what we’ll discuss

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%