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