Glauber Symposium

1. Glauber Symposium RIKEN Workshop on High pT Physics @ RHIC December 2-6, 2003

2. Glauber Symposium • Thanks to our three speakers: • Boris Kopeliovich • Mike Miller • Brian Cole (No slides!)

3. What’s 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 nucleons;conceivable nuclear edges aresharper (atrue<a)

6. 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 whensNNis 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 • Random impact parameter, nucleon positions • Interactions occur for D < sqrt(sNN/p) • Can directly count Npart, Ncoll for each event • Look at the Woods- Saxon tails! PHOBOS Glauber MC Cu+Cu s=42mb

9. 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

10. Proof of Gribov Compare simple Glauber extrapolation (measured sNN) vs.extrapolation corrected for increasingly fluctuating hadron

11. 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

12. Comparing Experiments: A+A Preliminary sNN = 200 GeV Uncorrected PHOBOS PHENIX y=0 y=3 y>6 NA49

13. Two Different Answers! HIJING 130 GeV Monte Carlo approach Gaussian nucleon Kharzeev/Nardi Optical-limit approach Point nuclei PHOBOS Collaboration, PRC-RC 65 (2002)

14. 2 years later, still 2 answers… We’re still stumbling on this: can’t decide if one iswrong or if this is “theoretical uncertainty”!

15. MC vs. Optical: b-dependence Baker, Decowski, Steinberg, “Glauber Workshop 2001” • 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(-ABsNNTAB) • Not simply fixed by modifying cross section! Ncoll Ncoll Npart Npart = 2 Ncoll = 1 Npart Impact Parameter Impact Parameter

16. The Right Cross Section

17. Geometry of pp collisions Rapidity Gap Rapidity Gap h h h b b IP IP Total Cross Section hasmany components: What do we use? Spectators Spectators Participants Participants Spectators 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

18. Comparing Experiments: d+A Boris’ Proposal: Different experiments should use appropriate cross section

19. Various Definitions for R

20. 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?

21. 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) PHENIX + BK Now PHENIX goesdown!

22. Access to p+A in d+A M. Miller PRL. 91, 072304 (2003) Without a non-standard cross section,STAR can explain ZDC selection

23. 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 sNN depends on the trigger condition • STAR ZDC cuts suggest otherwise • Must strive for true commensurability between RHIC & SPS experiments!

24. 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 , & n? • Do I really have to summarize this at 9am Saturday morning? 