Bose-Einstein Correlations from pp Collisions at RHIC
Thomas D. Gutierrez
University of California, Davis
UCD Nuclear Physics Seminar
• Introduction
• Analysis
• Results
• Outlook
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
1
What are Bose-Einstein Correlations?
Bose-Einstein correlations (BEC) are a joint measurement
of more than one boson in some variable of interest.
For example, if the variable of interest is momentum then
P1 information about the geometry of boson emission source
can be obtained (more on this later)
rA1
d
rB1
rA2
rB2
R
P2
In its simplest form, BEC often predicts
an enhancement of boson coincident counts (relative
to the experiment performed with non-bosons).
This is usually associated
with Bose-Einstein statistics.
But things are rarely this simple.
L >> (d & R)
BEC often goes under the name HBT or GGLP.
I’ll use HBT.
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
2
What is HBT?
The technique was originally developed by two English astronomers
Robert Hanbury-Brown and Richard Twiss (circa 1952)
It’s a form of “Intensity Interferometry”
-- as opposed to “regular” amplitude-level
(Young or Michelson) interferometry -and was used to measure the angular sizes of stars
A quantum treatment of HBT generated much controversy and
led to a revolution in quantum optics
Later it was used by high energy physicists to measure
source sizes of elementary particle or heavy ion collisions (the GGLP effect)
But how does HBT work? And why use it instead of “regular” interferometry?
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
3
Two slit interference
(between coherent sources at A and B)
k
2

P1
rA1
A

Plane wave
d
rB1
Monochroma
tic Source
B
rB1  rA1  d sin 
“source geometry”(d) is
related to interference pattern
L >> d
I P1 | e

ik rA1
I P1  I P1
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
e

ik rB1 2
|  2(1  cos[ k (rB1  rA1 )])
(brackets indicate time average -- which is what is usually measured)
Thomas D. Gutierrez
UC Davis
4
“Two slit interference”
(between incoherent sources at A and B)
Two monochromatic but incoherent
sources
(i.e.with random, time dependent phase)
produce no interference pattern
at the screen -assuming we time-average
our measurement over many
fluctuations
I P1  2
rA1
A
d
P1
rB1
(brackets again indicate time average)
B
L >> d
I P1 | e
 
ik rA1  i A ( t )
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
e
 
ik rB 1  i B ( t ) 2
|  2(1  cos[ k (rB1  rA1 )  ( B   A )])
Thomas D. Gutierrez
UC Davis
5
HBT Example (incoherent sources)
P1
rA1
As before...
I P1 | e
 
ik rA1  i A ( t )
I P 2 | e
 
ik rA 2  i A ( t )
e
 
ik rB 1  i B ( t ) 2
e
|
rB1
 
ik rB 2  i B ( t ) 2
R
rA2
|
I P2  2
I P1  2
A
d
P2
rB2
But if we take the product before time averaging...
I P1I P 2  4  2 cos[k (r1  r2 )]
B
where
r1  r2  rA1  rB1  (rA2  rB 2 )
L >> (d & R)
Important: The random phase terms completely dropped out.
We can extract information about the source geometry!
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
6
Increasing angular size
C
I1 I 2
Notice that the “widths” of these correlation functions are
inversely related to the source geometry
Astronomy
I1 I 2
For fixed k
1
C  1  cos[( k ) R]
2
C
I1 I 2
I1 I 2
source
Width w
Increasing source size d
A source can also be a continuous distribution
rather than just points
Particle physics
The width of the correlation function
will have a similar inverse relation to
the source size
Correlation function
1
C  1  cos[Qd ]
2
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
I’ll drop

Width ~1/w
Thomas D. Gutierrez
UC Davis
7
More About HBT
As we’ve seen, when treated with classical waves, HBT is basically
just a kind of beat phenomenon
When treated quantum mechanically (i.e. actually counting particles)
the situation is more complex
Lets define the two particle correlation function as:
C2 
I1 I 2
I1 I 2
d 6N


3
3



Tr a p 2 a p1a p 2 a p1 
dp
dp
1
2 

 3
3
3
Tr ap1a p1 Tr ap 2 a p 2 
d N / dp1 d 3 N / dp2



he density matrix in the second expression tells us two very important things
C2 is sensitive not only to the quantum statistics
(determined by the commutation relations of the a and a’)
but also the quantum field configuration;
C2 is sensitive to the source distribution, the dynamics of the problem,
as well as any space-momentum correlations
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
8
Sill more about HBT
Measuring the correlation
function is really just a
counting game
Joint probability of measuring a
particle at both detectors 1 and 2
P(1 | 2)
C2 
P(1) P(2)
Probability of measurement at 1 times
probability of a measurement at 2
Note: if the two measurements
are statistically independent then C2=1
C2
Thermal Bosons   1
Two quantum field configurations of interest: 2
coherent state (like a “laser”) and
thermal state (following a Bose-Einstein distribution)
Partly coherent bosons+thermal+contamination
 1
C2 is often measured as a function of the momentum
ifference and can often be parameterized like a Gaussian:
C(Q)  1  λe
 Q2 R 2
1
~1/R
 0
Totally coherent
Q=|p1-p2|
Momentum difference
Chaoticity parameter   C (Q  0)  1
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
0
Non-interacting fermions   1
Thomas D. Gutierrez
UC Davis
9
Practicalities of HBT Interferomertry using particles in HEP
•
•
Compare relative 4-momenta (Qinv) of identical particles (e.g. pions) to
determine information about space-time geometry of source.
Experimentally, 1D C2 correlation functions are created by comparing relative 4momenta of pairs from a “real” event signal to pairs from “mixed” events.
• The mixed background presumably has no HBT signal!
Qinv  p1  p2 
STAR Preliminary
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
E1  E2 
2
  2
  p1  p2 
STAR Preliminary
Thomas D. Gutierrez
UC Davis
10
More HBT practicalities in HEP
•The correlation function, C2, is created by dividing the “real” pairs by “mixed”
pairs. The histogram is then normalized to the baseline.
•The data are fit to a Gaussian or an exponential to extract fit parameters Rinv
and λ.
C2g = 1 + λexp(-Qinv2Rinv2)
C2e = 1 + λexp(-QinvRinv)
STAR Preliminary
 g=0.397 +/- 0.013;
Rg=1.16 fm +/- 0.032;
e=0.749 +/- 0.030;
~λe
Re=1.94 fm +/- 0.071
The Coulomb
repulsion experienced
by identical charged pairs tends to deplete
the correlation function at low Q
-- this can be corrected
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
~1/R
Both fits are to the
Coulomb corrected
data (dark blue)
Thomas D. Gutierrez
UC Davis
11
Why study HBT in pp Collisions?
• There is a long history of doing Bose-Einstein pion
correlations in elementary particle collisions
• In the context of RHIC, it provides a baseline for the heavy
ion results
Just a sampling
•Dowell., Proc. Of the VII Topical
Workshop on Proton-AntiProton
Collider Physics, p115, Word Scientific
1989.
NA22
π+/p
AMY
fm
p/pbar
•OPAL Collaboration. Physics Letters
B. Vol 267 #1, 5 September, 1991.
e+/eUA1
OPAL
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
E735
•Lindsey. “Results from E735 at the
Tevetron Proton-AntiProton Collider
with root s= 1.8TeV”, Presented at the
Quarkmatter 1991, Gatlinberg,
Tennessee, Nov 11-15, 1991.
•NA22 Collaboration “Estimation of
Hydrodynamical model parameters from
the invariant spectrum and the BoseEinstein Corrilations…”, Nijmegen
preprint, HEN-405, Dec. 97.
Thomas D. Gutierrez
UC Davis
12
What is HBT Actually Measuring?
In this 1D inside-out fragmentation picture,
For non-static sources, HBT becomes sensitive to
t
rapidity and z are correlated. Particles
regions of homogeneity; this gives
near each other in rapidity, will also
rise to a phase space dependence of the radii
be near each other in space.
Particles close in space and momentum contribute
 
most strongly to the HBT signal
N  K
y1
y2
HBT radii will often be much
smaller than actual
hadronization
surface
Hadronization “freeze out”
surface (mean)
z
Regions of Homogeneity
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
P
T
Quark scattering and
creation
Thomas D. Gutierrez
UC Davis
13
HBT Study of the pp System
• HBT studies in pp interactions provide a peek into the fascinating softphysics regime of hadronic collisions
•
•
•
•
•
Some HBT-related questions:
What do the regions of homogeneity look like?
What is the pair source distribution function?
How do the HBT parameters depend on event multiplicity?
Do the HBT parameters depend on the polarization of the initial state
(a fun idea but won’t have time to talk about it today)?
This analysis is a first step in answering some of these questions
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
14
The STAR Experiment
STAR main detector: Time Projection Chamber
(a large-acceptance cylindrical detector)
E field and B field along the beam direction.
12 million reversed full field and full field,
minimum bias pp events at 200GeV from
RHIC using the STAR detector; some data
presented include only the 7 million RFF
Particle identification done by measureing
dE/dx (specific energy loss)
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
15
Track and Event Selection (I)
•For negative and positive
pions at two mid-rapidity
ranges
(-0.5<y<0.5; 1<y<1), four kt ranges were
analyzed (0.15<kt<0.25,
0.25<kt<0.35, 0.35<kt<0.45,
0.45<kt<0.65 GeV/c)
Kt is the average PAIR transverse moment
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
P
e
•Particle identification was
done by taking a one sigma
cut around the pion bethebloch curve while excluding
other particles at the two
sigma level.
Y is the TRACK rapidity
dEdx vs. P (GeV/c)
K

STAR Preliminary

  similar
Thomas D. Gutierrez
UC Davis
16
Track and Event Selection (II)
Some additional cuts used for this analysis
• Verices accepted 3m across the STAR TPC
STAR
Preliminary
pass
• Analysis done separately for 20cm wide regions
(results then added)
• For the non-multiplicity dependent analyses: event
Multiplicity < 30
fail
• Analysis performed separately for like-multiplicity
events (results then added)
•Only accept events with at least 2 tracks
zvertex
The effects of pileup in pp
have not yet been studied in
the context of HBT
The first order effect would
be to reduce the lambda factor
(a pileup would act like a mixed event
thus “watering down” the signal)
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Track level
-0.5 < y < 0.5 and -1<y<1
•PID cuts as discussed
•Primary tracks only
Pair level
Four kt bins between: 0.15 < kt <0.65 GeV/c
anti-merging and anti-splitting cuts applied
Thomas D. Gutierrez
UC Davis
17
Pair Cuts (I): Track Merging


-0.5<y<0.5


-1<y<1
STAR Preliminary
STAR Preliminary
Accept >9cm
Accept > 9cm
0.15 < kt <0.65 GeV/c for Qinv<0.2 GeV/c
The above correlation functions are a measure of track merging (2 tracks mistaken as one)
relative to a mixed background which presumably has no track merging
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
 looks similar
Thomas D. Gutierrez
UC Davis
18
Pair Cuts (II): Track Splitting


-0.5<y<0.5
Splitting is when one track is mistaken as 2
STAR Preliminary
Quality 
Accept
-0.5<Quality<0.6
 PADS with1hit   PADS with 2 hits
Total number of hits
Pads with two hits are circled
Qual~0 no splitting
(really DO have 2 tracks)
Qual=1 totally split
0.15 < kt <0.65 GeV/c
(one track mistaken as 2)
The above correlation function is a measure of the quality
relative to a mixed background.
The mixed background presumably has no splitting
(high quality means more splitting)
Wednesday April 30, 2003
UCD Nuclear Physics Seminar


and +/- 1 y looks similar
Thomas D. Gutierrez
UC Davis
19
1D Qinv Correlation Functions (I)
All fits are to the Coulomb corrected data:
The pi+ picombined
over -1<y<1
will serve
as the
standard
All plots here
0.15<kt<0.25 GeV
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
All STAR Preliminary
Thomas D. Gutierrez
UC Davis
20
1d Qinv Correlation Functions (II)
The strength of this high
Qinv tail depends on the
kinematic cuts; The effect
is currently under study
All plots here
0.15<kt<0.25 GeV;
-1<y<1;
pi+ and pi-
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
The traditional
Gaussian fit (black)
isn’t very good;
The exponential fits do
much better;
various parameterizations
are under study
All STAR Preliminary
Thomas D. Gutierrez
UC Davis
21
1D Qinv Correlation Functions (III)
Pythia pi- (no
C2 curvature depends only very weakly
afterburner);Baseline
0.15<pt<1.1; on particle species and zvertex choices;
-0.5<y<0.5;depends more strongly on rapidity and kt cuts;
1M events;
Still a rather small effect overall
ignore
normalization;
The current hypothesis is that the effect
evidence of
is due to energy-momentum conservation
some sloping;
will perform a
Qinv
more systematic
study
All STAR Preliminary
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
All plots here
0.15<kt<0.25 GeV;
Thomas D. Gutierrez
UC Davis
22
1D Qinv HBT Parameters
C g  (1  e
 R 2Q 2
R Q
C

(
1


e
) B1  (1  Q 2 ) B2  (1  Q  Q 2 )
) e
Cg
R (fm)
Ce
1.02+/-0.011 1.81+/-0.023
Ce * B1
Ce * B2
1.62+/-0.037
1.96+/-0.095

0.426+/0.007
0.803+/0.014
0.780+/0.014
0.684+/0.022

-
-
-
-0.232+/0.042

-
-
0.032+/0.005
All are from
0.15<kt<0.25 GeV;
0.184+/-1<y<1;
pi+ and pi0.029
Highly parameterization dependent values = bad
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
23
Source Image
Another interesting way to approach HBT is one can transform
the correlation function to obtain the actual source numerically
Tr ap 2 ap1a p 2 a p1 
C2 (Qinv ) 
 4  r 2 S (r ) K 0 dr  1
Tr ap1a p1 Tr ap 2 a p 2 
Thermal limit: Koonin-Pratt equation
S is the source distribution and represents the probability of emitting a pair of particles
with relative 4-momentum=Qinv separated by a distance r;
S is the quantity we want to extract
  ( q , r )

K0 is the angle averaged integration kernel and is given by
1
K0 
4
2
 1 d
i
s the pair wavefunction and includes all the appropriate quantum statistics and
relevant interactions between the pair
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
24
Source Image
C2
log(S)
0.15<kt<0.25;
-0.5<y<0.5;
pi- Qinv
Reconstructed
correlation function;
red is the nonCoulomb corrected
input Qinv
Correlation function
STAR Preliminary
Pair source emission
function S(r);
log scale
Qinv
r (fm)
Generated using Brown and Danielewicz's HBTprogs v.1.0 `
The different colors represent different parameters in the HBTprogs program
Is there a double Gaussian structure in the source function?
More work needs to be done to really determine this.
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
A promising method:
still a work in progress
Thomas D. Gutierrez
UC Davis
25
3D Correlation Functions
y pT1
  
KT  pT 1  pT 2

pT 2

y Qside  QsideKˆ T
  
pT  pT1  pT 2
x

pT

KT

Qout  Qout Kˆ T


Qout | pT  Kˆ T |


Qside  pT  Kˆ T

Qlong  p z1  p z 2
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
x
By looking at a 3D correlation function we
can extract a more complete picture of the source.
Thomas D. Gutierrez
UC Davis
26
3D Correlation Functions
kt cut with ~0.15 GeV/c pid pt cut
causes Qout “hole”
y cuts cause Qlong
“cutoff”
C2
All plots here
0.15<kt<0.25 GeV;
-1<y<1;
pi+ and piout
Fits and correlations projected 80MeV in
the “other” directions
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
side
long
C2 = N[1 + λexp(-qout2Rout2 -qside2Rside2 -qlong2Rlong2)]
All STAR Preliminary
Thomas D. Gutierrez
UC Davis
27
3D Correlation Parameters
C2 = N[1 + λexp(-qout2Rout2 -qside2Rside2 -qlong2Rlong2)]
Wednesday April 30, 2003
UCD Nuclear Physics Seminar

0.411+/-0.008
Rout
0.728+/-0.047
Rside
0.969+/-0.012
Rlong
1.13+/-0.020
0.15<kt<0.25 GeV;
-1<y<1;
pi+ and pi-
Thomas D. Gutierrez
UC Davis
28
3D Correlation Functions: kt dependence
AuAu 200GeV
Central
STAR Preliminary
Midcentral
Rlong
Rside
Rout
R(fm)

Peripheral
kt
What causes kt dependence?
kt
mT  m2  kT2
M. Lopez-Noriega QM2002
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
29
What Causes Kt Dependence?
Space momentum correlations
We are looking at a region of homogeneity caused by:Space momentum correlations
Space momentum correlations
Kt = pair Pt
Rout
If the source is not static or collective effects are present
Rsidethen space-momentum correlations can develop and cause
the radii to change as you look in different locations
in phase space.
Some examples
Inside-out fragmentation/ hadronization
jets (the ultimate space-momentum correlation)
fireball-like expansion
Not all of these will give the
collective flow
same kt dependence. The
rick is in distinguishing between them.
This is currently under study
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
30
Multiplicity Dependence of HBT parameters
It has been reported by some experiments (e.g. UA1 ppbar at 630 GeV)
that lambda tends to drop with
event multiplicity while the radius increases slowly
Other experiments (e.g. NA27 pp at 27 GeV) report that lambda is
flat as a function of event multiplicity
This puzzle has numerous explanations from the mundane to the exotic.
Some current speculations:
Pion emission becomes more coherent in high multiplicity events involving
particle-antiparticle collisions but not particle-particle
High multiplicity events from ppbar may involve multistring fragmentation
-- pions from different strings will not correlate strongly
Resonance contributions and other contaminates may contribute
to different degrees at different multiplicities at different experiments
All of the above would have the tendency to reduce lambda
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
31
Multiplicity dependence of 1D HBT
Using full RFF+FF
STAR Preliminary
STAR Exponential
This preliminary STAR
pp result indicates
lambda is flat as a function
of event multiplicity
NA27, NA23, and NA22
all reported
similar results
NA27 pp 27 GeV (Gaussian)
STAR Gaussian
UA1 ppbar 630 GeV (Gaussian)
This is clearly not the case
at UA1
•NA27 ZPC 54,21 1992
•UA1 PLB 226, 410, 1989
charged
Very Important: Not corrected for resonances or efficiency
Low multiplicity bins (<4) have large systematic error bars -- still being studied
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
32
Multiplicity Dependence of 1D Radius
STAR Preliminary
•NA27 ZPC 54,21 1992
•UA1 PLB 226, 410, 1989
STAR Exponential
This preliminary STAR
pp result indicates
rinv is flat as a function
of event multiplicity
STAR Gaussian
Very Important: Not corrected for resonances or efficiency
Low multiplicity bins (<4) have large systematic error bars -- still being studied
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
33
Summary
Bose-Einstein correlations provide a means of probing
the space-time geometry of the pion emission source in high energy collisions;
The pion emission source size is ~1 fm
A kt dependence is seen in the 3D HBT parameters of pp collisions
indicating a pion source with space-momentum correlations;
The nature of ths source is still under study
Lambda and rinv are constant
as a function of event multiplicity;
This is consistent with other pp experiments
but differ from ppbar results;
The effect is still under study
Wednesday April 30, 2003
UCD Nuclear Physics Seminar
Thomas D. Gutierrez
UC Davis
34