

- In principle, we could work with % of cross section
- Final measurement of Npart is best attempt to correct for facts of life

- Multiplicity in 3<||<4.5

**N****part**

- Clearly, fluctuations affect your centrality estimator

## Why we should use Npart

- Very difficult to compare experimental results without serious estimate of Npart
- Must incorporate fluctuations in the measurement of the centrality estimators
- OK, Glauber implementation is a real uncertainty
- Even if you don’t “like” participants, the exercise is critical for inter-experiment comparisons

## ZDC as centrality device

- Only shared detector
- Rates: luminosity via well-known reference process
- Timing: substantial background rejection
- Pulse height: measures centrality
- Directly confirms monotonic relationship between participants with multiplicity

## Mutual Coulomb Dissociation

- Reference: zdc =10.7+/-0.5 b
**Measurement: (********geo**** / ********tot****)****exp ****=**
**(N****bbc****/ N****tot****)****exp****/ ********bbc****= (0.668 ******** 0.022)**
**Theory: ********geo**** / ********tot ****= (0.673 ******** <0.034)**

- (measured)

- (from Glauber)

## Multiplicity: what is learned

- Can the models get the “big picture” right?
- However, let’s not ignore the details...
- Magnitude
- Integral over energy density, stopping, shadowing, quenching, flow
- Centrality dependence
- Study effect of system size (onset of interesting effects above critical volume)
- Interplay between Npart and Ncoll
- Shape
- Stopping, Final state interactions

## Energy dependence 

**PHENIX**

**STAR prelim. 10%**

**PHOBOS**

**BRAHMS prelim.**

## dN/d: Predictions

- with quenching

- no quenching

## dN/d: Post-dictions

**AMPT**

**LEXUS**

- AMPT, LEXUS, DSM, HIJING, EKRT
- Please be careful about scaling y to 
- Not boost invariant!
- Not .9, .95 etc.
- Jacobian depends on velocity: dy =  d
- Depends on species and mean pT!
- Still not sure who gets the champagne...wait for 200 GeV

## dN/d  vs Centrality at =0

**dN/d********  vs Centrality at ********=0**

- dN/d / .5Npart

- Npart

## Uncertainty on Npart

- Estimating 96% when really 90% overestimates Npart
- Creates “pivot point” at central events
- Hard to rule out EKRT...

**Uncertainty on N****part**

- Measurement sensitive to trigger bias
- “Minimum-bias” still has bias
- Affects most peripheral events

- This measurement

- % Error on Npart

- Npart

## PH: OBOS vs. ENIX

- dN/d / .5Npart

- Npart

## dNch/d vs. Centrality

- 45-55%

- 35-45%

- 25-35%

- 15-25%

- 6-15%

- 0-6%

- 

- 

- 

- dNch/d**

- dNch/d**

**dN****ch****/d******** vs. Centrality**

**Notes:**
So now lets look at the data.  First of all let me show some distributions for a selected set of centrality bins, here described by the fraction of the cross section they correspond to. The colors are there just to show you that the data from these disparate pieces of the experiment actually match up together quite nicely.  And just looking at these distributions you can start to get a sense of  what’s happening as the data evolve with centrality.  For instance, its clear that for the most central collisions the data in the fragmentation region are relatively lower to those at mid rapidity than for more peripheral collisions.  But lets look at these things in a bit more detail.

## Shapes of dNch/d for different Npart

**Shapes of dN****ch****/d******** for different N****part**

**

**

- dNch/d

- (dNch/d)/(1⁄2Npart)

- dNch/d

- Data

- HIJING

- HIJING

- (dNch/d)/(1⁄2Npart)

- Systematic error ±(10%-20%)

- 354

- 216

- 102

- Mean Npart

- %

- 0-3

- 15-20

- 35-40

- Data

**Notes:**
To see how these data evolve with centrality, on the left we’ve plotted the
multiplicity distributions for three different centrality bins, here expressed as
numbers of participants.  On the top are the data unscaled, and on the bottom the
data are scaled by the number of participants. The corresponding results from
HIJING appear on the right.  We observe some rather striking behavior.  For
instance, whereas on the right, the scaled HIJING data all more or less converge
to the same values, we see that the shapes of the data are quite different. In 
particular, at large rapidity, for the most central collisions the scaled data are 
actually below there more peripheral counterparts – there is an apparent cross
over around eta=4 or so.  This could indicate some extra stuff coming from 
spectator matter, or possibly the influence of hadronic rescattering.  Also, just
in general the measured distributions are markedly wider than those predicted by
HIJING.  This could reflect a number of different effects, but we’d rather not
speculate about it for now.

## Centrality dependence of dNch/d|

- Npart

- (dNch/d)/(1⁄2Npart)

- ||

- <1

- 5-5.4

- 4-4.4

- 3-3.4

- 2-2.4

- Symbols:

- Solid lines:  HIJING

- Errors are systematic

**Centrality dependence of dN****ch****/d**********|******

## Total Multiplicity (||<5.4)

- Npart

- Nch

- HIJING

## Multiplicity Results

- EKRT, HIJING disfavored by both PHENIX & PHOBOS
- Initial state saturation looks like modified Glauber
- No way to resolve using Nch alone
- What about ET?
- Hydro does *p dV *work during longitudinal expansion, decreases dET/d
- Eskola: “ET will be more efficient model killer”...
- So far, few papers predicting ET, but surely on the way
- PHOBOS got 9 in two months after the first paper...

## Centrality dependence of ET

- ET and charged particles appear to vary in lockstep
- Fits are a modified WNM, possibly allow extraction of fraction of hard production (NB. ambiguities persist...)

- PHENIX Preliminary

- PHENIX submitted

## ET per charged particle

- Independent of centrality
- Appears to be same as WA98 (@SPS)

- Energy dependence
- Possible 20% discrepancy betw. NA49/WA98
- Where is the increased <pT> seen by STAR/PHENIX?

- PHENIX Preliminary

- PHENIX Preliminary

## “So what’s the Energy Density?”

- Sorry, I won’t tell you...
- Implication of PHENIX
- Constant ET/charged particle
- Energy density (via Bj formula) simply scales with multiplicity!
- (Even PHOBOS can do it!)
- ~50% higher than SPS...

- Ambiguities persist
- Formation time might be substantially less

## “Flow”

- Radial flow
- Not seen in angular distributions
- Use HBT, spectra (T = To + m<2> - Nu Xu)
- Directed flow
- Forward rapidities
- Not measured yet
- Sensitivity estimated at PHOBOS/STAR
- Interesting predictions for phase transition...

- Elliptic flow
- Early time push, hydrodynamic evolution
- Strongest at midrapidity

## v2 from azimuthal correlations

- Method used by PHENIX
- Similar information content as Fourier method
- OK for partial acceptance
- Sensitive to other correlations
- Jets (at 180o) , HBT (at 0o)
- But is that bad?
- CERES data

****

**0-5%**

**15-30%**

** ****5-15%**

## v2 versus centrality

**v****2**** versus centrality**

- Boxes show “initial spatial anisotropy”  scaled by 0.19-0.25

- PRL 86, (2001) 402

- || < 1.3
- 0.1 < pt < 2.0

## Centrality Dependence

**Hydrodynamic model**

**V****2**

**Normalized Paddle Signal**** **

- midrapidity : |h| < 1.0

**SPS**

**AGS**

**Preliminary**

## CERES slides

- Excitation function
- CERES 40 GeV fits in with existing energy systematics
- Back-to-Back correlations
- Extraction of v2 is substantially higher than normal event plane analysis

## pT dependence for ,p

**p****T**** dependence for ********,p**

- Hydro calculations: P. Huovinen, P. Kolb and U. Heinz

## v2 at high pT

**v****2**** at high p****T**

- Hydro fails at large transverse momentum
- Possible interpretations suggested by jet quenching (wait for A. Drees talk)
- However, perhaps composition is a critical part of this effect...

**PHENIX Preliminary**

## Comparison of all v2 results

**PHENIX (p****T****>500 MeV)**

- nch/nmax

- v2

## v2 vs. (pseudo)rapidity

- NA49 (y),  PHOBOS() (mainly pions)
- Different shape at midrapidity
- PHOBOS shape similar to dN/d!
- Low-density limit??  **v****2**** ~ ********dN/dy**
- However, v2 appears to fall faster than multiplicity

- PHOBOS Preliminary

- PHOBOS Preliminary

- 

- 

- dN/d

- v2

**y**

- v2

## Conclusions

## Assumptions:

**Assumptions:**
-     in Lab                    in C.M.** **
**Energy density (Bjorken):**
**From SPS to RHIC**
- ~50% increase in *dN**ch**/dy *
- ~50% increase in* dE**t**/dy*
- at least 50% increase in **

## Mean  pt versus number of participants

**Mean  p****t**** versus number of participants**

- Pions
- steep rise and plateau
- Protons
- gradual rise and higher <pt>

## Sub Event Correlation

**Sub Event Correlation**

- Non-Flow Effects
- Momentum conservation
- HBT, Coulomb (final state)
- Resonance decays
- Jets