What we’ll discuss.. Techniques used to scale and compare from pp to NN Description of ingredients recipes used by experiments caveats and uncertainties Aim: everyone on same page for rest of workshop. High pt @ RHIC, 11/1/2001

pp data: What do we have? ISR s = 24 - 64 GeV pp SppS s = 200 - 900 GeV Tevatron s = 500 - 1800 GeV Ignore difference btw and , small compared to other uncertainties UA1 and CDF: (h+ + h-)/2 ISR: p, K, p and p High pt @ RHIC, 11/1/2001

Parameterization: The power law fits Phys. Rep. 23 (1976) 1 Sivers, Brodsky, Blankenbecler CERN-ISR A+B  C + X: N depends on particle, for pp  0 + X q-q : ~ p^ -4 from QCD h-h : ~ p^ -8?, no real guidance … current form (used already by UA1) : perhaps born out of desperation? High pt @ RHIC, 11/1/2001

Compilation Data available over wide range of s, but not for 130 GeV High pt @ RHIC, 11/1/2001

Consistency in data: same experiment UA1 at 500 GeV Data and power law are consistent UA1 at 200 GeV Data and reported power law are offset High pt @ RHIC, 11/1/2001

Consistency in Data: between experiments CDF UA1 Difference of ~3 at 6 GeV High pt @ RHIC, 11/1/2001

pp @ s = 130 GeV Obtain  (needed for Npart and Ncoll) Obtain power law parameters A, p0 and n Procedure: Use the available data and interpolate Not all data sets are of equal quality Not all data sets are for h+ , h- Check for consistency difficult to estimate systematic uncertainties High pt @ RHIC, 11/1/2001

Cross section  @ 200 GeV not measured UA5 measured at 900 GeV, and ratio 200/900 Must use parameterization e.g. PDG gives High pt @ RHIC, 11/1/2001

Obtaining parameters... One way… Another way… Interpolate the s dependence of the fit parameters need care, p0 and n are highly correlated Another way… Interpolate the measured cross sections at several fixed p^ Gives interpolated p^ distribution Fit this distribution, obtain parameters High pt @ RHIC, 11/1/2001

First method: use scaling with s High pt @ RHIC, 11/1/2001

First method:Constraints on p0 and n Can constrain <pt> and dNch/d Useful relations for power law High pt @ RHIC, 11/1/2001

First Method: Extrapolate Try various fits: 1st & 2nd deg. poly., exp, etc. Fit p0, obtain n via <pt> and vice versa Errors above denote: STAR: variations in fits to parameters PHENIX: variations in parameters from different data interpolations (2nd method) Leads to a 20-30% uncertainty at p^=6 GeV High pt @ RHIC, 11/1/2001

Resulting pt-Uncertainties, and “R(130/200)” Power law: E d3/dp3 = A (1+pt/p0) –n Ratio between power law at 130 to power law at 200 GeV PHENIX n=12.4, p0 = 1.71 STAR n=12.98, p0=1.895 High pt @ RHIC, 11/1/2001

pp to AA: Glauber model and TAB Woods-Saxon: from e-A Overlap Integral: s: Binary Collisions: Participants: Calculation can be done (even on the web)… but how big are the uncertainties? High pt @ RHIC, 11/1/2001

Uncertainties! For 5% most central collisions: <Ncoll> = 1050-1100 TAB=26±2 mb-1 Calculate Npart and Ncoll What happens for peripheral? PHOBOS M.C. study P. Steinberg QM’01 High pt @ RHIC, 11/1/2001

Plotting the data: RAA High p^ processes ~ Ncoll Nuclear modification factor : If no anomalous effects, data at high p^ should approach 1 when plotted in this form. … the deviations from 1 are what this workshop is all about... High pt @ RHIC, 11/1/2001

Conclusions s = 200 GeV s = 130 GeV Ratios Ok, since measure pp @ RHIC (maybe pA too?) s = 130 GeV Uncertainties, no data, so must extrapolate currently available data differ by ~3 at high pt will there be pp at this energy at RHIC? Ratios central/pp Ok, measure with same systematics (== same experiment) central/peripheral Ok for trends, syst. cancel in same experiment Uncertainties in normalization, Ncoll for peripheral of the order of 20-30% High pt @ RHIC, 11/1/2001