# Presentation: 604616

## Charged particle multiplicities in ultra-relativistic Au+Au  and Cu+Cu collisions

- 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),  Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson,
- David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,
- Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizeides, Steven Manly, Alice Mignerey,
- Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed,
- Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith,
- Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak,
- Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres,
- Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs,  Barbara Wosiek, Krzysztof Woźniak, A.H.Wuosmaa, Shaun Wyngaardt, 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

**Notes:**
This is the present roster of the PHOBOS collaborations. 
It incorporates about 62 collaborators from 8 institution in 3 countries. 
A very bad this happened at the latest update. 
I’m no longer automatically first author on PHOBOS papers
Hard working students are in RED
Hangers-on, like me, are in yellow.

## -5.4 <  < 5.4

- -5.4 <  < 5.4
- 0.5o <  < 179.5o

**Notes:**
The PHOBOS consists mostly of Si-pad detectors – about 135,000 pads are read out each event.
Triggering is done by plastic scintillator paddle detectors covering 3<<4.5.
The multiplicity data that I’ll talk about today were obtained by the Si multiplicity array.
It consists of a 1m long octagon array, shown here, which covers -3<<3.
Charged particles escaping out the end of the octagon barrel are registered in sic Si ring detector arrays located at 1, 2, and 5 m from the nominal vertex position extending the eta coverage to ||<5.4 – a unique angular coverage at RHIC, and I believe also at the future LHC.

## dN/d basics

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

## 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%.

## Where are particles emitted?

- 22%

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

**Notes:**
Keeping in mind that pseudorapidity distributions REALLY are just angular distributions if the emitted particles.
So what does a typical pseudorapidity distributions, such as the one for 200 GeV Au+Au look like in real angular coordinates.
Well, that’s what we see here.
Note that the mid-rapidity plateau turns into a minumum in both the dN/d and the dN/d representations.
The highest density of particles in real space is really seen at very forward/backward angles 

## 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

- First RHIC
- results
- New data

**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.

## 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.

## Factorization of centrality and energy dependence

- ||<1

## 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 Au+Au Data

- * PHOBOS  PRL 91,52303 (2003)

- *

- *

- *

**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

## 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.

## System size dependence

## Centrality dependence 200 GeV

## Centrality dependence  62.4 GeV

## Total charged particle multiplicities

- 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.

## Extended longitudinal scaling

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

- independent of energy

- Works also for dN/d because:

- PHOBOS
- PRL 91,52303 (2003)

**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 

## Total multiplicity

- 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 Nch

- 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) 

## Summary

- Complete dN/d measured for Au+Au and Cu+Cu
- ~ Logarithmic esNN dependence of dN/d at =0
- Factorization of energy and centrality at mid-rapidity
- Total particle production scales with Npart
- Rough system size scaling in total charged particle production between Au+Au and Cu+Cu