1 jim thomas - lbl energy loss and flow in heavy ion collisions at rhic preparing to open a new...
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Energy Loss and Flow in Heavy Ion Collisions at RHICPreparing to open a new chapter at RHIC with Charm + Beauty
Jim ThomasLawrence Berkeley National Laboratory
Berkeley, CA
Argonne National Laboratory
March 5th, 2008
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Who is RHIC and What Does He Do?
RHIC
• Two independent rings
• 3.83 km in circumference
• Accelerates everything, from p to Au
s L p-p 500 1032
Au-Au 200 1027
(GeV and cm-2 s-1)
• Polarized protons
• Two Large and two small detectors were built
h
BRAHMS
PHOBOS
PHENIX
STARSTAR
And for a little while longer, it is the highest energy heavy ion collider in the world
Long Island
Long Island
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STAR is a Suite of Detectors
Barrel EM Calorimeter
FTPCs
Time Projection Chamber
Silicon TrackerSVT & SSD
Endcap Calorimeter
Magnet
Coils
TPC Endcap & MWPC
Central Trigger Barrel & TOF
Beam Beam Counters
4.2 meters
Not Shown: pVPDs, ZDCs, and FPDs
A TPC lies at the heart of STAR
PMD
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RHIC Physics is Relativistic Nuclear Physics
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Unlike Particle Physics, the initial state is important
• The nucleus is not a point like particle, it is macroscopic
• Only a few of the nucleons participate in the collision as determined by the impact parameter
• The initial state is Lorentz contracted
• There is multiple scattering in the initial state before the hard collisions take place
– Cronin effect
• Cross-sections become coherent. – The uncertainty principle allows wee
partons to interact with the front and back of the nucleus
– The interaction rate for wee partons saturates ( ρσ = 1 )
• The intial state is even time dilated– A color glass condensate
• proton • neutron • delta • pion string
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Au on Au Event at CM Energy ~ 130 GeV*A
Two-track separation 2.5 cm
Momentum Resolution < 2%
Space point resolution ~ 500 m
Rapidity coverage –1.8 < < 1.8
A Central Event
Typically 1000 to 2000 tracks per event into the TPC
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Particle ID using Topology & Combinatorics
Secondary vertex: Ks + p +
+ + K e++e-
Ks + + - K + + K -
p + - + + -
from K+ K- pairs
K+ K- pairs
m inv
m inv
same event dist.mixed event dist.
background subtracted
dn/dm
dn/dm
“kinks”
K +
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Strange Baryons and Mesons: Au+Au @ 200 GeV
, , and yields .vs. pTPhys. Rev. Lett. 98 (2007) 060301
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Transverse Radial Expansion: Isotropic Flow
The transverse radial expansion of the source (flow) adds kinetic energy to the particle distribution. So the classical expression for ETot
suggests a linear relationship
-
K -
p
Au+Au at 200 GeV
Typical STAR Data
2KFOObs massTT
Slopes decrease with mass. <pT> and the effective temperature increase with mass.
T ≈ 575 MeV
T ≈ 310 MeV
T ≈ 215 MeV
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Kinetic Freezeout from Transverse Radial Flow
<ßr> (RHIC) = 0.55 ± 0.1 cTKFO (RHIC) = 100 ± 10 MeV
Explosive Transverse Expansion at RHIC High Pressure
Tth
[GeV
]< r
> [
c]
STA
RPH
EN
IX
Thermal freeze-out determinations are done with the blast-wave model to find <pT>
STAR Preliminary
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Dependent Distributions – Flow
• The overlap region in peripheral collisions is not symmetric in coordinate space
• Almond shaped overlap region
– Larger pressure gradient in the x-z plane drives flow in that direction
– Easier for high pT particles to emerge in the direction of x-z plane
• Spatial anisotropy Momentum anisotropy
• Perform a Fourier decomposition of the momentum-space particle distribution in the plane
– For example, v2 is the 2nd harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane
))2cos(2)cos(21(2
121
2
3
3
vvdydpp
Nd
pd
dNE
TT
directed elliptic isotropic
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Interpreting Flow – order by order
n=1: Directed Flow has a period of 2 (only one maximum)
– v1 measures whether the flow goes to the left or right – whether the momentum goes with or against a billiard ball like bounce off the collision zone
n=2: Elliptic flow has a period of (two maximums)
– v2 represents the elliptical shape of the momentum distribution
))4cos(2)2cos(2)cos(21(2
1421
2
3
3
vvvdydpp
Nd
pd
dNE
TT
directed elliptic isotropic higher order terms
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v2 vs. pT and Particle Mass
• The mass dependence is reproduced by hydrodynamic models
– Hydro assumes local thermal equilibrium
– At early times
– Followed by hydrodynamic expansion
D. Teaney et al., QM01 Proc.P. Huovinen et al., nucl-th/0104020
PRL 86, 402 (2001) & nucl-ex/0107003
Anisotropic transverse flow is large at RHIC
• v2 is large– 6% in peripheral
collisions (for pions average over all pT )
• Flow is developed very rapidly
– Data suggests very early times ~ fm/c
• Hydro calculations are in good agreement with the data
– Hydro assumes local thermal equilibrium
– Followed by hydrodynamic expansion
– The mass dependence is reproduced by the models
M. Oldenberg, nucl-ex/0412001.P. Huovinen et al., QM04
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Elliptic Flow: in an ultra-cold Fermi-Gas
Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions
– Elliptic flow is a general feature of strongly interacting systems!
A Simulation of Elliptic Flow
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v2 at high pT shows meson / baryon differences
Asym. pQCD Jet Quenching
Bulk PQCD Hydro
qn Coalescence
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The Recombination Model ( Fries et al. PRL 90 (2003) 202303 )
The flow pattern in v2(pT) for hadrons
is predicted to be simple if flow is developed at the quark level
pT → pT /n
v2 → v2 / n ,
n = (2, 3) for (meson, baryon)
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A Macroscopic many body system: It Flows
Spatial anisotropy Momentum anisotropy
– For example, v2 is the 2nd harmonic Fourier coefficient of the distribution of particles with respect to the reaction plane
))2cos(2)cos(21(2
121
2
3
3
vvdydpp
Nd
pd
dNE
TT
directed elliptic isotropic
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Elliptic flow scales with the number of quarks
Implication: (uds) quarks, not hadrons, are the relevant degrees of freedom at early times in the collision history
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v4 Exhibits Constituent Quark Scaling, too
S.L. Huang QM08
))4cos(2)2cos(2)cos(21(2
1421
2
3
3
vvvdydpp
Nd
pd
dNE
TT
directed elliptic isotropic higher order terms
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Constituent Quark Scaling?
• Hadrons are created by the recombination of quarks and this appears be the dominant mechanism for hadron formation at intermediate pT
• Baryons and Mesons are produced with equal abundance at intermediate pT
• The collective flow pattern of the hadrons appears to reflect the collective flow of the constituent quarks.
• up, down, and strange quarks do it … despite the difference in their masses
Partonic Collectivity
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Hints of Elliptic Flow with Charm
• D e +X
Single electron spectra from PHENIX show hints of elliptic flow
Is it charm or beauty?
• Very profound, if it is true, because the Charm quark is rare and heavy compared to u, d, or s quarks
• Indicator for rapid thermalization
• Their will be RHIC upgrades to cut out large photonic backgrounds:
e+e-
and reduce other large statistical and systematic uncertainties
A Look to the Future: better if we can do direct topological identification of Charm
Shingo Sakai, QM 2006 PRL 98, 172301 (2007)
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Lets look at some collision systems in detail …
Final stateInitial state
Au + Au
d + Au
p + p
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Partonic Energy Loss and Jet Quenching
Energy loss suppression of leading hadron yieldThe jet can’t get out!
ddpdT
ddpNdpR
TNN
AA
TAA
TAA /
/)(
2
2
Binary collision scaling p+p reference
d+Au
Au+Au
No quenching
Quenching!
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Heavy Flavor Energy Loss … RAA for Charm
• Heavy Flavor energy loss is an unsolved problem
– Gluon density ~ 1000 expected from light quark data
– Better agreement with the addition of inelastic E loss
– Good agreement only if they ignore Beauty …
• Beauty dominates single electron spectra above 5 GeV
• In the future, RHIC upgrades will separate the Charm and Beauty contributions
Theory from Wicks et al. nucl-th/0512076v2
Where is the contribution from Beauty?
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Jet Physics … it is easier to find one in e+e-
Jet event in eecollision STAR Au+Au collision
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Angular Distribution: Peripheral Au+Au data vs. pp+flow
C2(Au Au)C2(p p) A *(1 2v22 cos(2))
Ansatz: A high pT triggered Au+Au event is a superposition of a high pT triggered p+p event plus anisotropic transverse flow
v2 from reaction plane analysis
“A” is fit in non-jet region (0.75<||<2.24)
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Angular Distribution: Central Au+Au data vs. pp+flow
C2(Au Au)C2(p p) A *(1 2v22 cos(2))
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Lessons learned – Dark Matter … its opaque
• The backward going jet is missing in central Au-Au collisions when compared to p-p data + flow
• The backward going jet is not suppressed in d-Au collisions
• These data suggest opaque nuclear matter and surface emission of jets
Surface emission
Suppression of back-to-back correlations in central Au+Au collisions
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Where does the Eloss go?
PHENIX p+p Au+Au
Lost energy of away-side jet is redistributed to rather large angles!
Trigger jetAway-side jet
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Mach Cone: Theory vs Experiment
• Hint of a Mach Cone?
STAR preliminary
0-12% 200 GeV Au+Au
away
near
Medium
mach cone
Mediumaway
neardeflected jets
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The Ridge (after v2 subtraction)
d+Au, 40-100% Au+Au, 0-5%
d+Au Au+Au
3 < pT(trig) < 6 GeV2 < pT(assoc) < pT(trig)
Jet
Ridge
STAR Preliminary
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The Ridge May be due to Very Strong Fields
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Strong Fields Run Away Thermalisation
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AdS/CFT correspondence (from H. Liu)
N = 4 Super-Yang-Mills theory with SU(N)
Maldacena (1997) Gubser, Klebanov, Polyakov, Witten
A string theory in 5-dimensional anti-de Sitter spacetime
NN = 4 Super-Yang-Mills (SYM):
anti-de Sitter (AdS) spacetime: homogeneous spacetime with a negative cosmological constant.
maximally supersymmetric gauge theory
scale invariant
A special relative of QCD
The value turns out to be universal for all strongly coupled
QGPs with a gravity description. It is a universal lower bound.
1
4s
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PHENIX PRL 98, 172301 (2007)
• RAA of heavy-flavor electrons in 0%–10% central collisions compared with 0 data and model calculations
• V2 of heavy-flavor electrons in minimum bias collisions compared with 0 data and the same models.
• Conclusion is that heavy flavor flow corresponds to /s at the conjectured QM lower bound
0 0
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Old Chinese Proverb
Beware of theorists waiting for data– Confusion
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Nuclear Fluid Dynamics ... with friction
• The energy momentum tensor for a viscous fluid
• Conservation laws: and where
• The elements of the shear tensor, , describe the viscosity of the fluid and can be thought of as velocity dependent ‘friction’
• Simplest case: scaling hydrodynamics– assume local thermal equilibrium
– assume longitudinal boost-invariance
– cylindrically symmetric transverse expansion
– no pressure between rapidity slices
– conserved charge in each slice
• Initially expansion is along the Z axis, so viscosity resists it– Conservation of T means that energy and momentum appear in the
transverse plane … viscosity drives radial flow
• Viscosity is velocity dependent friction so it dampens v2 – Viscosity (/z ) must be near zero for large elliptic flow to be observed
pguupT )(
0 T 0
j uj ii
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3D Hydro … new insights
• Romatschke2 performed relativistic viscous hydrodynamics calculations including the new 2nd order terms beyond Landau’s prescription
• Data on the integrated elliptic flow coefficient v2 are consistent with a ratio of viscosity over entropy density up to /s 0.16
• But data on minimum bias v2 seem to favor a much smaller viscosity over entropy ratio, below the bound from the anti–de Sitter conformal field theory conjecture
PRL 99, 172301 (2007)
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Which theory is correct? Only the data can tell.
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Caption: The viscosity to entropy ratio versus a reduced temperature.
Lacey et al. PRL 98:092301(07) hep-lat/0406009; hep-ph/0604138 Csernai et al, PRL97, 152303(06)
The universal tendency of flow to be dissipated due to the fluid’s internal friction results from a quantity known as the shear viscosity. All fluids have non-zero viscosity. The larger the viscosity, the more rapidly small disturbances are damped away.
Quantum limit: /sAdS/CFT ~ 1/4
pQCD limit: ~ 1
At RHIC: ideal (/s = 0) hydrodynamic model calculations fit to data
Perfect Fluid at RHIC?!
H2O N2
He
hadronicpartonic
Viscosity and the Perfect Fluid
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STAR Upgrades to keep the discoveries rolling …
• Forward Meson Spectrometer– Gluon density distributions, saturation effects, and transverse spin
• DAQ Upgrade– order of magnitude increase in rate
– extra bandwidth opens the door to ‘small’ physics
• Full Barrel MRPC TOF– extended particle identification at intermediate pT
• Forward GEM Tracker
– end cap tracker for W sign determination
• Heavy Flavor Tracker
– high precision Heavy Flavor Tracker near the vertex
– opens the door to direct topological ID of Charm & Beauty
• Muon Telescope
• Forward Reaction Plane Detector
• A Crystal Calorimeter for low E photons - HBT
In t
he
qu
eue
En
gin
es r
un
nin
gW
arm
ing
Up
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Opening New Frontiers at RHIC
• (Hint … Segue to new hardware)
• Direct topological reconstruction of open charm (explain why)
• The prevailing hypothesis is that we have partonic collectivity at RHIC
• Is there collective behavior in the charm sector, too?– If so, it would be extraordinary because charm is so heavy
• Beauty is accessible but difficult
• What is the challenge … with the hardware
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The Properties of the Open Charm Hadrons
Particle Decay Channel c (m) Mass (GeV/c2)
D0 K + (3.8%) 123 1.8645
D+ K + + (9.5%) 312 1.8694
K+ K + (5.2%)+ + - (1.2%)
150 1.9683
p K + (5.0%) 59.9 2.2865
+
SD
+
C
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44Jim Thomas - LBL
Direct Topological Identification of Open Charm
The STAR Inner Tracking Upgrades will identify the daughters in the decay and do a direct topological
reconstruction of the open charm hadrons.
No ambiguities between charm and beauty.
Goal: Distinguish secondary from primary vertices by putting a high precision detector near the IP to extend the TPC tracks to small radius
50-150 m
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45Jim Thomas - LBL
The Heavy Flavor Tracker = PXL + IST + SSD
• A new detector
– 30 m silicon pixelsto yield 10 m space point resolution
• Direct Topological reconstruction of Charm
– Detect charm decays with small c, including D0 K
• New physics
– Charm collectivity and flow to test thermalization at RHIC
– Charm Energy Loss to test pQCD in a hot and dense medium at RHIC
• The SSD … is part of the plan for tracking TPC HFT
• The technical design is evolving but converging rapidly to final form.
PXL: 2 layers of Si at small radii
IST: 1 layer of Si at intermediate radius
SSD: an existing detector at 23 cm radius
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46Jim Thomas - LBL
Active Pixel Sensors from IPHC Strasbourg
• 30 m pixels
• 640 x 640 pixels per chip
• 10 chips per ladder
• 100 – 200 sec integration time
• 164 M pixels, total
• 300 kRad hardness (~1 yr under certain conditions)
Properties:
• Signal created in low-doped epitaxial layer (typically ~10-15 μm)
• Sensor and signal processing integrated in the same silicon wafer
• Standard commercial CMOS technology
Inner layer
Outer layer
20 cm
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47Jim Thomas - LBL
Getting a Boost from the TPC
• The TPC provides good but not excellent resolution at the vertex and at other intermediate radii
~ 1 mm
• The TPC provides an excellent angular constraint on the path of a predicted track segment
– This is very powerful.
– It gives a parallel beam with the addition of MCS from the IFC
• The best thing we can do is to put a pin-hole in front of the parallel beam track from the TPC
– This is the goal for the Si trackers: SSD, IST, and PXL
• The SSD and IST do not need extreme resolution. Instead, the goal is to maintain the parallel beam and not let it spread out
– MCS limited
– The PXL does the rest of the work
TPC
MCS Cone
VTX
The Gift of the TPC
OFC
IFC
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48Jim Thomas - LBL
Optimized HFT Configuration
The HFT configuration described in the Addendum
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49Jim Thomas - LBL
Calculating the Performance of the Detector
• Billoir invented a matrix method for evaluating the performance of a detector system including MCS and dE/dx
– NIM 225 (1984) 352.
• The ‘Information Matrices’ used by Billoir are the inverse of the more commonly used covariance matrices
– thus, ’s are propagated through the system
• ITTF tracking software uses a similar method (aka a Kalman Filter)– The ‘hand calculations’ go outside-in
– STAR Software goes outside-in and then inside-out, and averages the results, plus follows trees of candidate tracks. It is ‘smart’ software.
MCS D M MCS D M MCS
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50Jim Thomas - LBL
Hand Calculations .vs. GEANT & ITTF
- - - - PXL stand alone configurationPaper Proposal configuration
GEANT & ITTF Updated configuration … no significant changes in pointing at VTX
TPC alone
Full System
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51Jim Thomas - LBL
MinBias Pileup – The PXL Layers Integrate over Time
A full study of the integrated hit loading on the PIXEL detector includes the associated pileup due to minBias Au-Au collisions and the integration time of the detector.
2022
00
1 1( , , , )
2 ( )2
za
a
dN dN dMinBias z r ZDC e dz
dA d r d z z
PIXEL-1 Inner Layer
PIXEL-2 Outer Layer
Radius 2.5 cm 8.0 cm Central collision hit density 17.8 cm-2 1.7 cm-2
Integrated MinBias collisions (pileup) 23.5 cm-2 4.2 cm-2
UPC electrons 19.9 cm-2 0.1 cm-2
Totals 61.2 cm-2 6.0 cm-2
Pileup is the bigger challenge
Integrate over time and interaction diamond
200 sec
2022
02 20
2720 1 1( , , , )
2 2 ( )
za
a
dNMinBias z r e dz
dA r r z z
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52Jim Thomas - LBL
Efficiency Calculations in a high hit density environment
The probability of associating the right hit with the right track on the first pass through the reconstruction code is:
P(good association) = 1 / (1+S)
where S = 2 x y
P(bad association) = (1 – Efficiency) = S / ( 1 + S )
and when S is small
P(bad association) 2 x y
x is the convolution of the detector resolution and the projected track error in the ‘x’ direction, and is the density of hits.
The largest errors dominates the sum
x = ( 2xp + 2
xd )
y = ( 2yp + 2
yd )
Asymmetric pointing resolutions are very inefficient … try to avoid it
An areaA density, depends on and pileup
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53Jim Thomas - LBL
The performance of the TPC pointing at the PXL
• The performance of the TPC acting alone to point at the PXL detector depends on the integration time of the PXL chips
P(good association) = 1 / (1+S) where S = 2 x y
Integration Time (sec)
Sin
gle
Lay
er E
ffic
ien
cy
The purpose of intermediate tracking layers is to make 55% go up to ~100%
depends on
2.5 cm
8.0 cm
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54Jim Thomas - LBL
The performance of the TPC + SSD + PXL
• The performance of the TPC + HFT acting together depends on the integration time of the PXL chip … but overall the performance is very good
P(good association) = 1 / (1+S) where S = 2 x y
Integration Time (sec)
Sin
gle
Lay
er E
ffic
ien
cy
Random errors only included in hand calculations and in GEANT/ITTF simulations
Note that systematic errors are not included in the hand calculations nor in the GEANT Simulations
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55Jim Thomas - LBL
The challenge is to find tracks in a high density environment with high efficiency because a D0 needs single track 2
Raw HFT Tracking Efficiency: 0.98 x 0.98 x 0.93 x 0.94 = 0.84
Geometric acceptance and TPC track finding efficiencies 0.9 x 0.9 x 0.8 = 0.65 In this example Tot = 0.55
– Goal: graded resolution and high efficiency from the outside in
– TPC – SSD – IST – PXL
– TPC pointing resolution at the SSD ~ 1 mm = 0.98
– SSD pointing at the IST is ~ 400 m = 0.98
– IST pointing at PXL 2 is ~ 400 m = 0.93
– PXL 2 pointing at PXL1 is ~ 125 m = 0.94
– PXL1 pointing at the VTX is ~ 40 m
The performance of the TPC + SSD + IST + PXL
~ 50 cm
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D0 reconstruction
θ
MD0 = 1.8645 GeV/c2 c = 123 m
V0(D0)
dca K
0.5 < pT < 1.5 GeV/c
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57Jim Thomas - LBL
D0 expected invariant mass distributions
pT
pT distributions for (S,B) at high p
T are from power-law guess and Hijing, respectively.
D0 Background slope at high pT could be uncertain due to limited statistics in MC.
For 100 M Au+Au central collisions at 1x RHIC II luminosity
38BS
S
22 BS
S
69BS
S
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58Jim Thomas - LBL
• The predicted absolute efficiency of the HFT detector. – The red squares show the efficiency for finding the D0 meson with the full set
of Geant/ITTF techniques. The black circles show the efficiency AFTER cuts.
• The tracking efficiency is improved by 20-30% compared to the simulation in the proposal. Mostly due to improved hit selection in PXL.
D0 Reconstruction Efficiency
Geant/ITTF
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59Jim Thomas - LBL
Improved understanding of signal / background
Updated: S: D0 yield dN/dy = 2 Loosen the # of PIXEL hits selection D0 background in more real estimation
Assume perfect PID at pT<1.5 GeV and no PID at p
T>1.5 GeV/c
100 M Au+Au central @ 200 GeV
| | < 1, D0+D0_
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60Jim Thomas - LBL
Estimate v2 sensitivity – focus on the error bars
From central to minimum bias, assume: D0 scaled by N
bin Hijing background scaled by N
part
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61Jim Thomas - LBL
Estimate Rcp sensitivity: focus on the error bars
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62Jim Thomas - LBL
The next level of difficulty: Charm baryon - c
M = 2.286 GeV/c2 c = 60 m
pT
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63Jim Thomas - LBL
Nuclear Matter at RHIC … a perfect liquid … an sQGP
• Its hot– Chemical freeze out at 175 MeV & Thermal freeze out at 100 MeV
• Its fast– Transverse expansion with an average velocity greater than 0.55 c
– Large amounts of anisotropic flow (v2) suggest hydrodynamic expansion and high pressure at early times in the collision history
• Its opaque and strongly interacting– Saturation of v2 at high pT
– RAA … suppression of high pT particle yields relative to p-p
– Jet Quenching … suppression of the away side jet
• It has partonic degrees of freedom– Constituent quark scaling of v2 and v4 for u, d, s and perhaps charm
• There are hints that it is thermally equilibrated– Excellent fits to particle ratio data with equilibrium thermal models
• And it has nearly zero viscosity and perhaps a Mach cone– Perhaps it is at or below the quantum bound from the AdS/CFT conjecture
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Backup Slides
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65Jim Thomas - LBL
TPC Pointing at the PXL Detector
• The TPC pointing resolution on the outer surface of the PXL Detector is greater than 1 mm … but lets calculate what the TPC can do alone
– Assume the new radial location at 8.0 cm for PXL-2, with 9 m detector resolution in each pixel layer and a 200 sec detector
– Notice that the pointing resolution on PXL-1 is very good even though the TPC pointing resolution on PXL-2 is not so good
• The probability of a good hit association on the first pass– 55% on PXL2
– 95% on PXL1
Radius PointResOn(R-)
PointResOn(Z)
Hit Density(cm-2)
8.0 cm 1.4 mm 1.5 mm 6.0
2.5 cm 90 m 110 m 61.5
This is surprising: The hard work gets done at 8 cm!
The purpose of the intermediate tracking layers is to make 55% go up to ~100%
All values quoted for mid-rapidity Kaons at 750 MeV/c
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66Jim Thomas - LBL
D0 Decay Kinematics
PT of the Kaon (GeV/c)
PT o
f th
e P
ion
(G
eV/c
)
• D0’s thrown by Pythia for p-p collisions
• D0 pT shown by different color dots (e.g. Blue = 1.3 GeV D0s)
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67Jim Thomas - LBL
• pT distributions of electrons from semi-leptonic decay of heavy flavor mesons (left D-mesons, right B-mesons) as a function of parent pT. The inserted plots represent the projections to the corresponding heavy flavor distributions. The widths of the electron pT windows are indicated by dashed boxes.
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68Jim Thomas - LBL
3<pt,trigger<4 GeV
pt,assoc.>2 GeV
Au+Au 0-10%
preliminary
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The Development of a Weibal Instability
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0
0 . 2
0 . 4
0 . 6
0 . 8
1
1 . 2
1 . 4
1 . 6
-6 -4 -2 0 2 4 6y
dy
dn
Nomenclature: Rapidity vs xf
• xf = pz / pmax
– A natural variable to describe physics at forward scattering angles
• Rapidity is different. It is a measure of velocity but it stretches the region around v = c to avoid the relativistic scrunch
– Rapidity is relativistically invariant and cross-sections are invariant
)/(tanh 1 Epyor z
Rapidity and pT are the natural kinematic variable for HI collisions( y is approximately the lab angle … where y = 0 at 90 degrees )
When the mass of the particle is unknown, then y
1tanh yy
z
z
pE
pEy ln
2
1
β
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V1: Pions go opposite to Neutrons
• hi
62 GeV Data
At low energy, the pions go in the opposite direction to the ‘classical’ bounce of the spectator baryons
200 GeV Data
At the top RHIC energy, the pions don’t flow(v1 at =0 )but at ALICE, v1 may have a backward wiggle.Reveals the EOS
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72Jim Thomas - LBL
Interpreting Flow – order by order
n=1: Directed Flow has a period of 2 (only one maximum)
– v1 measures whether the flow goes to the left or right – whether the momentum goes with or against a billiard ball like bounce off the collision zone
n=2: Elliptic flow has a period of (two maximums)
– v2 represents the elliptical shape of the momentum distribution
))2cos(2)cos(21(2
121
2
3
3
vvdydpp
Nd
pd
dNE
TT
directed elliptic isotropic
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73Jim Thomas - LBL
TPC Gas Volume & Electrostatic Field Cage
• Gas: P10 ( Ar-CH4 90%-10% ) @ 1 atm
• Voltage : - 28 kV at the central membrane 135 V/cm over 210 cm drift path
420 CM
Self supporting Inner Field Cage: Al on Kapton using Nomex honeycomb; 0.5% rad length
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74Jim Thomas - LBL
Cold nuclear matter:0 ~ 0.16 GeV/fm3
30x0
nucl-ex/0311017
PRL 87 (01) 52301
R2
dydz 0
Boost invariant hydrodynamics: Bjorken Estimate of Initial Energy Density
d
dNp
Rdy
dE
Rch
TT
2
31122
~ 0.2 - 1 fm/ctime to thermalize the
system
~ 6.5 fm
Bjorken Estimate of Initial Energy Density
3/5.4 fmGeV3/7.0 fmGeVC
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75Jim Thomas - LBL
This gap is a manifestation of the approximate SU(2)R x SU(2)L chiral symmetry of QCD with pions as the Nambu-Goldstone bosons
QCD is a Rich Theory with Many Features
Hadron “level” Diagram
Hadron 'level' diagram
0
500
1000
1500
0 10 20 30 40
Degeneracy
Mass (MeV)
Kfo
{W. Zajc
MFFDiL a
aˆ~
4
1We have a theory of the strong
interaction
Low(er) energy nuclear physics uses OPEP or descriptions in terms of a pion gas. These worked because QCD is a theory with a mass gap.
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Something Funny Happens at T > mc2
An exponentially increasing density of hadronic states suggests– A “limiting temperature” TH
– A phase transition(?) in hadronic matter
This was noticed before quarks were identified as the constituents of matter– ( Hagedorn, Nuovo Cimento Supp., 3 (147) 1965 )
Fit this form with TH = 163 MeVDensity of States .vs. Energy
HTmaemdm
dnm /~)(
dmem
dmem
TTm
a
Tm
H
)11
(
/
~
)(
Which requires T < TH
Thermal equilibrium suggests
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Charm Cross Sections at RHIC
1) Large systematic uncertainties in the measurements2) Theory under predict by a factor ~ 2 and STAR ~ 2 x PHENIX3) Directly reconstructed charm hadrons Upgrades
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Au on Au Event at CM Energy ~ 130 GeV*A
Real-time track reconstruction
Pictures from Level 3 online display. ( < 70 mSec )
Data taken June 25, 2000.
The first 12 events were captured on tape!
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Identified Mesons and Baryons: Au+Au @ 200 GeV
and p yields .vs. pTPhys. Rev. Lett. 97 (2006) 152301
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The Large Detectors – PHENIX and STAR
STAR PHENIX
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Partonic energy loss via leading hadrons
Energy loss softening of fragmentation suppression of leading hadron yield
ddpdT
ddpNdpR
TNN
AA
TAA
TAA /
/)(
2
2
Binary collision scaling p+p reference
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Au+Au and p+p: inclusive charged hadrons
p+p reference spectrum measured at RHIC
PRL 89, 202301
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PHENIX data on the suppression of 0s
Factor ~5 suppression for central Au+Au collisions
lower energy Pb+Pb
lower energy
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84Jim Thomas - LBL
Pixel & IST – optimizations and progress
2.5 cm radius
8 cm radius
Inner layer
Outer layer
End view ALICE style carbon
support beams (green)
See talks by
HH Wieman B Surrow
• One IST layer at 14 cm• Good performance• Utilizes the existing SSD
• Fewer channels• Lower cost• Extra space for PXL layers
• Basic Parameters– Short strips ( < 1 cm )
– Wide strips ( ~ 500 m )
– Approx 150 m x 2000 m resolution
The proposed changes and optimizations have been verified with hand calculations and are scheduled to be put thru a full system test with GEANT/ITTF simulations.
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85Jim Thomas - LBL
Central Collisions: Density of hits on the Detectors
dN dN d
dz d dz
2 2
1( , )
dr z
dz r z
where
22
1 700( ) 17.8
2 2
dN dNCentral cm
dA dz r r
Au+Au Luminosity (RHIC-II) 80 x 1026 cm-2s-1
dn/d (Central) 700 dn/d (MinBias) 170 MinBias cross section 10 barns MinBias collision rate (RHIC-II) 80 kHz Interaction diamond size, σ 15 cm Integration time for Pixel Chips 200 sec
Radius Simple Formulas
HIJING thru GEANT
PXL 1 2.5 cm 17.8 cm-2 19.0 cm-2
PXL 2 8.0 cm 1.7 cm-2 1.8 cm-2
IST 14.0 cm 0.57 cm-2 0.66 cm-2
SSD 23.0 cm 0.21 cm-2 0.23 cm-2
The density of hits is not large compared to the number of pixels on each layer. The challenge, instead, is for tracking to find the good hits in this dense
environment.
Slightly conservative numbers
100,000 pixels cm-2
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86Jim Thomas - LBL
Monte Carlo Simulation Strategy & Updates
Central Au-Au events from Hijing
Geometry definition in GEANT
Detector response simulation
Digitization to raw hits
STAR ITTF reconstruction chain
User's analysis code
Real data from DAQ
Association between rec and MC
PIXEL hits pileup
D0 Measurements: dN/dy per NN collision ~ 0.004 (STAR) we take half of this as our estimate of the rate
# Hits selection in PIXEL: MC hits and Rec hits can be > 2 we include these tracks
D0 Background: K from D decays and from other decays -- important at high p
T . D0 -> K- + X (53%)
PID with TOF: Assume perfect K/ at pT< 1.5 GeV/c, no PID for K/ beyond
that. Background also includes PID contamination.
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87Jim Thomas - LBL
Geometry definition in MC and event sample
Hit position in silicon layers from MC
Segment sizes and resolutions
Central (b = 0-3 fm) Au-Au Hijing + 10 D0 per event (flat pT, eta)
|Vertex_z| < 5 cm BR=100%
9x99x9
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88Jim Thomas - LBL
D0 S,B evolution with different pileup levels
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89Jim Thomas - LBL
Pixel Prototype – Geant .vs. Hand CalculationsGEANT
• Three arm PXL prototype configuration (early deployment / engineering test)• Good acceptance around the expected mean pT of D0 ’s (i.e. ~1 GeV)• Ideal to measure charm cross-section via direct topological reconstruction
Hand Calculations
pT of the D0 (MeV/c)pT of the D0 (GeV/c)A
cc
ep
tan
ce
(f
or
D0s
th
row
n in
to t
he
TP
C
acce
pta
nce
)
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90Jim Thomas - LBL
The Simplest ‘Simulation’ – basic performance check
• Study the last two layers of the system with basic telescope equations with MCS
– PXL 1 and PXL 2 alone ( no beam pipe )
– Give them 9 m resolution
0
( / )13.6mcs
MeV c x
p X
2 22 2 2 22 11 2 2 1
2 2
2 1sin ( )
mcs rr r
r r
hh
• In the critical region for Kaons from D0 decay, 750 MeV to 1 GeV, the PXL single track pointing resolution is predicted to be 20-30 m … which is sufficient to pick out a D0 with c = 123 m
• The system (and especially the PXL detector) is operating at the MCS limit
• In principle, the full detector can be analyzed 2 layers at a time …
TPC alone
PXL alone
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91Jim Thomas - LBL
HFT Performance & Simulation Studies
A marriage of Intuition, Hand Calculations, and Detailed Geant Simulations
Jim ThomasLawrence Berkeley National Laboratory
February 25-26, 2008
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92Jim Thomas - LBL
Graded Resolution from the Outside In
• A PXL detector requires external tracking to be a success– The TPC and intermediate tracking provide graded resolution from the
outside-in• The intermediate layers form the elements of a ‘hit finder’
– The spatial resolution is provided by the PXL layers• The next step is to ensure that the hit finding can be done
efficiently at every layer in a high hit density environment
TPCvtx
PXL alone
TPCSSD
SSDIST
ISTPXL2
PXL2PXL1
PXL1VTX
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93Jim Thomas - LBL
Ghosting increases as pileup increases
Pile-up level: 1x RHIC II luminosity
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94Jim Thomas - LBL
Secondary Vertex Resolution
cm
c
Co
un
ts
Left figure, observed decay length (including realistic pT weighting) Right figure, D0 decay length scaled by a factor of 1/ No beamline constraint required … In central AuAu collisions, the D0 secondary vertices are clearly
separated from the primary vertex
cm
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95Jim Thomas - LBL
The Phase Diagram for Nuclear Matter
The goal is to explore nuclear matter under extreme conditions – T > mc2 , > 10 * 0 and net 0
• The goal at RHIC is to understand the QCD in the context of the many body problem
• Another goal is to discover and characterize the Quark Gluon Plasma
• RHIC is a place where fundamental theory and experiment can meet after many years of being apart
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96Jim Thomas - LBL
Chemical and Kinetic Freeze-out
• Chemical freeze-out (first)– End of inelastic interactions
– Number of each particle species is frozen
• Useful data– Particle ratios
• Kinetic freeze-out (later)– End of elastic interactions
– Particle momenta are frozen
• Useful data– Transverse momentum distributions
– and Effective temperatures
space
tim
e
inelasticinteractions
Chemicalfreeze-out
elasticinteractions
Kineticfreeze-out
blue beam yellow beam
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97Jim Thomas - LBL
Chemical Freeze-out – from a thermal model
• The model assumes a thermally and chemically equilibrated fireball at hadro-chemical freeze-out which is described by a temperature T and (baryon) chemical potential : dn ~ e-(E-)/T d3p
• Works great, but there is not a word of QCD in the analysis. Done entirely in a color neutral Hadronic basis!
Thermal model fits
Compare to QCD on the (old) Lattice:
Tc = 154 ± 8 MeV (Nf=3)
Tc = 173 ± 8 MeV (Nf=2)(ref. Karsch, various)
MeV 629(RHIC)μ
MeV 7177(RHIC)T
B
ch
MeV 270(SPS)μ
MeV 170160(SPS)T
B
ch
input: measured particle ratios output: temperature T and baryo-chemical potential B
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• Final-state analysis suggests RHIC reaches the phase boundary
• Hadron spectra cannot probe higher temperatures
• Hadron resonance ideal gas (M. Kaneta and N. Xu,
nucl-ex/0104021 & QM02)
– TCH = 175 ± 10 MeV
– B = 40 ± 10 MeV
• <E>/N ~ 1 GeV(J. Cleymans and K. Redlich, PRL 81, p. 5284, 1998 )
Lattice results
Neutron STAR
Putting RHIC on the Phase Diagram
We know where we are on the phase diagram but eventually
we want to know what other features are on the diagram
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99Jim Thomas - LBL
-meson Flow: Partonic Flow
-mesons are special: - they show strong collective flow and - they are formed by coalescence of thermalized s-quarks ‘They are made via coalescence of seemingly thermalized quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC’
Phys. Rev. Lett. 99 (2007) 112301 and Phys. Lett. B612 (2005) 81
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The Suppression occurs in Au-Au but not d-Au
d+Au
Au+Au
No quenching
Quenching!
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101Jim Thomas - LBL
Hand calculations assume the acceptance is flat in pT and assume a single track at = 0.5
Single Track Efficiencies & Ghosting
Au + Au central collisions @ 200 GeV
TPC tracking efficiency ~80-85%
Ghosting =
# of tracks with 2 PIXEL hits & either of 2 PIXEL hits is a wrong hit
# of track with 2 PIXEL hits
Hand Calculations Ghost Rate = 1 – Raw Tracking
Efficiency
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• The HFT is thin, unique, innovative and robust
• The design have been tested extensively with hand calculations and a few key examples have been simulated with GEANT/ITTF software
• Simulations … completed tasks A full Monte Carlo simulation + reconstruction chain with HFT in STAR Comprehensive study on the pointing resolution and single track
efficiency for the STAR system with HFT with full MC simulations. Comprehensive study on the D0 reconstruction in Au+Au central
collisions, including realistic signal/background study. D0 reconstruction efficiency in Au+Au Quantify the pile-up effect on the single track efficiency (ghosting), D0
background and signal significance.
• To do Improved understanding of single track efficiency and ghosting at low pT
Optimization of D0 reconstruction at low pT – improving efficiency
Systematic study of other Charm hadrons, such as the c, and Bottom p+p 200/500 GeV simulations, pile-up effect and improved vertex finders
Summary: A rich physics program with the HFT