# Presentation: 479638

## Charged particle multiplicity studies with PHOBOS

*Birger Back*
*Argonne National Laboratory*
*for the*
*PHOBOS Collaboration*

## PHOBOS Collaboration

- Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel,
-  Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova,  Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey,
- Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland, Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov,
- Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs,  Barbara Wosiek, Krzysztof Woźniak, Bolek Wysłouch
- 	ARGONNE NATIONAL LABORATORY	BROOKHAVEN NATIONAL LABORATORY
- 	INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW	MASSACHUSETTS INSTITUTE OF TECHNOLOGY
- 	NATIONAL CENTRAL UNIVERSITY, TAIWAN	UNIVERSITY OF ILLINOIS AT CHICAGO
- 	UNIVERSITY OF MARYLAND	UNIVERSITY OF ROCHESTER

## PHOBOS experiment: June 2000 – June 2005	

***PHOBOS experiment: June 2000 – June 2005******	***

- -5.4 <  < 5.4
- 0.5o <  < 179.5o

- Main emphasis:
- 4 multiplicity and
- low pT particles

## PHOBOS multiplicity measurements

- System		s1/2 (GeV)
- Au+Au		200, 130, 62.4, 19.6
- Cu+Cu		200, 62.4, 22.4
- d+Au		200
- p+p			200, 410

## dN/d basics

**Notes:**
Let me start by showing some of the basic characteristics of dN/deta distributions.

## What would an isotropic source look like?

***What would an isotropic source look like?***

- Isotropic emission:
- 1/cosh2

- Only 22% emitted
- with pT > pL
- These
- particles carry
- information about
- the densest region
- formed in the
- collisions

**Notes:**
Having realized this simple fact we may ask ourselves “What does a truly isotropic distribution look like?”
This is the kind of distributions you would expect from a hot source formed in full ‘stopping’ reactions without any hydrodynamics effects, such as flow, etc.
The answer is shown here: 
Isotropy means a flat distrubution in dN/d, a sin distributions in dN/d
and a 1/cosh2 distributions in dN/d.
Much narrower than the experimental distribution emphasizing again the fact that the observed angular distributions is very forward-backward peaked – highly non-isotropic.

## What happens to the original protons?

- (BRAHMS preliminary)

- dN/dy

- I.Bearden (BRAHMS), QM2006

- Net (original) protons move away from mid-rapidity region with increasing collision energy
- Mid-rapidity region begins to look like a pure energy-density region reminiscent of the early universe

## dN/d @ =0

**Notes:**
Let’s now concentrate on the particle emission in the mid-rapidity region – the minimum of the angular distribution dN/d, but the mid-rapidity plateau in the pseudo-rapidity space.

## Pre-RHIC theoretical predictions

***Pre-RHIC theoretical predictions***

- PHOBOS, Nucl. Phys. A747, 28 (2005)

- First RHIC
- results
- New data
- PRC 74, 021901
- (2006)

**Notes:**
First a quick look back in the history.
Before RHIC turned on there was a large number of theoretical predictions for the multiplicity of particles emitted at mid-rapidity in 200 GeV Au+Au collisions.
The predictions varied by up to a factor of two as illustrated here.
In retrospect we see that the experimental value for 200 GeV lies in in the lower range of the predictions.
In fact, the increase in charged particle multiplicity at eta=0 with energy turns out to be only logarithmic as shown in the right panel.

## Factorization of centrality and energy dependence

- ||<1

- Data: PHOBOS, PRL 97, 012301 (2006); PRC70, 021902(R) (2004); PRC65, 061901(R) (2002)

## Energy density

**Notes:**
Let’s now concentrate on the particle emission in the mid-rapidity region – the minimum of the angular distribution dN/d, but the mid-rapidity plateau in the pseudo-rapidity space.

## Energy density estimates?

- Absolute maximum:
- Total available energy:
- Volume at instant of overlap:
- Instantaneous energy density:
*Not equilibrated matter*
- Birger’s estimate:
- Isotropic energy:
- Volume after 0 =1 fm/c:
- Equilibrated energy density:

## Bjorken estimate of energy density

- Phenix: ET measurement at 130 GeV
- 0 = 4.6 [GeV/fm3] PRL 87, 052301 (2001)
- NA49: ET measurement at 17 GeV
- 0 = 3 [GeV/fm3] PRL 75, 3814 (1995)

- Brahms

- Conclusion: All reasonable estimates
- are substantially larger than the
- predicted transition density of
- 0 = 0.7-1.0 GeV/fm3

**Notes:**
Finally, if  we use the traditional Bjorken estimate, based on the particle multiplicity at mid-rapidity and again an equilibration time of 1 fm/c, we find an energy density of ~5 GeV/fm3

The conclusion is that all “reasonable” estimates of the energy density, based on the particle multiplicity and reasonable equilibration times give values well in excess of the predicted threshold density of 0.7-1 GeV/fm3. 
Thus, there is reason to believe that central Au+Au collisions at RHIC energies do provide the conditions for creating this new state of matter.

## CompletedN/ddistributions

**Notes:**
The PHOBOS setup is unique among RHIC experiments (and essentially also at lower energy facilities, as well as those planned for LHC) by being able to simultaneously measure essentially all (95%-99%) charged particles emitted in heavy-ion collisions.
In the following I’ll explore what we can learn about particle production based on this capability.

## PHOBOS Au+Au Data 

- * PHOBOS  PRL 91,52303 (2003)

- PHOBOS, PRL 91, 052303 (2003); PRC 74, 021901 (2006)

**Notes:**
This slide shows the complete set of multiplicity data for Au+Au collisions published by PHOBOS.
We also have measurements for Au+Au at 62.4 GeV and Cu+Cu at 200 GeV, which are present being analyzed and prepared for publication.
Note the very modest increase in the height of the mid-rapidity plateau with beam energy.
Note the increase in width of the distributions with collision energy.The latter is largely responsible for accounting for the factor 10 increase in energy between 20 and 200 GeV, because it becomes increasingly expensive to emit particles at large pseudorapidities because of the cosh_eta term in the energy of such particles.
Also note that for 20 GeV we see an ABSOLUTE increase in particle production in the wings of the distribution when going to more peripheral collisions. We believe that this growth reflects emission from spectator fragments. Simple model of such emission patterns support this hypothesis.

## Cu+Cu data

## d+Au centrality dependence

| Centrality   (%) | Npart
(total) | Npart
(Au) | Npart
(d) |
| --- | --- | --- | --- |
| 0-20 | 15.5 | 13.5 | 2.0 |
| 20-40 | 10.8      | 8.9 | 1.9 |
| 40-60 | 7.2 | 5.4 | 1.7 |
| 60-80 | 4.2  | 2.9 | 1.4 |
| 80-100 | 2.7 | 1.6 | 1.1 |

***d+Au centrality dependence***

- PHOBOS, Phys. Rev. C72,  031901(R) (2005)

- d                  Au

- Central:         asymmetric
- Peripheral:     symmetric
- Momentum conservation?

- Peripheral

- Central

**>**

**~**

## System size:Au+Au vs.Cu+Cu

**Notes:**
The PHOBOS setup is unique among RHIC experiments (and essentially also at lower energy facilities, as well as those planned for LHC) by being able to simultaneously measure essentially all (95%-99%) charged particles emitted in heavy-ion collisions.
In the following I’ll explore what we can learn about particle production based on this capability.

## dN/d in Cu+Cu vs Au+Au for Npart ~ 100

- _Unscaled_ dN/d very similar for Au+Au and Cu+Cu at same Npart

- Scaling Laws

**Cu+Cu**
**Preliminary**
**3-6%, N****part**** = 100**

- PHOBOS

- PHOBOS

**62.4 GeV**

**200 GeV**

**Au+Au**
**35-40%,N****part ****= 98**

**Cu+Cu**
**Preliminary**
**3-6%, N****part**** = 96**

**Au+Au**
**35-40%, N****part ****= 99**

- See poster by Richard Hollis

***dN/d************ in Cu+Cu vs Au+Au for N******part****** ~ 100***

## dN/d in Cu+Cu vs Au+Au for Npart ~ 60

- _Unscaled_ dN/d very similar for Au+Au and Cu+Cu at same Npart

- Scaling Laws

**Cu+Cu**
**Preliminary**
**15-25%, N****part**** = 61**

- PHOBOS

- PHOBOS

**62.4 GeV**

**200 GeV**

**Au+Au**
**45-50%,N****part ****= 62**

**Cu+Cu**
**Preliminary**
**15-25%, N****part**** = 60**

**Au+Au**
**45-55%, N****part ****= 56**

- Also true for mid-central Cu+Cu vs peripheral Au+Au

***dN/d************ in Cu+Cu vs Au+Au for N******part****** ~ 60***

## Extended longitudinal scaling

**Notes:**
The PHOBOS setup is unique among RHIC experiments (and essentially also at lower energy facilities, as well as those planned for LHC) by being able to simultaneously measure essentially all (95%-99%) charged particles emitted in heavy-ion collisions.
In the following I’ll explore what we can learn about particle production based on this capability.

## Extended longitudinal scaling – Au+Au

- PHOBOS Phys. Rev. Lett. 91, 052303 (2003) / Nucl. Phys. A**757**, 28 (2005)

- independent of energy

- Works also for dN/d because:

**Notes:**
I’ll now return to Au+Au collisions and see what we can learn from studying the wings of the distributions.
Again, in pp collisions it has been known for a long time that the particle production seen in the rest frame of one of the collision partners is essentially independent of the collision energy. This phenomenon has been given the term “limiting fragmentation scaling”
 For dN/deta distributions in Au+Au collisions we also observe this scaling feature. i.e. when the distributions are plotted istead againsy the parameter ’=  +- ybeam they line up with an astonishing degree of accuracy over a certain region before peeling off as the mid-rapidity plateau is approached.
The reason that this works also for dN/deta distributions is that dN/dy and dN/deta distributions are the same away from mid-rapidity as long as a small shift ln(pT/mT) is applied
Note again the contribution of spectator emission for the peripheral collisions at 20 GeV 

## Extended longitudinal scaling – Au+Au

- “Extended Longitudinal Scaling” of all longitudinal distributions

****** ****- y****beam**

- preliminary

- PHOBOS

**Au+Au**
**0-6%**

**Au+Au**
**0-40%**

**Au+Au**
**0-40%**

- 200GeV
- 130GeV
- 62.4 GeV (prel)
- 19.6 GeV

***Extended longitudinal scaling – Au+Au***

## Same for Cu+Cu

***Same for Cu+Cu***

- ‘Extended Longitudinal Scaling’ also seen in Cu+Cu
- Persists from p+p to Au+Au over large range in ’

- preliminary

- preliminary

- PHOBOS

****** ****- y****beam**

**Cu+Cu**
**0-6%**

- 200GeV

- 62.4GeV

**Cu+Cu**
**0-40%**

## Extended longitudinal scaling in p-A and d-A 

- PHOBOS, Phys. Rev. C72,  031901(R) (2005)

**Notes:**
The limiting fragmentation scaling is also seen in the d+Au data when compared to lower energy p+Emulsion data from the literature (Reference) after the d+Au data have been corrected for the number of participants in the collision. 

The fact that this scaling applies is used to obtain a reliable extrapolation of the distribution in the Au direction to  estimate the total particle production in this system.

## Total charged particle multiplicity

**Notes:**
The PHOBOS setup is unique among RHIC experiments (and essentially also at lower energy facilities, as well as those planned for LHC) by being able to simultaneously measure essentially all (95%-99%) charged particles emitted in heavy-ion collisions.
In the following I’ll explore what we can learn about particle production based on this capability.

## Total charged particle multiplicities in Au+Au

***Total charged particle multiplicities in Au+Au***

- Nch Q  Npart

- Width x height = const

**Notes:**
Again, because PHOBOS covers the ~full pseudorapidity, we can obtain the total multiplicity of charged particles as a function of centrality (Npart) as shown in the upper panels.
1) We see that the multiplicity increases linearly with Npart, slightly faster than predicted by HIJING (solid lines)
2) This feature is brought out more clearly in the middle panels, where the total multiplicity is normalized to the number of participant pairs Npart /2. 
3) Within experimental uncertaincies (including those associated with the extrapolation) we see that the dependence is completely flat, i.e. Nch scales with Npart. 
4) This means that Nch also is directly proportional to the total available energy in the collisions, which is Npart/2 * sqrt(s).
5) But we saw before that dN/deta at mid-rapidity exceeds N-part scaling  
6) This still works because the width of the distributions, shown as FWHM in the lower panels, are seen to DECREASE with centrality, thus compensating for the increase in mid-rapidity density to keep the total area constant.

## Total multiplicity as a function of energy

***Total multiplicity as a function of energy***

- Nch= dN/dx(2ybeam+0.3-dN/d/195)
-         height  x  width

- PHOBOS
- PRL 91,52303 (2003)

**Notes:**
Finally, since we now have a good description of the energy dependence of the height of the mid-rapidity plateau and the extented longitudinal scaling describes the position of the flanks of the dN/deta distributions, we can now write down a simple empirical expression for the total charged particle multiplicity as a function of collision energy.
To do this we note that the flanks are well described by straight line of the form: dN/d=195(ybeam+0.15+-)
The height is given by: dN/d=132 ln[s1/2]-53
Approximating the distributions by a trapezoid and calculating its area we thus find: Nch= dN/d  x (2ybeam+0.3-dN/d/195)

## Energy dependence of Nch

***Energy dependence of N******ch***

- 0-6% Central AuAu collisions
- Npart=344

- PHOBOS, PRL 91,52303 (2003)

**Notes:**
How well does this description work in reality?
The solid line represents this simple expression
If we use the gluon saturation expression instead to approximate the height of the mid-rapidity plateau, we obtain the dotted line.
Both are seen to describe the data very well.
If we are brave (or wreckless) we may use these expressions to extrapolate to LHC energies for Pb+Pb collisions at 5500 GeV and find midrapidity densities of 1200 to 1800 charged particles, substantially lower that the densities for which the LHC detectors were designes (which is good) 

## Universality – comparing AA to pp and e+e-

- PHOBOS, PRC 74, 021902(R) (2006)

- Shapes: Au+Au and e+e- “similar”

- Total Nch: Au+Au same as e+e-
- p+p: leading hadron removes
- 50% of energy

## d+Au: Centrality dependence of total Nch 

- Nch/(Npart/2)  constant with centrality
- d+Au also lower than Au+Au

- d+Au data similar to low-energy p+A NchdAu=0.5 Npart  Nchpp
- (1 Deuteron = 2 protons)

***d+Au: Centrality dependence of total N******ch****** ***

- PHOBOS, Phys. Rev. C72,  031901(R) (2005)

## Other new PHOBOS results (QM2006)

- New data on antiparticle/particle ratios
- Identified particle spectra for 62.4 GeV Au+Au
- Event-by-event v2 measurement and flow fluctuations
- Two-particle correlations and cluster size

**Notes:**
The PHOBOS setup is unique among RHIC experiments (and essentially also at lower energy facilities, as well as those planned for LHC) by being able to simultaneously measure essentially all (95%-99%) charged particles emitted in heavy-ion collisions.
In the following I’ll explore what we can learn about particle production based on this capability.

## New Data: antiparticle/particle ratios

- PHOBOS, QM2006

- 200, 62.4 GeV Cu+Cu

- 200 GeV Cu+Cu and Au+Au

- Energy dependence for Cu+Cu

- System dependence at 200 GeV

## Identified particle spectra for 62.4 GeV Au+Au 

- First published identified spectra for 62.4 GeV Au+Au at RHIC
- (down to very low pT, a unique PHOBOS measurement)

- blast-wave fits

- PHOBOS, nucl-ex/0610001
- Accepted for PRC

## New Analysis: event-by-event v2 measurement

***New Analysis: event-by-event v******2****** measurement***

- Measure v2 on an event-by-event basis
- Average and compare to our standard analysis
- Agreement with both hit and track based PHOBOS results

- 200 GeV Au+Au

- PHOBOS, QM2006;
- arXiv:nucl-ex/0608025
- Submit to PRL this week

## Event-by-event flow: fluctuations

- PHOBOS, QM2006
- Submit to PRL this week

- v2 fluctuations
- mirror
- part fluctuations

- (v2)/<v2> and (part)/<part> in 200 GeV Au+Au Collisions

- PHOBOS
- part prediction

- PHOBOS v2 result

- 90% CL

- MC with nofluctuations

## Effective cluster size analysis

- On average, particles produced in clusters with a size of 2-3.
- Interesting centrality dependence – compare to other systems

- p+p

- scale error

- 2

**K****eff**** = effective cluster size**

- PHOBOS, QM2006

## Summary and conclusion

- Multiplicity
- PHOBOS have performed complete charged particle multiplicity measurements for Au+Au, Cu+Cu, d+Au, and p+p collisions
- Systen size dependence
- ‘Complete’ pseudorapidity distributions
- Midrapidity multiplicity
- Factorization of centrality and energy dependencies
- Limiting fragmentation – extended longitudinal scaling
- Seen for Au+Au, Cu+Cu, and d+Au
- Also observed in flow observables
- Total charged particle multiplicity
- Nch/Npart constant with centrality
- ‘Universality’ – compared to elementary e+e- collisions
- Future: Finish up many analysis and reviews

## Why mid-rapidity?

- Emphasize
- produced
- or scattered
- particles
- Triple Gaussian
- fit function

- 200 GeV Au+Au 0-6% central

**Notes:**
It is of special interest to study particles in the mid-rapidity region 0.88<eta<0.88, where the p_T is larger than p_L. 
Higher probability to come from an equilibrated source.
A simple fact to note: Only a small fraction of all particles are emitted in this angular region. 
For 200 GeV 0-6% central Au+Au collisions the fraction is about 22%.

## System size dependence  -  Au+Au vs. Cu+Cu

## Centrality dependence 200 GeV

## Centrality dependence  62.4 GeV

## Cu+Cu elliptical flow – eccentricity scaling

- PHOBOS, QM2006