# Presentation: 401842

## Glauber               Symposium 

**Peter Steinberg**
**Brookhaven National Laboratory**
**RIKEN Workshop on High p****T**** Physics @ RHIC**
**December 2-6, 2003**

## Glauber Symposium

- Yes, I really did have to summarize this at 9am on Saturday!
- Again, thanks to our three speakers:
- Boris Kopeliovich
- Mike Miller
- Brian Cole (No slides!)
- And thanks to Dave Morrison for organizing

## What’s the Big Deal?

**b**

*Participant*

*Binary**Collisions*

- Glauber is the _real_ initial state!

## The Glauber Approach

- Simple assumptions
- Woods-Saxon nuclei
- Nucleons travel in straight lines (eikonal approximation)
- Interactions controlled by  NN inelastic cross section measured in pp collisions
- First collision does not change cross section

- Roy Glauber

## Nuclear Profile & Thickness

**H. DeVries, C.W. De Jager, C. DeVries, 1987**

- NB: These measurements seeonly the charge, not the nucleons;conceivable nuclear edges aresharper (atrue<a)

## Total AB Cross Section

- Configuration Space

- Nuclear Thickness

- Interaction Terms

- Intractable.  Instead, most people use “optical limit”:

- where

- Supposedly valid for large A and/or when NN is small

- Bialas & Czyz 1976

## Npart and Ncoll in Optical Limit

- Number of participants
- Number of collisions

- Linear in NN cross section!

- NOT Linear in NN cross section

## Glauber Monte Carlo

- Random impact parameter, nucleon positions
- Interactions occur for *D < sqrt** **(****NN****)*
- Can directly count Npart, Ncoll for each event
- Look at the Woods- Saxon tails!

- Cu+Cu =42mb

***PHOBOS Glauber MC***

## MC vs. Optical: Gribov

- Let’s recall Boris’ discussion of Gribov’s inelastic shadowing corrections
- In his context, the hA cross section is
- So we average over the hadron configurations _before_ it hits the nucleus
- No “hiding”, so larger cross section

## Proof of Gribov

- Compare simple Glauber extrapolation (measured NN) vs.extrapolation corrected for increasingly fluctuating hadron

## MC vs. Optical

- In optical Glauber, we average over the nuclear density independent of its interaction w/ another hadron or nucleus
- In MC, fluctuations at edgereduce cross section!

- M. Miller

## Comparing Experiments: A+A

| NA49 | ZDC Only |
| --- | --- |
| PHOBOS | Paddle only |
| STAR | TPC only |
| PHENIX  | BBC & ZDC |

- y=0

- y=3

- y>6

**PHOBOS**

**PHENIX**

**NA49**

## Two Different Answers!

- HIJING 130 GeV
- Monte Carlo approach
- Gaussian nucleon

- Kharzeev/Nardi
- Optical-limit approach
- Point nuclei

- PHOBOS Collaboration, PRC-RC 65 (2002)

## 2 years later, still 2 answers...

- We’re still stumbling on this: can’t decide if one iswrong or if this is “theoretical uncertainty”!

## MC vs. Optical: b-dependence

- Both approaches yield _same_ Npart(b), Ncoll(b) !
- We have fixed Npart to prevent Npart<2, not Ncoll
- Npart(b) x (1-P0(b)) where P0(b) = exp(-ABNNTAB)
- Not simply fixed by modifying cross section!

- Ncoll

- Npart

- Npart

- Ncoll

- Ncoll = 1

- Npart = 2

- Impact Parameter

- Impact Parameter

- Baker, Decowski, Steinberg, “Glauber Workshop 2001”

## The Right Cross Section

## Geometry of pp collisions

- Single Diffractive

- Double Diffractive

- Non-Diffractive

**Inelastic Collisions – slightly lower multiplicity,****harder to trigger on!**

**Non-single-diffractive (NSD) Collisions**

**Total Cross Section has****many components:**
**What do we use?**

- Elastic Interaction

***Spectators***

***Participants***

***Spectators***

- PAS,  UCSB Workshop 2002

## Comparing Experiments: d+A

| Experiment | Trigger | Cross section |
| --- | --- | --- |
| PHOBOS | Paddles + ZDC | NSD 41mb |
| PHENIX | High pT | Trigger 31mb |
| STAR | ZDC | Total 51mb |

- Boris’ Proposal:
- Different experiments should use appropriate cross section

## Various Definitions for R

| “Cronin” | RHIC | PHOBOS |
| --- | --- | --- |
| Pure cross sections, nuclear masses | “Process independent” | “No” cross section needed! |
| Impossible at RHIC, also“minbias” only | Requires d/dpT from Vernier scan | Ncoll still needs it! |

## What we (Brian) want(s)

- A ratio that expresses the relative likelihood of a hard process, given a certain overlap of nuclear matter
- Want to remove dependence on precise cross section
- Questions arose about normalization
- For me, what about Ncoll = 1 or more?

## Consequences

- Inelastic corrections lead to large modifications to published RdA
- Over summer BK said that Ncoll would decrease with NN: RdA would increase linearly (e.g. 31 vs 41 implies 30% increase)
- Now, the smaller cross section is seen to lead to a *larger* number of collisions on average.

- PHENIX + BK

- Now PHENIX goesdown!

## Access to p+A in d+A

| Class | Ncoll |
| --- | --- |
| 0-100%
d+Au | 7.5  0.4 |
| 0-20%
d+Au | 15.0  1.1 |
| 1-neut.
d+Au | 2.9  0.2 |

- PRL. **91**, 072304 (2003)

**Access to p+A in d+A**

- M. Miller

- Without a non-standard cross section,STAR can explain ZDC selection

## Conclusions

- Glauber is a crucial part of understanding the initial state of p(d)+A and A+A
- MC & Optical are really different
- Gribov captures key differences in approaches
- Not just a cross section away
- It’s possible that the right cross section NN depends on the trigger condition
- STAR ZDC cuts suggest otherwise
- Must strive for true commensurability between RHIC & SPS experiments!

## Beyond the Optical Limit

- Franco & Varna, 1977
- Include higher order terms in optical limit
- Next higher order decreases cross section
- Addition of next term *increases* it again
- Not clear if series is convergent
- Shows difficulty of problem

## Issues to Consider

- List of topics, started by Dave, amended by me
- Is there a “right” cross section?  Inelastic, NSD, trigger, etc.?
- Do all the experiments handle things the same way?
- Does “shadowing” require us to modify our definition of Ncoll for low-x physics?
- “Optical limit” and “Monte Carlo” calculations?  Which is “right”?
- Analytic corrections to optical limit?
- How should we handle Ncoll<1 in optical limit calculations?
- Is peripheral data equivalent to p+p?  In A+A?  In d+A?
- Distinguishing features?
- What  is “minimum bias”?  Effect of wide centrality bins?
- Effect on high-pT yields, elliptic flow, etc.
- Can we use Glauber to extract p+A/n+A from d+A?  Is there interesting physics here?
- Is there more to life than Npart , Ncoll , & ?
- _Do I really have to summarize this at 9am Saturday morning? ___

## Geometry of AA Collisions

**Geometry of AA Collisions**

- “Glauber” model of AA

- b

**Binary Collisions**

**Participants**

**b (fm)**

**N****part****, N****coll**

**Color Exchange:**
**Soft Hadron Production**
**Transverse Energy**

**Binary Collisions:**
**Jet Production**
**Heavy Flavor**

## Effect of Wide Centrality Bins

- This is a “known” effect in Au+Au, but we rarely quote “minimum bias” Au+Au...
- Obviously affects d+Au and minimum bias is all we have...

## Kopeliovich

- Gribov inelastic shadowing:
- Hadron is a composite system experiencing quantum fluctuations
- Time dilation freezes decomposition for time of interaction
- If set of states is eigenstates of interaction, then cross section is simple averaging over configurations
- Can use glauber formula for exponential
- Glauber approximation is when you average cross section, not the average exponential
- Nuclear medium, average of exponential> exponential of average.  Difference is inelastic shadowing correction
- Are these corrections mainly out of the elastic or inelastic part?
- QCD: eigenstates are dipoles.  Use dipole cross section
- Nuclear medium is more transparent for hadrons than is given by glauber: presence of small fluctuations (“color transparency”)
- Gluon shadowing are fluctuations containing gluons: 20% effect at high energies (RHIC)
- Gribov correction should lead to reduction of nuclear ratios measured at RHIC: about 10%
- Other models predict strong suppression (.3, .6, .42)
- Factor may be .7?  So then KLM prediction does not contradict the data

- Glauber Model
- Usually we use s_inel.
- Differs from subtracting elastic bit
- STAR uses ZDC, PHENIX uses BBC
- Is this true???
- So star needs 51mb, phenix 30?!
- Conclusions:
- Normalization of high-pT cross section is overestimated since it misses the gribov correction
- Uncertainty is 10-30%
- To fix, need to measure cross sections directly, or study the corrections with spectator nucleons
- BRAHMS data?! Glauber?
- Strong suppression – strong gluon shadowing, or CGC
- Most result is glauber shadowing!
- Sitting in valence region x~0.1-0.3
- Supression should be stronger by 2/3
- Why does integrated cross section go as A, but inelastic goes at A^(2/3).
- Regge approach, comes from Mueller’s theorem, AGK cancellation
- Projectile parton hits A^{1/3} and can be emitted from any of them.  Bethe-Heitler regime
- Multiplicity dependence * cross section gives A dependence at eta=0
- But number of valence quarks is fixed and independent of A.  So at eta=3.4, scales as A^{2/3}
- What is this bump at moderate pT?
- So it’s a certain scaling of valence quark production?