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
Jan 24, 2016
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%