# Presentation: 604611

## Recent results from PHOBOS

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

## PHOBOS Collaboration

- Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Abigail Bickley,
- Richard Bindel, Wit Busza (Spokesperson), Alan Carroll, Zhengwei Chai, Vasundhara Chetluru,
- Patrick Decowski, Edmundo García, Tomasz Gburek, Nigel George, Kristjan Gulbrandsen,
- Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane, Nazim Khan, Piotr Kulinich,
- Chia Ming Kuo, Wei Lik, Willis Lin, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen,
- Rachid Nouicer, Andrzej Olszewski, Robert Pak, Heinz Pernegger, Corey Reed, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Wojtek Skulski, Chadd Smith, Maciej Stankiewicz,
- Peter Steinberg, George Stephans, Andrei Sukhanov, Marguerite Belt Tonjes, Adam Trzupek,
- Carla Vale, 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

**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.

## Slide 3

**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.

## dN/d shapes

- dN/d shapes

- Midrapidity plateau
- Boost invariant?
- Increase with energy
- Fall off at high ****
- Increase with energy
- Small extrapolation into
- unmeasured region

- Au+Au

- PHOBOS
- PRL 91,52303 (2003)

**Notes:**
At all energies, 20, 130, and 200 GeV  we see a mid-rapidity plateau which appears to increase with beam energy.
This is reminiscent of a boost invariance predicted by Bjorken.
Remember, however, that the transformation from rapidity to pseudo-rapidity 
space leads to s suppression in the mid-rapidity region.
We expect that this is a contributing cause of this plateau.
BRAHMS sees only very small hints of boost invariance in dN/dy distributions for identified pions, although there are some inconsistancies between the BRAHMS dN/dy measurements and the dN/deta distributions from both BRAHMS and PHOBOS.
From the mid-rapidity plateau the distributions fall off toward higher eta values.
The range of this fragmentation region also increases with collision energy.
Note that only a very small extrapolation is required to obtain the total charged particle multiplicities. 

## Why mid-rapidity?

- Emphasize
- produced
- or scattered
- particles

- 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
- However, 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 

## What would an isotropic source look like?

- Isotropic emission: 1/cosh2

**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.

## 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

**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.

## Important early RHIC result

**Models prior to RHIC**

**CGC ****(McLerran, **
**Venugopalan)**

**- - Minijet**

**Notes:**
To some theorists this slow increase in particle production came as a surprise. For example, the multiplicity results caused people to abandon the “minijet” mechanism of particle production.
On the other hand this behavior was in reasonable agreement with the ideas of “gluon saturation” as a limiting factor for particle production. 

## Gluon saturation: Kharzeev, Levin, Nardi

- =0.205
- Qs= Qs0(s/s0)/2

- Logarithmic fit:

- Central Au+Au collisions:
- Npart=344

- Calculation using re-adjusted parameters

**Notes:**
Taking the analytical expressions from the gluon saturation model of Kharzeev, Nardi, and Levin, we see here that a quite reasonable value of the lambda parameter, (which controls the energy dependence) is able to account for the mid-rapidity density from about sqrt(s)=20 GeV up to the top RHIC energy.
The accuracy of the experimental data is not (and will probably never be) sufficient to discriminate between the straight logarithmic dependence and the slight curvature predicted by the Gluon Saturation Model”

In any case we see again that a simple logarithmic dependence with the parameters shown here gives an excellent description of the data over the entire range spanning two orders of magnitude in collision energy. 

## 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:

**Notes:**
Let us discuss briefly what the mid-rapidity multiplicity can teach us about the energy density of the fire-ball procuced in central collisions. As we will see, the uncertaincy in these estimates are largely of theoretical origin.
Let’s start out with an outrageous estimate, which surely constitutes an upper limit to the energy density.
This is based on taking the total available energy of the system (~35 TeV in a central Au+Au collision at 200 GeV) and stuffing it inside a volume described by the instantaneous overlap of the two colliding ions – including the Lorentz contraction.  This gives an energy density of about 2500 GeV/fm^3. It probably does not have much relation to the thermally equilibrated Quark Gluon Plasma phase of matter that we’re seeking. It shows, however, that there is plenty of energy around to hope to traverse the predicted phase transition at about 0.7-1 GeV/fm3 – by three orders of magnitude.
The second estimate is based on considering only the fraction of the particles that could be consistent with an isotropic, equilibrated source at rest in the lab system. That would reduce the total energy to ~1250 GeV. Allowing for an equilibration time of ~1fm/c results in a volume of ~300fm3 and an energy density of  ~4 GeV/fm3

## 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.

## Ncoll or Npart scaling at =0 for soft particles?

- Ncoll or Npart scaling at =0 for soft particles?

- ~Ncoll

- ~Npart

- Hard collisions Q Ncoll
- Soft collisions  QNpart

- Both energies:
- x=0.13**F**0.01(stat) **F**0.05(syst)
- PHOBOS: PRC70, 021902 (2004)

- /3.3

- x1.7

- pp

- PHOBOS
- PRC 70, 21902 (2004)

**Notes:**
Let’s briefly discuss the centrality dependence of particle production at mid-rapidity.
Here is shown the density dN/deta normalized by the number of participant pairs Npart/2 for both 200 and 20 GeV.
The corresponding values for pp/pp-bar are shown as back symbols.
Analyzing the data in a two-component model of particle production from hard collisions (scaling with Ncoll ~ Npart4/3) and soft collisions (scaling with Npart)
We see that reality falls in-between these two limits (as expected) with only about 13% of the particle production exhibiting the N_coll scaling.
The surprising observation is that this fraction is the same (within experimental errors) at both 20 and 200 GeV.
One might have suspected that the hard collisions would have been suppressed at 20 GeV but contributed more strongly at 200 GeV

## 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 Data

- 62.4 GeV data coming soon - stay tuned

- 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.

## Total charged particle multiplicities

- Nch Q  Npart
- Epart =  s1/2Npart/2
- Nch Q  Epart

- 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.

## 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 |

| 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 |

- PHOBOS Submitted PRL nucl-ex/0409021

- d                  Au

- Central:      asymmetric
- Peripheral: symmetric

- PHOBOS

**Notes:**
Let’s now take a small detour to deuteron+Au collisions.
Here we show the pseudorapidity distributions for different centrality bins, as well as the min-bias result. 
First we note that the distributions are asymmetric (except for the most peripheral bin). In some sense, they have to be since the larger number of Au participants (see table) forces a linear momentum imbalance in the collision. 
More particles have to be emitted in the Au direction to account for this momentum imbalance in the entrance channel.
For the most peripheral collisions this momentum balance is roughly restored, and, indeed, the distribution again becomes symmetric.
Finally, we may again estimate the total number of charges particles by extrapolating into the unmeasured region, which in this case is a little more serious. I’ll show later how this was done.

## Comparison to pp, e+e-, and d+Au

- Comparison to pp, e+e-, and d+Au

- Why are e+e- and Au+Au so similar?

**Notes:**
Now we can perform a comparison of the normalized particle production
between systems ranging from e+e-, via pp, and d+Au to Au+Au collisions.
Here we show the results as a function of the number of participants, and a rather striking feature appears:
The production in pp and five d+Au centrality bins are quite consistent (within error bars)
The Au+Au collisions produce ~40% more charged particles per participant pair.   But as we have seen before the level is independent of centrality
Surprisingly, the elementary e+e- system produces charged particles at the same level as the very complicated Au+Au system, which allows for multiple collisions between primary particles as well as coliisions between secondary particles etc.
The difference between pp and e+e- has been observed many years ago and it is attributed to leading particles in pp collisions carrying away abou 50% of the total energy, which is then not available for particle production.
It maybe somewhat surprising that this effect also applies to d+Au collisions in which these leading particles has the possibility of further interactions.

## Extended longitudinal scaling

- PHOBOS Phys. Rev. Lett. 91, 052303 (2003) / PHOBOS white paper

- independent of energy

- Works also for dN/d because:

- Spectator emission?

- 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 

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

**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 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

- Extrapolate to LHC:
- 5500 GeV 208Pb+208Pb
- Npart = 380
- dNch/d = 1200-1800
- Nch = 14000-16500

- 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) 

## Collectiveflow

**Notes:**
Finally, let me turn to the signals of collective motion within the fireball

## Flow

-  Flow measured by decomposing the azimuthal angle particle distributions into Fourier components:

- directed flow

- elliptic flow

**Notes:**
This is a simple illustration of the geometry in peripheral collisions which leads to a differential in pressure gradients in and out of the reaction plane. 
This gives rise to the elliptical flow signal as an anisotropy in azimuthal emission of particles expressed in terms of the v2 parameter.

## Nearly hydrodynamic flow

- PHOBOS, Submitted to Phys. Rev. C / nucl-ex/0407012

- Calculations: P.F.Kolb, P. Huovinen, U.W.Heinz, and H.Heiselberg, Phys. Lett. B500, 232 (2001);
- 		      P.Huovinen, Private Communication

- Centrality dependence

- pT dependence

- 200 GeV Au+Au

- PHOBOS

- PHOBOS

**Notes:**
Here we see the centrality dependence of the v2 signal in 200 GeV Au+Au collisions as measured by PHOBOS.
It is seen to approach the purely hydrodynamic limit as predicted by Kolb et al. solid line.
Also the pT dependence is seen to follow the hydrodynamic limit up to about 2 GeV/c, at which point it falls off. The high energy particles are less likely to participate in the collective flow of the bulk of the particles.

## Pseudorapidity dependence of flow

- PHOBOS 130 & 200 GeV Au+Au, Submitted to Phys. Rev. C ,  nucl-ex/0407012

- PHOBOS

**Notes:**
Again, uniquely to PHOBOS, the v2 signal has been measured over the entire pseudo-rapidity range shown here for the 200 and 130 GeV data.
We see that the strength of the flow signal is rather sharply peaked at mid-rapidity and then falls off immediately toward higher pseudo-rapidities.
This behavior has been difficult to reproduce in hydrodynamical calculations (Kolb et al).
However a recent attempt by Csanad et al, using the Buda-Lund hydrodynamic model and including a directed flow component appears to be able to account for this behavior.

## Flow continued Au+Au at 200 GeV

- PHOBOS, Submitted to Phys. Rev. C / nucl-ex/0407012

- PHOBOS

- PHOBOS 130 & 200 GeV Au+Au, Submitted to Phys. Rev. C ,  nucl-ex/0407012

**Notes:**
The shape of the pseudorapidity dependence is here seen to apply also to different centrality bins.
Shown here are the dependences for 0-6%, 15-25% and 25-50%.

## Energy dependence of elliptical flow

- PHOBOS, Submitted to Phys. Rev. Lett., nucl-ex/0406021

- PHOBOS

- PHOBOS 19.6, 62.4,130 & 200 GeV Au+Au, Submitted to Nucl. Phys. A

**Notes:**
Recently, we have obtained the flow signal for all four collision energies measureed at RHIC in Au+Au collisions.
We see that the general triangular feature of the signal is observed at all four energies.

## Extended longitudinal scaling in Elliptic Flow?

- PHOBOS, Submitted to Phys. Rev. Lett., nucl-ex/0406021

- PHOBOS

- PHOBOS

- PHOBOS

**Notes:**
Finally, we observe the extended longitudinal scaling also for the elliptic flow signal.

## Summary

- dN/d basics - only 22% emitted within 45o-135o
- Logarithmic esNN dependence of dN/d at =0
- Total particle production scales with Npart Q Epart
- Extended longitudinal scaling in dN/d
- Extended longitudinal scaling in v2