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Particle correlations
at STAR
Jan Pluta
Some results from the STAR HBT
Heavy Ion Reactions Group
(HIRG),
Faculty of Physics,
Warsaw University of
Technology
group, presented recently by:
Z.Chajecki, A.Kisiel, M.Lisa,
M.Lopez-Noriega, S.Panitkin,
F.Retiere, P.Szarwas.
3-rd Budapest Winter School on Heavy Ion Physics, 10 XII 2003
Outline:
•The STAR experiment
•RHIC HBT Puzzle
•General analysis
•asHBT
•Two K0-short correlations
•p-Au, d-Au data
•Nonidentical particles - emission asymmetry
•Plans for future
Relativistic Heavy Ion Collider (RHIC)
12:00 o’clock
PHOBO
10:00
S o’clock
PHENIX
8:00 o’clock
BAF (NASA) m g-2
LINAC
RHIC
STAR
6:00 o’clock
U-line
1 MeV/u
Q = +32




4:00 o’clock
=3.8 km
1740 superconducting magnets
9 GeV/u
Q = +79
BOOSTER
AGS

BRAHM
S o’clock
2:00
HEP/NP
TANDEMS
Beam energy up to 100 GeV/A (250 GeV for p)
Two independent rings (asymmetric beam collisions are possible)
Beam species: from p to Au
Six interaction points
Four experiments: STAR, PHENIX, PHOBOS and BRAHMS
Solenoidal Tracker At RHIC
STAR Detector – side view
STAR Detector – side view
and STAR Collaboration – face view
STAR Collaboration
•
•
•
•
500 Collaborators
including
–
~65 graduate students
–
~60 postdocs
12 countries
49 institutions
Spokesperson:
John Harris 1991 - 2002
Tim Hallman 2002 - now
USA, Brazil, China,
Croatia Czech Republich,
England, France,
Germany, India,
Netherlands, Poland,
Rusia
Particle correlations
The idea:
HBT+FSI
Quantum statistics and Final-State Interaction
Space-time
sizes and
dynamics
Correlation
function
Momenta and
momentum
difference
Central Event: AuAu 200GeV/A
STAR Event 2
4m
Real-time track reconstruction
Pictures from Level 3 Trigger, online
display.
Typically 1000 to 2000 tracks
per event into the TPC
Event and Particle Selection
Au+Au Collisions at Sqrt(SNN)=200GeV
Minbias trigger
•
Centrality selection based on
number of charged hadrons.
three different centralities
•
Midrapidity
-0.5 < y < 0.5
N ch
•
Particle identification via specific
ionization (dE/dx)
electron band removed by cuts
•
Optimum performance for p HBT:
0.150 < pT (GeV/c) < 0.550
for K0s:
0.100 < pT (GeV/c) < 3.500
Some base definitions - to be used for results presentation
Two-particle kinematics
Main
(approximative)
relations:
Qout <--> Pt
Qside <--> 
Qlong <--> 
KT <--> Pt
LCMS: (P1+P2)z=0
HBT Excitation Function
Comparison with lower energies for
~ 10% most central events at
midrapidity
kT ~ 0.17 GeV/c
No significant increase in radii with
energy
RO/RS ~ 1
Gap in energy that needs to be
closed
RHIC HBT Puzzle
Most “reasonable” models still do not
reproduce RHIC sqrt(SNN) = 130GeV
HBT radii
Hydro + RQMD
STAR 130 GeV
PHENIX 130 GeV
PHENIX PRL 88 192302 (2002)
√SNN = 130GeV
p+
p-
“Blast wave” parameterization (Sollfrank model)
can approximately describe data
…but emission duration must be small
•  = 0.6 (radial flow)
from
spectra, v2
• T = 110 MeV
• R = 13.5  1fm (hard-sphere)
• emission= 1.5  1 fm/c (Gaussian)
3Dimensional Pion HBT
Sqrt(SNN) = 200 GeV
p – p–
Pratt-Bertsch Parameterization
raw
Coulomb
corrected
LCMS frame: (p1+p2)z=0
Central Events pT = 0.15-0.25 GeV/c
Coulomb correction
→ spherical Gaussian source of 5fm
momentum resolution corrected
(~1% effect at 200GeV, due to higher B-field)
C (q , q , q )  1  e
O
q* (GeV/c)
S
 ( qO2 RO2  qS2 RS2  qL2 RL2 )
L

Rout (fm)
Rside (fm)
Rlong (fm)
0.66 ± 0.01
6.41 ± 0.14
6.03 ± 0.09
6.65 ± 0.11
Statistical errors only!!
Centrality and mT dependence at 200 GeV
STAR PRELIMINARY
200GeV
Central
Midcentral
Peripheral
RL varies similar to RO, RS
with centrality
HBT radii decrease with mT
(flow)
Roughly parallel mT
dependence for different
centralities
RO/RS ~ 1
(short emission time)
Comparison: 200 to 130 GeV. Longitudinal radius
200GeV - 130
Central
GeV
Midcentral
Peripheral
PHENIX
Central
(fit to STAR Y2 data only)
STAR PRELIMINARY
Longitudinal radius:
at 200GeV identical to 130 GeV
Evolution timescale from RL
Simple Mahklin/Sinyukov fit
(assuming boost-invariant
longitudinal flow)
200GeV - 130 GeV
Central
Midcentral
Peripheral
TK
mT
R L  t fo
PHENIX Central
Makhlin and Sinyukov,
Z. Phys. C 39 (1988) 69
STAR PRELIMINARY
Assuming TK=110 MeV
(from spectra at 130 GeV)
t fo
central
 10 fm/c
t fo
periph
 7.6 fm/c
(fit to STAR Y2 data only)
Comparison: 200 to 130 GeV. Transverse radii
STAR PRELIMINARY
200GeV - 130 GeV
Central
Midcentral
Peripheral
*
PHENIX Central
Higher B-field  higher pT
Transverse radii:
• similar but not identical
• low-pT RO, RS larger at 200 GeV
• steeper falloff in mT
(PHENIX 130GeV)
• Ro falls steeper with mT
Azimuthally sensitive HBT (asHBT)
• sensitive to interplay b/t anisotropic geometry & dynamics/evolution
• “broken symmetry” for b0 => more detailed, important physics information
• another handle on dynamical timescales – likely impt in HBT puzzle
P. Kolb and U. Heinz, hep-ph/0204061
HBT respect Reaction Plane
side
y
K
fp
b
out
Lines: projections of 3D
Gaussian fit

q i q j R ij2 f 
x
C(q, f)  1  f  e
1D projections, f=45°
√SNN = 130GeV
HBT(φ) Results – 130 GeV
T=100 MeV 0.6
a.37, R=11.7 fm,
=2.2 fm/c
Data corrected for both
event plane resolution
and merging systematic
Minbias events @130GeV
Bolstered statistics by summing
results of p- and p+ analyses
Star preliminary
Blast-wave calculation (lines)
indicates out-of-plane extended
source
A model of the freezeout - BlastWave
BW: hydro-inspired parameterization
of freezeout
• longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost ~ r
 (r ) 
r
0  ~r 0
R
RY
 (r,fs )  ~
r 0  a cos(2fb )
RX
• coordinate space
• transverse extents RX, RY
• freezeout in proper time 
• evolution duration 0
• emission duration 
    0 
dN
~ exp 
2
d
2



2





00
A model of the freezeout- BlastWave
BW: hydro-inspired parameterization
of freezeout
• Longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost ~ r
r
 (r )  0  ~r 0
 (r,fs )  ~
r 0  a cos(2fb )
RY
R
• Coordinate space
• transverse extents RX, RY
• freezeout in proper time 
• evolution duration 0
• emission duration 
    0 2 
dN

~ exp 
2 
d
 2 
RX
7 parameters describing freezeout
central
midcentral
peripheral
BlastWave fits
to published
RHIC data
Central
T (MeV) 108  3
0
0.88 
0.01
a
0.06
0.01
RX (fm) 12.9
 0.3
RY (fm) 12.8  0.3
0 (fm/c) 8.9  0.3

0.0  1.4
2 / ndf
80.5 / 101
(fm/c)
Midcentra Peripheral
106l  3
95  4
0.87 
0.81  0.02
0.02
0.05
0.04  0.01
0.01
10.2
 0.5 8.0  0.4
11.8  0.6 10.1  0.4
7.4  1.2
6.5  0.8
0.8  3.2
0.8  1.9
153.7 / 92
74.3 / 68
• reasonable
centrality evolution
• OOP extended
source in noncentral collisions
Estimate of initial vs F.O. source shape

R 2y  R 2x
R 2y  R 2x
• estimate INIT from Glauber
• from asHBT:
 FO  2
R S2, 2
R S2,0
• FO < INIT → dynamic expansion
• FO > 1 → source always OOP-extended
• constraint on evolution time
asHBT at 200 GeV in STAR – R(f) vs centrality
12 (!) f-bins b/t 0-180 (kTintegrated)
• 72 independent CF’s
• clear oscillations observed in
transverse radii of symmetryallowed* type
• Ro2, Rs2, Rl2 ~ cos(2f)
• Ros2 ~ sin(2f)
• centrality dependence reasonable
• oscillation amps higher than 2ndorder ~ 0→
(*) Heinz, Hummel, MAL, Wiedemann, Phys. Rev. C66 044903 (2002)
Pion Correlations d-Au and p-Au
Pion correlation in d – Au : data selection
p-Au selection
1D correlation function
3D correlation function
d-Au vs p-Au
KT dependence
Centrality dependence
p-Au selection:
FTPC E -Au
ZDC-d
Au
ZDC-Au
d
All trigger events
Using information from ZDC-d
STAR can separate events with
neutron spectator from
deuteron
1D Correlation Function:
Gaussian fit:
theoretical CF: Rinv=6 fm,  = 0.5
collision
➢
CF is very wide (rel Au-Au)
➢ Coulomb/merging less important
➢ CF looks reasonable
➢ 1D Gaussian fit is not good
➢ needed more deeply study of fit
method
Rinv [fm]

  NDF
d* – Au
1.89 +- 0.01 0.364 +- 0.003 4672 / 33
d – Au
1.85 +- 0.01 0.362 +- 0.003 5359 / 33
d*-Au : d-Au without p-Au
only statistical error included !
3D Correlation Function:
3D Gaussian fit:
Gaussian parametrization is not
perfect but HBT radii characterize
the width of CF
Fit results:
d – Au
p – Au
Rout
1.58 +- 0.02
1.21 +- 0.03
R side
1.51 +- 0.01
1.21 +- 0.02
R long
1.71 +- 0.02
1.67 +- 0.05

0.354 +- 0.003
0.372 +- 0.008
Rout, Rside sensitive to
the number of participants
cut on the others Q's
components < 30 MeV/c
[GeV/c]
KT dependence:
clear KT dependence
●Rout and Rside - sensitive
to the number of
participants
●Rlong – the same KT
dependence for dAu and
pAu
●
p – Au
d – Au
KT dependence: d-Au & Au-Au divided by p-p
STAR preliminary
the same trend of KT
dependence for d-Au
and Au-Au as for p-p
● HBT radii are scaled by
constant factors
●
MT dependence of Rlong:
STAR preliminary
Sinyukov fit:
Rlong= const (mT)-a
mT   kT2 + massp
a for different collisions
STAR preliminary
p-p
d-Au Au-Au Au-Au
peripheral
midcentral
Centrality definition in d-Au:
FTPC-Au: charged primary particle multiplicity in -3.8<<-2.8
centrality bin
FTPC multiplicity
percent of events
1
[0 , 9]
100 – 40
2
[10 , 16]
40 – 20
3
[17 , 99]
20 – 0
most peripheral
most central
1
2
FTPC E -Au
ZDC-d
Au
ZDC-Au
d
3
centrality
Centrality dependence:
●
clear centrality dependence
●
●
similar to AuAu
connection to geometry
p – Au
d – Au
minbias
1
<Npart> [*]
[*] - Glauber calculations (Mike Miller)
<Nch>
<Nch>
4.3 +- 0.1
2
3
10.4 +- 0.4 16.3 +- 0.7
TPC
. 7.9 .
. 12.1 .
. 17.1 .
FTPC E
. 5.2 .
. 12.8 .
. 24.3 .
K0sK0s Correlations
mt scaling violation?
inv
Next RHIC HBT puzzle ?
Non-identical particle correlations:
The asymmetry analysis
Catching up
•Interaction
time larger
•Stronger correlation
Moving away
•Interaction
time smaller
•Weaker correlation
“Double” ratio
Kinematics selection
on any variable
e.g. kOut, kSide, cos(v,k)
•Sensitive
to the space-time
asymmetry in the emission
R.Lednicky, V. L.Lyuboshitz,
B.Erazmus, D.Nouais,
Phys.Lett. B373 (1996) 30.
Double ratio definitions
simulation
2k* = p1 – p2
P = p1 + p2
kside < 0
Correlation
functions
p1
kout > 0
p2
Double
ratios
2k* [GeV/c]
klong is the z component
of the momentum
of first particle in LCMS
kout sign
selection
determined by
the direction
of the pair
momentum P
kside sign
selection
arbitrary
kout > 0
p2
p1
kside > 0
What to expect from double ratios
• Initial separation in Pair Rest
Frame (measured) can come
from time shift and/or space
shift in Source Frame (what
we want to obtain)
• We are directly sensitive to
time shift, the space shift
arises from radial flow –
possibility of a new radial
flow measurement
Flow velocity
F
y
Side
r
direction
x
Out
direction
observed
transverse
T velocity
thermal velocity
What do we probe?
Source of
particle 1
Source of
particle 2
Separation between
source 1 and 2 in pair
rest frame
Boost to pair rest frame
r
t
sr*
<r*>
r* (fm)
r (fm)
r* = gpair r – bpair t
Separation due to
space and/or time
shift
• Mean shift (<r*>)  seen in double ratio
• Sigma (sr*)  seen in height of CF
Correlation functions and ratios
Good agreement for like- CF
sign and unlike-sign pairs
points to similar emission
process for K+ and KOut
Clear sign of emission
asymmetry
Side
Two other ratios done as
a double check – expected
to be flat
Long
Preliminary
Results for Pion-Proton 130 AGeV
• Similar
preliminary
analysis done for
pion-proton
• We observe
Lambda peaks at
k*~minv of Λ
• Good agreement
for identical and
non-identical
Λ peaks
STAR
preliminary
Preliminary results for Kaon-Proton
• Using data from Year2 (200
AGeV) – sufficient statistics
• No corrections for
momentum resolution done
• No error estimation yet – fit
indicates theoretical
expectations
K+ p
K- anti-p
Best Fit
STAR
preliminary
Modeling the emission asymmetry
• Need models producing
strong transverse radial
flow:
– Blast-wave as a
baseline
– RQMD
– UrQMD
– T. Humanic's
rescattering model
• What do we measure and
how to compare it to the
models?
• Is our fitting method
working? And if yes, what
does it tell us?
• Need to disentangle flow
and time shift
Understanding models
Blast wave = Flow baseline
• Blast wave
Parameterization
of the final state
bt
Kt = pair Pt
R
Rside
Rout
– Parameterizes source size
(source radius) radial flow
(average flow rapidity) and
momentum distribution
(temperature):
– No time shift
– Only spatial shift due to flow
– Infinitely long cyllinder
(neglects long contribution)
Blast wave: how does the flow work
Pion
pt = 0.15 GeV/c
bt = 0.73
Average emission points
Kaon
pt = 0.5 GeV/c
bt = 0.71
Proton
pt = 1. GeV/c
bt = 0.73
Spatial shifts (r)
Particle momentum
Fitting and quantitative comparisons
• Fits assume gaussian
source in PRF
• r*out distributions have nongaussian tails
• Use the same fitting
procedure for models and
data - correlation functions
constructed with
“Lednicky's weights”
Example of r*out
distribution from RQMD
Comparing models to data
• Rescattering models and blastwave are consistent with data
• Blast wave parameters
constrained by STAR
measurements
• In models flow is required to
reproduce the data
• More points in βt needed to map and discriminate the flow profile – needs
STAR upgrades in PID capability (TOF barrel)
STAR HBT Matrix (circa 2003)
p+
p-
+
-
0
p
p


++
p+
0
p+
f
-
Analysis
in progress
0
Sergei's HBT matrix
published
Y1 ?
submitted
p
Y1
Y2 shown:
Not
3p Correlations (accepted PRL)
asHBT
Phase space density
Correlations with Cascades
dAu, pp
Cascades
p


“traditional”
HBT axis
What have we learned so far?
• RHIC HBT puzzle
– Break down of theoretical description of correlations at RHIC
– Indication of short source lifetime and freeze-out duration at RHIC
– Short lived hadronic phase?
• Out of plane extended pion source in non-central collisions
– Also points to short emission times
• Weak energy dependence of the HBT radii
– Where is the phase transition?
• Large pion phase space densities (non-universal)
– Small entropy per pion?
• Chaotic pion source from 3p correlations
– No multiparticle effects above Pt~200 MeV/c
• Source asymmetries from non-identical correlations
– Consistent with collective flow and short time scales
• Only systematics measurements may provide answers!
What will affect STAR HBT analysis?
• RHIC upgrades progress
• STAR upgrades
• Various other measurements (e.g. spectra,
high Pt,
strangeness, flow, etc)
• New theoretical ideas
Consequences for STAR HBT
• Large statistics AuAu datasets
• Plans for 2004: 14 weeks of AuAu “physics” running:
– ~30M central, ~50M peripheral events
• What can be done? Many analysis which were statistics limited!
– Rare particle correlations W, X,L, etc (identical, non-identical)
• Early freeze-out, sequence of emission, flow, FSI, etc
– Correlations relative to reaction plane
• Kaons
• Non-identical
– Baryon correlations: ppbar, LLbar, pL, etc
– Coalescence, light nuclei and anti-nuclei
• Large statistics pp (~100M events) datasets @200, 500 GeV
– STAR HBT matrix (e.g. non identical correlations)
– HBT in Jets?
– spin dependent HBT? (with polarized beams)
• Different energies
• Different beams
Add dependencies on centrality, Kt, reaction plane
Event by Event HBT
New analyses ideas (S.Pratt, imaging, etc)
Consequences for STAR HBT
• Better particle identification
• Extension of HBT systematics to higher Kt: 1-3
GeV/c
• Region of transition from Hydro to pQCD
• What is space-time picture in this region?
– Correlations of identical particles
– Scan in Pt for Non-identical correlations
• Sensitivity to flow profile, model details
– asHBT
• Higher efficiency of hyperons reconstruction
– ~x10 for W compare to TPC alone
– High statistics correlations with hyperons
Summary
• RHIC and STAR future seems to be certain for
next 5-10 years
• Upgrade path is visible
• The number of available datasets and possible
analysis topics will be rapidly increasing
• Data volumes will be unprecedented (at least for
us)
– Can we do analysis in a reasonable time?
• Analyses will be “moving” to rare particles
• Shall we continue with systematic approach?
– Probably yes
• If new results or theoretical predictions will
suggest promising measurement - we will
concentrate on it