Glauber Symposium

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Glauber Symposium

• Peter Steinberg
• Brookhaven National Laboratory
• RIKEN Workshop on High pT Physics _at_ RHIC
• December 2-6, 2003

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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

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Whats the Big Deal?
Glauber is the real initial state!
BinaryCollisions
b
Participant
4
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
5
Nuclear Profile Thickness
H. DeVries, C.W. De Jager, C. DeVries, 1987
NB These measurements seeonly the charge, not
the nucleonsconceivable nuclear edges
aresharper (atruelta)
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Total AB Cross Section
Bialas Czyz 1976
Configuration Space
Nuclear Thickness
Interaction Terms
Intractable. Instead, most people use optical
limit
where
Supposedly valid for large A and/or when sNN is
small
7
Npart and Ncoll in Optical Limit

• Number of participants
• Number of collisions

NOT Linear in NN cross section
Linear in NN cross section!
8
Glauber Monte Carlo
PHOBOS Glauber MC

• Random impact parameter, nucleon positions
• Interactions occur for D lt sqrt (sNN/p)
• Can directly count Npart, Ncoll for each event
• Look at the Woods- Saxon tails!

CuCu s42mb
9
MC vs. Optical Gribov

• Lets recall Boris discussion of Gribovs
  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

10
Proof of Gribov
Compare simple Glauber extrapolation (measured
sNN) vs.extrapolation corrected for increasingly
fluctuating hadron
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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
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Comparing Experiments AA
PHOBOS
PHENIX
y0
y3
ygt6
NA49
NA49 ZDC Only
PHOBOS Paddle only
STAR TPC only
PHENIX BBC ZDC
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Two Different Answers!

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

• HIJING 130 GeV
• Monte Carlo approach
• Gaussian nucleon

PHOBOS Collaboration, PRC-RC 65 (2002)
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2 years later, still 2 answers
Were still stumbling on this cant decide if
one iswrong or if this is theoretical
uncertainty!
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MC vs. Optical b-dependence
Baker, Decowski, Steinberg, Glauber Workshop
2001
Ncoll
Ncoll
Npart
Npart 2
Ncoll 1
Npart
Impact Parameter
Impact Parameter

• Both approaches yield same Npart(b), Ncoll(b) !
• We have fixed Npart to prevent Npartlt2, not Ncoll
• Npart(b) x (1-P0(b)) where P0(b) exp(-ABsNNTAB)
• Not simply fixed by modifying cross section!

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The Right Cross Section
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Geometry of pp collisions
Total Cross Section hasmany components What do
we use?
Spectators
Participants
Spectators
Non-single-diffractive (NSD) Collisions
Non-Diffractive
Double Diffractive
Single Diffractive
Elastic Interaction
Inelastic Collisions slightly lower
multiplicity,harder to trigger on!
PAS, UCSB Workshop 2002
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Comparing Experiments dA
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
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Various Definitions for R
Cronin RHIC PHOBOS
Pure cross sections, nuclear masses Process independent No cross section needed!
Impossible at RHIC, alsominbias only Requires ds/dpT from Vernier scan Ncoll still needs it!
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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?

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Consequences

• Inelastic corrections lead to large modifications
  to published RdA
• Over summer BK said that Ncoll would decrease
  with sNN 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!
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Access to pA in dA
M. Miller
PRL. 91, 072304 (2003)
Class Ncoll
0-100 dAu 7.5 ? 0.4
0-20 dAu 15.0 ? 1.1
1-neut. dAu 2.9 ? 0.2
Without a non-standard cross section,STAR can
explain ZDC selection
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Conclusions

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

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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

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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 Ncolllt1 in optical limit
  calculations?
• Is peripheral data equivalent to pp? In AA?
  In dA?
• 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 pA/nA from dA?
  Is there interesting physics here?
• Is there more to life than Npart , Ncoll , n?
• Do I really have to summarize this at 9am
  Saturday morning? ?

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Geometry of AA Collisions

• Binary Collisions
• Jet Production
• Heavy Flavor

b
Glauber model of AA
Binary Collisions
Npart, Ncoll

• Color Exchange
• Soft Hadron Production
• Transverse Energy

Participants
b (fm)
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Effect of Wide Centrality Bins

• This is a known effect in AuAu, but we rarely
  quote minimum bias AuAu
• Obviously affects dAu and minimum bias is all we
  have

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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 exponentialgt
  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 x0.1-0.3
• 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 Muellers theorem, AGK
  cancellation
• Projectile parton hits A1/3 and can be emitted
  from any of them. Bethe-Heitler regime
• Multiplicity dependence cross section gives A
  dependence at eta0