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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. pp data: What do we have?. ISR s = 24 - 64 GeV pp SppS s = 200 - 900 GeV - PowerPoint PPT Presentation
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High Pt Phenomena at RHIC, November 1, 2001
Manuel Calderón de la Barca Sánchez
Yale University
Extrapolating frompp to NNCollisions
Extrapolating frompp to NNCollisions
2 High pt @ RHIC, 11/1/2001
What we’ll discuss..
Techniques used to scale and compare from pp to NN
Description of ingredientsrecipes used by experimentscaveats and uncertainties
Aim:everyone on same page for rest of workshop.
3 High pt @ RHIC, 11/1/2001
pp data: What do we have?
ISR s = 24 - 64 GeV pp
SppS s = 200 - 900 GeVTevatron s = 500 - 1800 GeVIgnore difference btw and , small
compared to other uncertainties
UA1 and CDF: (h+ + h-)/2ISR: , K, p and p
pp
pp
pp pp
4 High pt @ RHIC, 11/1/2001
Parameterization: The power law fits
Phys. Rep. 23 (1976) 1 Sivers, Brodsky, Blankenbecler
CERN-ISRA+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?
Nppd
dE
23
3 1~
423
3
GeV/c 1
1~
ppd
dE
n
p
pA
pd
dE
03
3
1~
5 High pt @ RHIC, 11/1/2001
Compilation
Data available over wide range of s, but not for 130 GeV
6 High pt @ RHIC, 11/1/2001
Consistency in data: same experiment
UA1 at 500 GeVData and power law are consistent
UA1 at 200 GeVData and reportedpower law are offset
7 High pt @ RHIC, 11/1/2001
Consistency in Data: between experiments
UA1
CDF
Difference of ~3 at 6 GeV
8 High pt @ RHIC, 11/1/2001
pp @ s = 130 GeVObtain (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
9 High pt @ RHIC, 11/1/2001
Cross section @ 200 GeV not
measuredUA5 measured at 900
GeV, and ratio 200/900
Must use parameterizatione.g. PDG gives
s=200 s=130
tot 52.40 mb 49.26 mb
el 10.66 mb 8.91 mb
inel 41.74 mb 40.35 mb
10 High pt @ RHIC, 11/1/2001
Obtaining parameters...One 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 distributionFit this distribution, obtain parameters
11 High pt @ RHIC, 11/1/2001
First method: use scaling with s
2ln0053.0ln030.040.0 ssp sd
dnch ln55.032.0
12 High pt @ RHIC, 11/1/2001
First method:Constraints on p0 and n
Can constrain <pt> and dNch/d
Useful relations for power law
357.2 ,GeV/c 3795.0
GeV 130at
ln55.032.0
ln0053.0ln030.040.02
d
dnp
sd
dn
ssp
ch
ch
)1)(2(1
3
2
20
0 0
0
nn
pA
p
pAdpp
n
pp
n
13 High pt @ RHIC, 11/1/2001
First Method: ExtrapolateTry 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 parametersPHENIX: variations in parameters from different data interpolations (2nd method)
Leads to a 20-30% uncertainty at p=6 GeV
A(mb/GeV2)
p0 (GeV/c) n
Avg. STAR 267 6 1.895 0.086 12.98 0.97
Avg. PHENIX 275 20 1.72 0.2 12.4 1.1
14 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
15 High pt @ RHIC, 11/1/2001
pp to AA: Glauber model and TAB
Calculation can be done (even on the web)… but how big are the uncertainties?
•Woods-Saxon: from e-A
•Overlap Integral:
• :
crr
er
0
1)( 0
fmr
fmc
38.6
535.
169
0
0
)()(
bssdzdzsdT BABAAB
1)( 2bdbTAB
barnsbTbd BAppABAB 2.7}])(1[1{
0
)(r
r
nBA
AB
n
AB pppp bTbTn
BAbnP
)(1)(),(
)()( bTBAbN ABppBC
AppAB
BppBApart
sbTsTsdB
sbTsTsdAbN
])(1[1{)(
])(1[1{)()(
•Binary Collisions:
•Participants:
16 High pt @ RHIC, 11/1/2001
Uncertainties!
Calculate Npart and Ncoll
P. Steinberg QM’01
PHOBOS M.C. study
For 5% most central collisions:<Ncoll> = 1050-1100TAB=26±2 mb-1
What happens for peripheral?
17 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...
dydp
dN
dydpNd
N
dydpNd
T
dydpNd
NpR
ppinelpp
coll
AB
evt
inelppAB
AB
evtAB
2
2
2
2 11
)(
18 High pt @ RHIC, 11/1/2001
Conclusionss = 200 GeV
Ok, since measure pp @ RHIC (maybe pA too?)
s = 130 GeVUncertainties, no data, so must extrapolate
currently available data differ by ~3 at high ptwill there be pp at this energy at RHIC?
Ratioscentral/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%
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