1. High Pt Phenomena at RHIC, November 1, 2001 Manuel Calderón de la Barca Sánchez Yale University Extrapolating from pp to NN Collisions Extrapolating from pp to NN Collisions

2. 2 High pt @ RHIC, 11/1/2001 What we’ll discuss.. @Techniques used to scale and compare from pp to NN Description of Hingredients Hrecipes used by experiments Hcaveats and uncertainties @Aim: everyone on same page for rest of workshop.

3. 3 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: , K, p and  p

4. 4 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?

5. 5 High pt @ RHIC, 11/1/2001 Compilation Data available over wide range of  s, but not for 130 GeV

6. 6 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

7. 7 High pt @ RHIC, 11/1/2001 Consistency in Data: between experiments UA1 CDF Difference of ~3 at 6 GeV

8. 8 High pt @ RHIC, 11/1/2001 pp @  s = 130 GeV @Obtain  (needed for N part and N coll ) @Obtain power law parameters A, p0 and n @Procedure: HUse the available data and interpolate WNot all data sets are of equal quality WNot all data sets are for h +, h - WCheck for consistency Odifficult to estimate systematic uncertainties

9. 9 High pt @ RHIC, 11/1/2001 Cross section @  @ 200 GeV not measured @UA5 measured at 900 GeV, and ratio 200/900 @Must use parameterization He.g. PDG gives

10. 10 High pt @ RHIC, 11/1/2001 Obtaining parameters... @One way… HInterpolate the s dependence of the fit parameters Wneed care, p 0 and n are highly correlated @Another way…  Interpolate the measured cross sections at several fixed p   Gives interpolated p  distribution HFit this distribution, obtain parameters

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

12. 12 High pt @ RHIC, 11/1/2001 First method:Constraints on p 0 and n @Can constrain and dNch/d  @Useful relations for power law

13. 13 High pt @ RHIC, 11/1/2001 First Method: Extrapolate @Try various fits: 1st & 2nd deg. poly., exp, etc. HFit p0, obtain n via 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

14. 14 High pt @ RHIC, 11/1/2001 Resulting p t -Uncertainties, and “R(130/200)” Power law: E d 3  /dp 3 = A (1+p t /p 0 ) –n Ratio between power law at 130 to power law at 200 GeV PHENIX n=12.4, p 0 = 1.71 STAR n=12.98, p 0 =1.895

15. 15 High pt @ RHIC, 11/1/2001 pp to AA: Glauber model and T AB @Calculation can be done (even on the web)… but how big are the uncertainties? Woods-Saxon: from e-A Overlap Integral:  : Binary Collisions: Participants:

16. 16 High pt @ RHIC, 11/1/2001 Uncertainties! Calculate N part and N coll P. Steinberg QM’01 PHOBOS M.C. study For 5% most central collisions: = 1050-1100 T AB =26±2 mb -1 What happens for peripheral?

17. 17 High pt @ RHIC, 11/1/2001 Plotting the data: R AA  High p  processes ~ N coll @Nuclear modification factor :  If no anomalous effects, data at high p  should approach 1 when plotted in this form. W… the deviations from 1 are what this workshop is all about...

18. 18 High pt @ RHIC, 11/1/2001 Conclusions @  s = 200 GeV HOk, since measure pp @ RHIC (maybe pA too?) @  s = 130 GeV HUncertainties, no data, so must extrapolate Wcurrently available data differ by ~3 at high pt Hwill there be pp at this energy at RHIC? @Ratios Hcentral/pp WOk, measure with same systematics (== same experiment) Hcentral/peripheral WOk for trends, syst. cancel in same experiment WUncertainties in normalization, N coll for peripheral of the order of 20-30%