Glauber Symposium Peter Steinberg Brookhaven National Laboratory RIKEN

Glauber Symposium Peter Steinberg Brookhaven National Laboratory RIKEN Workshop on High p. T Physics @ RHIC December 2 -6, 2003 Peter Steinberg BNL/RIKEN High p. T Workshop

Glauber Symposium • Yes, I really did have to summarize this at 9 am on Saturday! • Again, thanks to our three speakers: • Boris Kopeliovich • Mike Miller • Brian Cole (No slides!) • And thanks to Dave Morrison for organizing Peter Steinberg BNL/RIKEN High p. T Workshop

What’s the Big Deal? Glauber is the real initial state! Binary Collisions b Participant Peter Steinberg BNL/RIKEN High p. T 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 Peter Steinberg Roy Glauber BNL/RIKEN High p. T Workshop

Nuclear Profile & Thickness H. De. Vries, C. W. De Jager, C. De. Vries, 1987 NB: These measurements see only the charge, not the nucleons; conceivable nuclear edges are sharper (atrue<a) Peter Steinberg BNL/RIKEN High p. T Workshop

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 s. NN is small Peter Steinberg BNL/RIKEN High p. T Workshop

Npart and Ncoll in Optical Limit • Number of participants NOT Linear in NN cross section • Number of collisions Linear in NN cross section! Peter Steinberg BNL/RIKEN High p. T Workshop

Glauber Monte Carlo • Random impact parameter, nucleon positions • Interactions occur for D < sqrt (s. NN/p) • Can directly count Npart, Ncoll for each event • Look at the Woods. Saxon tails! Peter Steinberg PHOBOS Glauber MC Cu+Cu s=42 mb BNL/RIKEN High p. T Workshop

MC vs. Optical: Gribov • Let’s recall Boris’ discussion of Gribov’s inelastic shadowing corrections • In his context, the h. A cross section is • So we average over the hadron configurations before it hits the nucleus • No “hiding”, so larger cross section Peter Steinberg BNL/RIKEN High p. T Workshop

Proof of Gribov Compare simple Glauber extrapolation (measured s. NN) vs. extrapolation corrected for increasingly fluctuating hadron Peter Steinberg BNL/RIKEN High p. T 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 edge reduce cross section! M. Miller Peter Steinberg BNL/RIKEN High p. T Workshop

Comparing Experiments: A+A PHOBOS PHENIX Preliminary s. NN = 200 Ge. V Uncorrected y=0 NA 49 ZDC Only PHOBOS Paddle only STAR TPC only PHENIX BBC & ZDC Peter Steinberg y=3 y>6 NA 49 BNL/RIKEN High p. T Workshop

Two Different Answers! • HIJING 130 Ge. V • Monte Carlo approach • Gaussian nucleon • Kharzeev/Nardi • Optical-limit approach • Point nuclei PHOBOS Collaboration, PRC-RC 65 (2002) Peter Steinberg BNL/RIKEN High p. T Workshop

2 years later, still 2 answers… We’re still stumbling on this: can’t decide if one is wrong or if this is “theoretical uncertainty”! Peter Steinberg BNL/RIKEN High p. T Workshop

MC vs. Optical: b-dependence Baker, Decowski, Steinberg, “Glauber Workshop 2001” Ncoll Npart = 2 Ncoll = 1 Npart Impact Parameter • Both approaches yield same Npart(b), Ncoll(b) ! • We have fixed Npart to prevent Npart<2, not Ncoll • Npart(b) x (1 -P 0(b)) where P 0(b) = exp(-ABs. NNTAB) • Not simply fixed by modifying cross section! Peter Steinberg BNL/RIKEN High p. T Workshop

The Right Cross Section Peter Steinberg BNL/RIKEN High p. T Workshop

Geometry of pp collisions Total Cross Section has many components: What do we use? Spectators b Participants Spectators Non-single-diffractive (NSD) Collisions Rapidity Gap h Elastic Interaction PAS, UCSB Workshop 2002 Peter Steinberg h IP IP Single Diffractive Double Diffractive h Non-Diffractive Inelastic Collisions – slightly lower multiplicity, harder to trigger on! BNL/RIKEN High p. T Workshop

Comparing Experiments: d+A Experiment Trigger Cross section PHOBOS Paddles + ZDC NSD 41 mb PHENIX High p. T Trigger 31 mb STAR ZDC Total 51 mb Boris’ Proposal: Different experiments should use appropriate cross section Peter Steinberg BNL/RIKEN High p. T Workshop

Various Definitions for R Peter Steinberg “Cronin” RHIC PHOBOS Pure cross sections, nuclear masses “Process independent” “No” cross section needed! Impossible at RHIC, also “minbias” only Requires ds/dp. T from Vernier scan Ncoll still needs it! BNL/RIKEN High p. T 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? Peter Steinberg BNL/RIKEN High p. T Workshop

Consequences • Inelastic corrections lead to large modifications to published Rd. A • Over summer BK said that Ncoll would decrease with s. NN: Rd. A would increase linearly (e. g. 31 vs 41 implies 30% increase) PHENIX + BK Now PHENIX goes down! • Now, the smaller cross section is seen to lead to a *larger* number of collisions on average. Peter Steinberg BNL/RIKEN High p. T Workshop

Access to p+A in d+A M. Miller PRL. 91, 072304 (2003) Without a non-standard cross section, STAR can explain ZDC selection Peter Steinberg 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 BNL/RIKEN High p. T 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 s. 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 p. T Workshop

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 Peter Steinberg BNL/RIKEN High p. T 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-p. T 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 9 am Saturday morning? Peter Steinberg BNL/RIKEN High p. T Workshop

Geometry of AA Collisions Spectators b. Participants Binary Collisions: 1. Jet Production 2. Heavy Flavor “Glauber” model of AA Color Exchange: 1. Soft Hadron Production 2. Transverse Energy Npart, Ncoll Spectators Binary Collisions Participants b (fm) Peter Steinberg BNL/RIKEN High p. T Workshop

Effect of Wide Centrality Bins • This is a “known” effect in Au+Au, but we rarely quote “minimum bias” Au+Au… • Obviously affects d+Au and minimum bias is all we have… Peter Steinberg BNL/RIKEN High p. T Workshop

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 exponential> 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 Peter Steinberg • Glauber Model • • • STAR uses ZDC, PHENIX uses BBC • • • Is this true? ? ? So star needs 51 mb, phenix 30? ! Conclusions: • • Usually we use s_inel. Differs from subtracting elastic bit Normalization of high-p. T 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 x~0. 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 Mueller’s theorem, AGK cancellation Projectile parton hits A^{1/3} and can be emitted from any of them. Bethe-Heitler regime Multiplicity dependence * cross section gives A dependence at eta=0 But number of valence quarks is fixed and independent of A. So at eta=3. 4, scales as A^{2/3} What is this bump at moderate p. T? So it’s a certain scaling of valence quark production? BNL/RIKEN High p. T Workshop