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STAR
Pion Interferometryand
RHIC Physics
Pion Interferometryand
RHIC Physics
John G. Cramer
Department of Physics
University of Washington
Seattle, Washington, USA
John G. Cramer
Department of Physics
University of Washington
Seattle, Washington, USA
Invited Talk presented atIX Mexican Workshop on Particles and Fields
Physics Beyond the Standard ModelUniversidad de Colima, Colima, Mexico
November 19, 2003
Invited Talk presented atIX Mexican Workshop on Particles and Fields
Physics Beyond the Standard ModelUniversidad de Colima, Colima, Mexico
November 19, 2003
November 19, 2003
John G. Cramer2STAR
Part 1Part 1
About RHIC
The Relativistic Heavy Ion Collider
and STAR
Solenoidal Tracker At RHIC
at BNL
Brookhaven National Laboratory
About RHIC
The Relativistic Heavy Ion Collider
and STAR
Solenoidal Tracker At RHIC
at BNL
Brookhaven National Laboratory
November 19, 2003
John G. Cramer3STAR
Systems:
Au + Au
CM Energies:
130 GeV/A
200 GeV/A
1st Collisions:
06/13/2000
Location:
BrookhavenNationalLaboratory,
Long Island,NY
Brookhaven/RHIC/STAR OverviewBrookhaven/RHIC/STAR Overview
pp
AGS
TandemVan de Graaff
RHICBlue Ring
Yellow Ring
Booster
Ring
November 19, 2003
John G. Cramer4STAR
What does RHIC do?What does RHIC do?
RHIC accelerates gold nuclei in twobeams to about 100 Gev/nucleon each(i.e., to kinetic energies that are over100 times their rest mass-energy)and brings these beams into a200 GeV/nucleon collision. Four experiments, STAR,PHENIX, PHOBOS, andBRAHMS study these collisions. In the year 2000 run, RHICoperated at a collision energyof 130 Gev/nucleon. In 2001-2 it operated at 200 GeV/nucleon.
November 19, 2003
John G. Cramer5STAR
ZDC
Barrel EMC
Endcap EMC
Magnet B= 0.5 T
ZDC
FTPCs
Vertex Position Scintillators (TOF)
Trigger Barrel(TOF)
Time Projection Chamber
Silicon Vertex Tracker
RICH
2 m
4 m
24 sectors x 5692 r pads x 350 t bins= 47,812,800 pixels
y1
The STAR Detector
November 19, 2003
John G. Cramer6STAR
Run: 1186017, Event: 32, central
colors ~ momentum: low - - - high
Central Au +Au Collision at sNN = 130 GeVCentral Au +Au Collision at sNN = 130 GeV
November 19, 2003
John G. Cramer7STAR
Part 2Part 2
RHIC Physics ExpectationsRHIC Physics Expectations
November 19, 2003
John G. Cramer8STAR
A Metaphor for RHIC Physics Understanding
A Metaphor for RHIC Physics Understanding
November 19, 2003
John G. Cramer9STAR
Surprises from RHICSurprises from RHIC
1. The “Hydro Paradox”: Relativistic hydrodynamic calculations work surprisingly well, while cascade string-breaking models have problems.
2. Strong absorption of high pT pions: There is evidence for strong “quenching” of high momentum pions.
3. The “HBT Puzzle”: The ratio of the source radii Rout/Rside is ~1, while the closest model predicts 1.2, and most models predict 4 or more. RLong is smaller than is consistent with boost invariance. In essence, all models on the market have been falsified by HBT.
In the remainder of this talk we will focus on theRHIC HBT Puzzle.
November 19, 2003
John G. Cramer10STAR
In Search of the Quark-Gluon Plasma (QGP)
In Search of the Quark-Gluon Plasma (QGP)
A pion gas should have few degrees of freedom.
A quark-gluon plasma should have many degrees of freedom and high entropy.
Entropy should be roughly conserved during the fireball’s evolution.
Hence, look in phase space for evidence of:
Large source size, Long emission lifetime, Extended expansion,
Large net entropy …
November 19, 2003
John G. Cramer11STAR
The Hanbury-BrownTwiss Effect and
Bose-Einstein Interferometry
The Hanbury-BrownTwiss Effect and
Bose-Einstein Interferometry
Part 3Part 3
November 19, 2003
John G. Cramer12STAR
A Happy Coincidence of ScalesA Happy Coincidence of Scales
For the Hanbury-Brown Twiss Effect to work, we must have ab/L 1, where
a = size of object,b = separation of detectors = wavelength of correlated
particlesL = object-detector distanceStars:
a = 2 Rsun = 1.5 x 109 m L = 10 light years = 1017 m
= 500 nm = 5 x 10-7 m
Therefore, need b = L/a = 33 m (OK!)
Pions:a = 10 fm
L = 1 m = 4.4 fm
Therefore, need b = L/a = 44 cm (OK!)
So the same technique can be used on stars and on RHIC collision fireballs!
November 19, 2003
John G. Cramer13STAR
The Hanbury-Brown-Twiss EffectThe Hanbury-Brown-Twiss Effect
y
X
1
2
Source
For non-interacting identical bosons:
S(x,p)=S(x)S(p)
Coherent interference between incoherent sources!
The “bump” results fromthe Bose-Einstein statistics ofidentical pions (J=0).
Width of the bump in theith momentum direction isproportional to 1/Ri.
November 19, 2003
John G. Cramer14STAR
Bertsch-Pratt Momentum CoordinatesBertsch-Pratt Momentum Coordinates
beam direction
p1 p2
Q T
Q
Q L
beam direction
p2p1
Q T
Q S
Q O
)qqR2qRqRqRexp(1 longout2ol
2long
2long
2side
2side
2out
2out
)q,q,q(C longsideout
)T2
PT1
P(2
1T
K
(long) (out, side)x
November 19, 2003
John G. Cramer15STAR
A Bose-Einstein Correlation “Bump”A Bose-Einstein Correlation “Bump”
This 3D histogram is STARdata that has been corrected forCoulomb repulsion ofidentical pairs andis a projection slice nearqlong=0 .
The central “bump” resultsfrom Bose-Einstein statisticsof identical pions (J=0).
November 19, 2003
John G. Cramer16STAR
+ - + - 0 p p ++ +
0 -
+
-
Sergei's HBT matrix 0
Y1 p
Y1 ? p
Y2
“traditional”HBT axis
STAR HBT Matrix (circa Nov. 2000)
STAR HBT Matrix (circa Nov. 2000)
Year 1
From the beginning - studycorrelations of nonidentical particlesand resonance production
Goal: reconstruct complete picture with full systematics
Year 1 ??
Year 2 AnalysisIn progress
November 19, 2003
John G. Cramer17STAR
STAR HBT Matrix (circa 2003)STAR HBT Matrix (circa 2003)
+ - + - 0 p p ++ +
0 -
+
-
Sergei's HBT matrix 0
Y1 p
Y1 ? p
Y2
“traditional”HBT axis
Analysisin progress
published
3 Correlations (accepted PRL)asHBTPhase space densityCorrelations with CascadesdAu, ppCascades
submittedNot shown:
November 19, 2003
John G. Cramer19STAR
Pre-RHIC HBT PredictionsPre-RHIC HBT Predictions
“Naïve” picture (no space-momentum correlations):
Rout2 = Rside
2+(pair)2
One step further: Hydro calculation of Rischke &
Gyulassy expects Rout/Rside ~ 2->4 @ kt = 350 MeV.
Looking for a “soft spot” Small Rout/Rside only for
TQGP=Tf (unphysical)).
Rout
Rside
November 19, 2003
John G. Cramer20STAR
• p-space observables well-understood within hydrodynamic framework
→ hope of understanding early stage
• x-space observables not well-reproduced• correct dynamical signatures with
incorrect dynamic evolution?
Heinz & Kolb, hep-ph/0204061
The RHIC HBT PuzzleThe RHIC HBT Puzzle
November 19, 2003
John G. Cramer21STAR time
dN/dt
PCM & clust. hadronization
NFD
NFD & hadronic TM
PCM & hadronic TM
CYM & LGT
string & hadronic TM
• p-space observables well-understood within hydrodynamic framework
→ hope of understanding early stage
• x-space observables not well-reproduced• correct dynamical signatures with
incorrect dynamic evolution?
• Over-large timescales are modeled?• emission/freezeout duration (RO/RS)• evolution duration (RL)
Heinz & Kolb, hep-ph/0204061
The RHIC HBT PuzzleThe RHIC HBT Puzzle
November 19, 2003
John G. Cramer22STAR
RO
(fm
)R
L (f
m)
λ
RS
(fm)
RO / R
S
<kT> GeV/c
centrality
6
6
6
4
4
4
1
1.2
0.8
0.2
0.4
0.6
0.2 0.20.3 0.30.4 0.40.5 0.5
STAR PRELIMINARY
• HBT radii increase with increasing centrality
• HBT radii decrease with kT (flow)
• RO / RS ~ 1 (short emission time) problem persists
HBT at 200 GeVHBT at 200 GeV
November 19, 2003
John G. Cramer23STAR
• HBT radii increase with increasing centrality
• HBT radii decrease with kT (flow)
• RO / RS ~ 1 (short emission time) problem persists
Longitudinal radius
• Modified Sinyukov fit
M. Herrmann and G.F. Bertsch, Phys. Rev. C51 (1995) 328
<tfo>central ≈ 9 fm/c
<tfo>peripheral ≈ 7 fm/c
Tfo = 90MeV/c (spectra)
TmK
TmKmT
tRT
T
TfoL /
/
1
2
HBT at 200 GeVHBT at 200 GeV
RO
(fm
)R
L (f
m)
λ
RS
(fm)
RO / R
S
<kT> GeV/c
centrality
6
6
6
4
4
4
1
1.2
0.8
0.2
0.4
0.6
0.2 0.20.3 0.30.4 0.40.5 0.5
STAR PRELIMINARY
November 19, 2003
John G. Cramer24STAR
HBT Source Radius Excitation Function
HBT Source Radius Excitation Function
Source radii from HBT interferometry do not show a significant increase between CERN energies and RHIC energies.
However, we would still liketo fill the gapwith future RHIC runs.
November 19, 2003
John G. Cramer25STAR
Conclusions from HBT AnalysisConclusions from HBT Analysis
1. The pion-emission source size is smaller than expected, with little growth from a factor of 10 increase in collision energy from the CERN SPS.
2. The time from initial collision to emission is also about the same as observed at the SPS, about 9 fm/c.
3. The emission duration is also very short, at most 1-2 fm/c.
4. These results imply an explosive system with a very hard equation of state.
We were expecting to bring the nuclear liquid to a gentle boil.
Instead, it is exploding in our face!
November 19, 2003
John G. Cramer26STAR
Part 5Part 5
Pion Phase Space Density
and Entropy
Pion Phase Space Density
and Entropy
November 19, 2003
John G. Cramer27STAR
Phase Space Density: Definition & Expectations
Phase Space Density: Definition & Expectations
Phase Space Density - The phase space density f(p,x) plays a fundamental role in quantum statistical mechanics. The local phase space density is the number of pions occupying the phase space cell at (p,x) with 6-dimensional volume p3x3 = h3.
The source-averaged phase space density is f(p)∫[f(p,x)]2 d3x / ∫f(p,x) d3x, i.e., the local phase space density averaged over thef-weighted source volume. Because of Liouville’s Theorem, for free-streaming particles f(p) is a conserved Lorentz scalar.
At RHIC, with about the same HBT source size as at the CERN SPS but with more emitted pions, we expect an increase in the pion phase space density over that observed at the SPS.
November 19, 2003
John G. Cramer28STAR
hep-ph/0212302
Entropy: Calculation & ExpectationsEntropy: Calculation & ExpectationsEntropy – The pion entropy per particle S/N and the total pion entropy at midrapidity dS/dy can be calculated from f(p). The entropy S of a colliding heavy ion system should be produced mainly during the parton phase and should grow only slowly as the system expands and cools.
Entropy is conserved during hydrodynamic expansion and free-streaming. Thus, the entropy of the system after freeze-out should be close to the initial entropy and should provide a critical constraint on the early-stage processes of the system.
nucl-th/0104023 A quark-gluon plasma has a large number of degrees of freedom. It should generate a relatively large entropy density, up to 12 to 16 times larger than that of a hadronic gas.
At RHIC, if a QGP phase grows with centrality we would expect the entropy to grow strongly with increasing centrality and participant number.
Can Entropy provide the QGP “Smoking Gun”??
November 19, 2003
John G. Cramer29STAR
Pion Phase Space Density at Pion Phase Space Density at MidrapidityMidrapidity
Pion Phase Space Density at Pion Phase Space Density at MidrapidityMidrapidity
The source-averaged phase space density f(mT) is the dimensionless number of pions per 6-dimensional phase space cell h3, as averaged over the source. At midrapidity f(mT) is given by the expression:
λ
1
RRR
πλ
ymmπ2
N
E
1)m(
LOS
3
TT
2
πT
)(
c
dd
df
Momentum Spectrum HBT “momentumvolume” Vp
PionPurity
Correction
Jacobianto make ita Lorentz
scalar
Average phasespace density
November 19, 2003
John G. Cramer30STAR
RHIC Collisions as Functions of Centrality
RHIC Collisions as Functions of Centrality
50-80% 30-50% 20-30% 10-20% 5-10% 0-5%
At RHIC we can classifycollision events by impact parameter, based on charged particle production.
Participants
Binary Collisions
Frequency of Charged Particlesproduced in RHIC Au+Au Collisions
of Total
November 19, 2003
John G. Cramer31STAR
0.05 0.1 0.15 0.2 0.25 0.3
150
200
300
500
700
1000
1500
2000
016
Vp
VeG
3 Corrected HBT Momentum Volume
Vp /½
Corrected HBT Momentum Volume Vp /½
LOS
3
p RRR
πλλV
)( c
STAR Preliminary
Central
Peripheral
mT - m (GeV)
0-5%
5-10%
10-20%
20-30%
30-40%
40-50%
50-80%
Centrality
Fits assuming:
Vp ½=A0 mT3
(Sinyukov)
November 19, 2003
John G. Cramer32STAR
0.1 0.2 0.3 0.4 0.5 0.6mT m
5
10
50
100
500
1000
d2 N2m Tmd
Tyd
Global Fit to Pion Momentum Spectrum
Global Fit to Pion Momentum Spectrum
We make a global fit of the uncorrected pion spectrum vs. centrality by:
(1) Assuming that the spectrumhas the form of an effective-TBose-Einstein distribution:
d2N/mTdmTdy=A/[Exp(E/T) –1]
and
(2) Assuming that A and T have aquadratic dependence on thenumber of participants Np:
A(p) = A0+A1Np+A2Np2
T(p) = T0+T1Np+T2Np2
Value ErrorA0 31.1292 14.5507A1 21.9724 0.749688A2 -0.019353 0.003116T0 0.199336 0.002373T1 -9.23515E-06 2.4E-05T2 2.10545E-07 6.99E-08
STAR Preliminary
November 19, 2003
John G. Cramer33STAR
0.1 0.2 0.3 0.4mTm
0.1
0.2
0.3
0.4
f
Interpolated Pion Phase Space Density f at S½ = 130 GeV
Interpolated Pion Phase Space Density f at S½ = 130 GeV
Central
Peripheral
NA49
STAR Preliminary
Note failure of “universal” PSDbetween CERN and RHIC.}
HBT points with interpolated spectra
November 19, 2003
John G. Cramer34STAR
0.05 0.1 0.15 0.2 0.25mTmGeV
0.05
0.1
0.2
0.5
fp
Fits to Interpolated Pion Phase Space Density
Fits to Interpolated Pion Phase Space Density
Central
Peripheral
STAR Preliminary
Warning: PSD in the region measured contributes only about 60% to the average entropy per particle.
HBT points using interpolated spectra fittedwith Blue-Shifted Bose Einstein function
November 19, 2003
John G. Cramer35STAR
fdxdp
fffffLogfdxdp
xpfdxdp
xpdSdxdp
NS
33
49653
612
2133
33
633 )([
),(
),(
Converting Phase Space Density to Entropy per Particle (1)
Converting Phase Space Density to Entropy per Particle (1)
...)(
)1()1()();,(4
9653
612
21
6
fffffLogf
fLogffLogfdSpxff
Starting from quantum statistical mechanics, we define:
To perform the space integrals, we assume that f(x,p) = f(p) g(x),where g(x) = 23 Exp[x2/2Rx
2y2/2Ry2z2/2Rz
2], i.e., that the source hasa Gaussian shape based on HBT analysis of the system. Further, we make theSinyukov-inspired assumption that the three radii have a momentum dependenceproportional to mT
. Then the space integrals can be performed analytically.This gives the numerator and denominator integrands of the above expressionfactors of RxRyRz = Reff
3mT(For reference, ~½)
An estimate of the average pion entropy per particle S/N can be obtainedfrom a 6-dimensional space-momentum integral over the local phase spacedensity f(x,p):
O(f)
O(f2)
O(f3) O(f4)
f
dS6(Series)/dS6
+0.2%
0.2%
0.1%
0.1%
November 19, 2003
John G. Cramer36STAR
Converting Phase Space Density to Entropy per Particle (2)
Converting Phase Space Density to Entropy per Particle (2)
0
31
0
4
22453
3942
2)8(5
2131
33
4
22453
3942
2)8(5
2133
33
633
][
][
),(
),(
fmpdp
fffffLogfmpdp
fmdp
fffffLogfmdp
xpfdxdp
xpdSdxdp
NS
TTT
LogTTT
T
LogT
The entropy per particle S/N then reduces to a momentum integralof the form:
We obtain from the momentum dependence of Vp-1/2 and performthe momentum integrals numerically using momentum-dependent fits to for fits to Vp-1/2 and the spectra.
(6-D)
(3-D)
(1-D)
November 19, 2003
John G. Cramer37STAR
50 100 150 200 250 300 350Npparticipants
3.6
3.8
4
4.2
4.4
4.6
S N
Entropy per Pion from Two Fit MethodsEntropy per Pion from Two Fit Methods
Central
PeripheralSTAR
Preliminary
Green = BSBE2: ~ T
Red = BSBE1: Const
Blue = BSBE3: Odd 7th order Polynomial in T
Black = Combined fits to spectrum and Vp/1/2
November 19, 2003
John G. Cramer38STAR
0 0.5 1 1.5 2 2.5 3Tm
2
4
6
8
10
SN
= 0
= m
Thermal Bose-Einstein Entropy per Particle
Thermal Bose-Einstein Entropy per Particle
1]/)[(
1 where
)]()1()1[(S/N
0
0
TmExpf
fdppm
fLnffLnfdppm
TBE
BETT
BEBEBEBETTT
0. 0.3 0.6 0.90.2 7.37481 5.86225 4.30277 2.431810.4 5.13504 4.33169 3.45065 2.251660.6 4.46843 3.89106 3.23476 2.288370.8 4.16727 3.70431 3.16747 2.369671. 4.00256 3.61107 3.15191 2.458511.2 3.90175 3.56032 3.15728 2.543751.4 3.83522 3.53137 3.17146 2.621951.6 3.78887 3.51456 3.18916 2.692441.8 3.75521 3.50489 3.20786 2.755532. 3.72997 3.49958 3.22638 2.8119
The thermal estimate of the entropy per particle can beobtained by integrating a Bose-Einstein distribution over3D momentum:
/mT/m
Note that the thermal-model entropy per particle usually decreases with increasing temperature T and chemical potential .
November 19, 2003
John G. Cramer39STAR
50 100 150 200 250 300 350Npparticipants3.4
3.6
3.8
4
4.2
4.4
4.6
S N
T90 MeV
T120 MeV
T200 MeV
Landau Limit: m0
BPB
Entropy per Particle S/N with Thermal EstimatesEntropy per Particle S/N with Thermal Estimates
Central
Peripheral STAR Preliminary
Dashed line indicates systematicerror in extracting Vp from HBT.
Dot-dash line shows S/N from BDBE2 fits to f
Solid line and points show S/Nfrom spectrum and Vp/1/2 fits.
For T=110 MeV, S/N impliesa pion chemical potential of=44.4 MeV.
November 19, 2003
John G. Cramer40STAR
50 100 150 200 250 300 350Np
500
1000
1500
2000
2500
Sdyd
Snuc
Total Pion Entropy dS/dyTotal Pion Entropy dS/dy
STAR Preliminary
Dashed line indicates systematicerror in extracting Vp from HBT.
Dot-dash line indicates dS/dy fromBSBEx fits to interpolated <f>.
Solid line is a linear fit through (0,0)with slope = 6.58 entropy unitsper participant
Entropy content ofnucleons + antinucleons
P&P
P&P
Why is dS/dylinear with Np??
November 19, 2003
John G. Cramer41STAR
0 50 100 150 200 250 300 350Npparticipants
20
25
30
35
40
45
Sd ydN p23
Initial collision overlap area is roughlyproportional to Np
2/3
Initial collision entropy is roughlyproportional to freeze-out dS/dy.
Therefore, (dS/dy)/Np2/3
should be proportionalto initial entropydensity, a QGPsignal.
Initial Entropy Density: ~(dS/dy)/Overlap Area
Initial Entropy Density: ~(dS/dy)/Overlap Area
Data indicates that the initialentropy density does grow withcentrality, but not very rapidly.
Solid envelope =Systematic errors in Np
Our QGP “smoking gun” seems to beinhaling the smoke!
STAR Preliminary
November 19, 2003
John G. Cramer42STAR
Conclusions from PSD/Entropy Analysis
Conclusions from PSD/Entropy Analysis
1. The source-averaged pion phase space density f is very high, in the low momentum region roughly 2 that observed at the CERN SPS for Pb+Pb at Snn=17 GeV.
2. The pion entropy per particle S/N is very low, implying a significant pion chemical potential (~44 MeV) at freeze out.
3. The total pion entropy at midrapidity dS/dy grows linearly with initial participant number Np, with a slope of ~6.6 entropy units per participant. (Why?? Is Nature telling us something?)
4. For central collisions at midrapidity, the entropy content of all pions is ~5 greater than that of all nucleons+antinucleons.
5. The initial entropy density increases with centrality, but forms a convex curve that shows no indication of the dramatic increase in entropy density expected with the onset of a quark-gluon plasma.
November 19, 2003
John G. Cramer43STAR
The useful theoretical models that has served us so well at the AGSand SPS for heavy ion studies have now been overloaded with a largevolume of puzzlingnew data from HBTanalysis at RHIC.
Things are a bitup in the air.
We need moretheoretical helpto meet the challengeof understandingwhat is going on inthe RHIC regime.
In any case, thisis a very excitingtime for the STARexperimentalistsworking at RHIC!
Overall ConclusionsOverall Conclusions