Glauber Symposium

Peter Steinberg BNL/RIKEN High pT Workshop

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?

3/4

12

1part

N

icoll NNpart

b

Participant

BinaryCollisions

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

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)


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


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


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


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


Proof of GribovCompare 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!

7.2 b 6.9 bAu Au Au AuOptical MC

M. Miller


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


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)


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(-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”


The Right Cross Section

~ 51tot mb


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


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

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!


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


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!


. 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


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!


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?


Documents

Glauber Symposium