2. 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 RHIC, 11/1/2001

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

4. 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 RHIC, 11/1/2001

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

6. 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 RHIC, 11/1/2001

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

8. 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 RHIC, 11/1/2001

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

10. 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 RHIC, 11/1/2001

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

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

13. 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 RHIC, 11/1/2001

14. 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 RHIC, 11/1/2001

15. 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 RHIC, 11/1/2001

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

17. 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 RHIC, 11/1/2001

18. Conclusions s = 200 GeV s = 130 GeV Ratios
Ok, since measure 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 RHIC, 11/1/2001