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Glauber Symposium. RIKEN Workshop on High pT Physics @ RHIC December 2-6, 2003. Glauber Symposium. Thanks to our three speakers: Boris Kopeliovich Mike Miller Brian Cole (No slides!). What’s the Big Deal?. Glauber is the real initial state!. Binary Collisions. b. - PowerPoint PPT Presentation
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Peter Steinberg BNL/RIKEN High pT Workshop
Glauber Symposium
RIKEN Workshop on High pT Physics @ RHIC
December 2-6, 2003
Peter Steinberg BNL/RIKEN High pT Workshop
Glauber Symposium
• Thanks to our three speakers:•Boris Kopeliovich•Mike Miller •Brian Cole (No slides!)
Peter Steinberg BNL/RIKEN High pT Workshop
What’s the Big Deal?
3/4
12
1part
N
icoll NNpart
b
Participant
BinaryCollisions
Glauber is the real initial state!
Peter Steinberg BNL/RIKEN High pT Workshop
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
Peter Steinberg BNL/RIKEN High pT Workshop
Nuclear Profile & Thickness
zssT AA ,
)/)exp((1
/1)(
220
aRr
Rwrr
Nucleus A R a w
C 12 2.47 0 0O 16 2.608 0.513 -0.051Al 27 3.07 0.519 0S 32 3.458 0.61 0Ca 40 3.76 0.586 -0.161Ni 58 4.309 0.516 -0.1308Cu 63 4.2 0.596 0W 186 6.51 0.535 0Au 197 6.38 0.535 0Pb 208 6.68 0.546 0U 238 6.68 0.6 0
H. DeVries, C.W. De Jager, C. DeVries, 1987
NB: These measurements seeonly the charge, not the nucleons;
conceivable nuclear edges aresharper (atrue<a)
Peter Steinberg BNL/RIKEN High pT Workshop
Total AB Cross Section
A
i
Bj
Ai
B
j
BB B
BB
AA A
AA
BB
B AA
AAB
s s b
s T s T s T s T
s d s d s d s d b d
1 1
1 1
21
2 21
2 2
1 1
... ...
... ...
Configuration Space
Nuclear Thickness
Interaction Terms
ABABNNAB bTbd ]1[12
Intractable. Instead, most people use “optical limit”:
sbTbTsdbT BAAB
2
where
Supposedly valid for large A and/or when NN is small
Bialas & Czyz 1976
Peter Steinberg BNL/RIKEN High pT Workshop
Npart and Ncoll in Optical Limit
• Number of participants
• Number of collisions
BA
bsTssTdAbNB
BNNAABpart
112
NNAAABcoll bsTssTdABbN
2
Linear in NN cross section!
NOT Linear in NN cross section
Peter Steinberg BNL/RIKEN High pT Workshop
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 =42mbPHOBOS Glauber MC
Peter Steinberg BNL/RIKEN High pT Workshop
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
12 2
12 2
2 1
2 1
i A
i A
T b
hA
i
T b
d b e
d b e
AT
Peter Steinberg BNL/RIKEN High pT Workshop
Proof of GribovCompare simple Glauber extrapolation (measured NN) vs.extrapolation corrected for increasingly fluctuating hadron
Peter Steinberg BNL/RIKEN High pT Workshop
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!
7.2 b 6.9 bAu Au Au AuOptical MC
M. Miller
Peter Steinberg BNL/RIKEN High pT Workshop
Comparing Experiments: A+A
Preliminary sNN = 200 GeV
Preliminary sNN = 200 GeV
UncorrectedUncorrected
NA49 ZDC Only
PHOBOS
Paddle only
STAR TPC only
PHENIX BBC & ZDC
y=0 y=3y>6
PHOBOS PHENIX
NA49
Peter Steinberg BNL/RIKEN High pT Workshop
Two Different Answers!• HIJING 130 GeV
• Monte Carlo approach• Gaussian nucleon
• Kharzeev/Nardi• Optical-limit approach• Point nuclei
%-ile <Npart>60-70 112.370-80 164.880-90 233.390-94 294.6
94-100 348
%-ile <Npart>60-70 10270-80 15380-90 22190-94 281.5
94-100 339
PHOBOS Collaboration, PRC-RC 65 (2002)
Peter Steinberg BNL/RIKEN High pT Workshop
2 years later, still 2 answers…
We’re still stumbling on this: can’t decide if one iswrong or if this is “theoretical uncertainty”!
Peter Steinberg BNL/RIKEN High pT Workshop
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(-ABNNTAB)
• Not simply fixed by modifying cross section!
Ncoll
Npart
Npart
Ncoll
Ncoll = 1Npart = 2
Impact Parameter Impact Parameter
Baker, Decowski, Steinberg, “Glauber Workshop 2001”
Peter Steinberg BNL/RIKEN High pT Workshop
The Right Cross Section
~ 51tot mb
Peter Steinberg BNL/RIKEN High pT Workshop
Geometry of pp collisions
IP
Rapidity Gap
IP
RapidityGap
Single Diffractive Double Diffractive Non-Diffractive
Inelastic Collisions – slightly lower multiplicity,harder to trigger on!
Non-single-diffractive (NSD) Collisions
b
Total Cross Section hasmany components:What do we use?
Elastic Interaction
Spectators
Participants
Spectators
PAS, UCSB Workshop 2002
b
Spectators
Participants
Spectators
Peter Steinberg BNL/RIKEN High pT Workshop
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
Peter Steinberg BNL/RIKEN High pT Workshop
Various Definitions for R
1 1 1
XAB AB AB
T T TAB X X
NN NN NNAB coll
T T T
d dN dNdp dp dp
R bd d dNAB T b Ndp dp dp
“Cronin” RHIC PHOBOSPure 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!
Peter Steinberg BNL/RIKEN High pT Workshop
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?
AB NNhard AB hardP b T b P
Peter Steinberg BNL/RIKEN High pT Workshop
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)
1AB
TAB
NNcoll
T
dNdp
R bdNNdp
PHENIX + BK
Now PHENIX goesdown!
Peter Steinberg BNL/RIKEN High pT Workshop
. 2.2 0.1 bMChad
1 (.18 .03)MCn had
.1 (.19 .01)Measn had
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+AM. Miller
Without a non-standard cross section,STAR can explain ZDC selection
Peter Steinberg BNL/RIKEN High pT Workshop
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!
Peter Steinberg BNL/RIKEN High pT Workshop
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?
Peter Steinberg BNL/RIKEN High pT Workshop