Azimuthal and HBT Correlations of
Particles with Strangeness
Outline
•HBT
Motivation
Selected Results/Implications
•Azimuthal Correlations
Motivation
Info in Correlations
Selected Results/Implications
•Summary
NOTE !!
Strange Particle Azimuthal and HBT Correlation
Measurements are NOT Pervasive.
Roy A. Lacey
Why Study HBT Correlations
HBT allows quantification of
contributions to spacetime evolution (STE) of
system
reaction
plane
Lifetime and duration of
fp=90°
emission
Rside (small)
Spatial extent of system
Rside (large)
Collective
flow at thermal
freeze-out
Probability to detect 2 particles at p1 and p2,
C2   d 4 x1d 4 x 2 12 x1 x 2 
2
(pair relative momentum)
 r

r
r
t 

 r ,t   exp  



2
2 
2
R
2
R
2
R
2

L


2
2
2
2
2
2
C 2  1   exp  q L R L  q TS R TS  q TO R TO  E 2  2
2
L

2
TS
2
TS
2
TO
2
TO
• HBT(f) provides direct
access to fshape
P=0° and
orientation of source
2

In the Longitudinal CMS, where (p1+p2)beam = 0,

  R 

2
2
2
2
C 2  1   exp  q 2L R 2L  q TS
R TS
 q TO
R TO
  2  2

2
R

exp 2
TO

exp 2
TS
2


exp
RTO
Observables
• Predicted
Signatures
for
2

R

2 2
3 radii: R L , R TS , R exp
TO
TO
QGP
Time duration :
chaoticity:

Roy A. Lacey
What is the Value of Strange Particle
Azimuthal and HBT Correlations ?
Roy A. Lacey
Value of Strange Particle HBT Correlations
Accurate Source Size Determination
4fm
6fm
F.Wang & S. Pratt
PRL 83, 3138, 1999
10fm
-p correlations are more sensitive than p-p for large sources
Roy A. Lacey
Value of Strange Particle HBT Correlations
Access to Space-time Asymmetries
Catching up
kz  0
p
 Large interaction time
 Large correlation
p
kz  0
p
C. Gelderloos et al
NIM A349, 618 (1994)
R. Lednicky et al
PLB 373, 30 (1996)
Moving away
 Small interaction time
 Small correlation
Ratio or Difference
 Sensitive to the
space-time asymmetry
Strange Particles aid Access to Possible
Space-time Asymmetries
Roy A. Lacey
Results
Chung et al (E895)
Imaging Technique
Brown Danielewicz
PRC 64, 14902 (2001)
C (q)  1  4  drr 2 K (q, r ) S (r )
Kernel
Encodes ( FSI)
Source Function:
Prob. of emitting a pair
of particles with separation
r in pair c.m.
 (short and long range)
 Fraction of particles
High Quality Source Functions Allow Detailed Comparisons
Between pp, pi-pi, and /\p
Roy A. Lacey
Results/Implications
Chung et al (E895)
•Half of the pions come from
A source with R1/ 2 8 fm
(1/2 from larger source)
•~ 51% of protons come
from a compact source
•~ 60% of p/\ pairs come
from intermediate size
source.
-- emission time diff.?
-- difference in flow ?
Estimates for /\ source
R1/ 2
6 1 fm
 ~ 1
The Naive Expectation of R p  Rpp  R is not Followed
Roy A. Lacey
Results
R1/ 2 Insensitive to pT over Range of Measurements. Substantial
change in fraction of particles which contribute to short-range
source
Roy A. Lacey
Results
/\p
Fit with theoretical CF
(effective range approx)
R. Lednicky
Sov. J. Nucl. Phys. 35, 770 (1982)
•S-wave scattering length
f0=-2.3/-1.8
(singlet/triplet)
Preliminary NA49 Data Indicate Similar Radius value
Roy A. Lacey
Results
 Correlations
Fit with theoretical CF
•S-wave scattering length
f0
Suggestive of Small Scattering Lengths
nn s-wave ~ 20 fm
Roy A. Lacey
Results
K 0 K 0 Correlations
Uncorrected
Large Radius ?
Mt Scaling ?
Roy A. Lacey
Value of Strange Particle HBT Correlations
Access to Space-time Asymmetries
Catching up
kz  0
 Large interaction time
 Large correlation
p
kz  0
p
C. Gelderloos et al
NIM A349, 618 (1994)
Moving away
 Small interaction time
 Small correlation
Ratio or Difference
 Sensitive to the
space-time asymmetry
R. Lednicky et al
PLB 373, 30 (1996)
Roy A. Lacey
Results
Fit in pair rest frame
<r*pion-r*kaon>
= -6.8 fm
r* = g (r -  t)
tpion-tkaon < 6.4 fm/c
rkaon-rpion < 4.6 fm
Data Suggest Important Space-time Asymmetry in
Emission Pattern for different Particles
Roy A. Lacey
Why Azimuthal Correlations
Jets:


Primarily from
gluons at RHIC
Sensitive to the
QCD medium
(dE/dx)
CGC:

Flow:
Provides insights
on Saturation
Physics


Primarily from
pressure build-up
Reflect conditions
in collision zone
(EOS)
Correlation Studies can provide information on the particle
production mechanism,the EOS, Initial State effects
QGP formation…. (Very Important Signal)
Roy A. Lacey
Extracting Azimuthal Correlations
There are Several Methods Currently being Exploited
to Extract the Anisotropy and Asymmetry of Correlations


Reaction Plane method
Correlation Function Method:
1.) correlate particles (1 and 2) from the same pT range
(fixed pT)
2.) Correlate particle 1 in a given pT bin
with particles of arbitrary or Fixed pT
(Assorted pT)

Multiparticle correlations:
Three-Particle Correlations, Cumulants
Roy A. Lacey
Establishing Definitions
Asymmetry (  )
1.2
C(f
1.1

1.0
Anisotropy ( v 2)
0.9
0.8
0
20
40
60
80
100 120 140 160 180
fdeg.)
2


2
dN
1

f




 a  1  2  v2  cos(2f )    exp    
 





d (f )
 2   
Azimuthal Distributions and Correlation Functions
are Characterized by an Anisotropy and an Asymmetry.
Roy A. Lacey
Information in Correlation Functions
Hydro or Transport
Saturation Model
With large Opacity
HIJING
1.2
C(f
1.1
1.0
0.9
0.8
0
Flow leads to strong
anisotropy
Mini-Jets, lead to
strong anisotropy
and an asymmetry
20
40
60
80 100 120 140 160 180
fdeg.)
Jets lead to strong
anisotropy and an
asymmetry
The anisotropy of the correlation function can reflect
both flow-like and Jet contributions – Detailed Differential Studies
Required !!
Roy A. Lacey
What Kind of Insights
Do Strange Particles Provide ?
E895
Clear Evidence for in-medium potential
at AGS Energies
Roy A. Lacey
Differential Measurements
Star
Flavor Composition of v2 is
Crucial
Roy A. Lacey
Anisotropy Pattern is Species Dependent
Roy A. Lacey
Differential Measurements
PHENIX
STAR
Good Agreement
Between Experiments
Preliminary
Flavor Composition of v2 is
Crucial
Roy A. Lacey
Differential Correlation Functions
a)
Au + Au
Au + Au
b)
1.04
1.02
1.02
1.00
1.00
0.98
0.98
0.96
0.96
c)
f
P+P
2
•
Charge
Selection
Consistent with
presence of
Jets/Minijets
P+P
Illustrative Sketch
Illustrative Sketch
2
C
1
1
0
40
80
120
fdeg.)
160 0
40
80
120
fdeg.)
•Asymmetry Sensitive to pTRef
160
Asymmetry of
Correlation
function sensitive
to:
• pT
Reference
•  Selection
d)
f
C
C
1.04
•
1.0 < pTRef < 3.0 (GeV/c)
C
0.3 < pTRef < 1.0 (GeV/c)
•
Extracted v2
relatively
insensitive
Roy A. Lacey
v2 Scaling
Scaling observed in models
b ~ 5.3
b ~ 6.2
b ~ 7.1
b ~ 10.9
v2(pT,b)/v2(b)
3
2
Molnar et al.
1
0
0
1
2
3
4
pT (GeV/c)
Goal:
Apply scaling to p+p & d+A and compare to A+A
Roy A. Lacey
Correlation Measurements serve as an important probe for
the high-energy-density nuclear matter .
Measurements Involving Strange Particles Provide:
– A Wealth of Insights on Reaction Dynamics
• Several Examples Given (HBT, Azimuthal Correlations)
– Better Understanding of Probes Crucial to the Search for
the QGP
Much Much More to Come !!
Roy A. Lacey