Quark-Gluon Plasma

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Quark-Gluon Plasma Introduction to
Experiments Part - 1
Tapan Nayak VECC, Kolkata nayak_at_veccal.ernet.in
nayak_at_cern.ch
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The QCD Phase diagram

• Deconfinement
• Chiral symmetry restoration

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Why do we expect in a phase transition from
hadronic phase to quark-gluon plasma?
e is energy density and T is temperature.
In hadronic phase both pions and nucleons are
regarded as elementary particles, and the system
would have a limiting temperature, called the
Hagedorn temperature (QM 84 proceedings). This
is analogous to the boiling temperature of water.
At around 100deg C even if heat supplied is more,
most of the heat energies are used to forming
bubbles and not increasing the kinetic energies
of water molecules. Similarly in hadronic matter
most energies are used to forming pion bubbles.
The boilng temp is of the order of pion mass. On
the other hand, q-q interactions become weaker as
the inter-quark distance becomes shorter
(asymptotic freedom). The system behaves like
free quarks and gluons. Therefore
Stephan-Boltzmann law holds and there is no
limiting temperature. Thus we expect a phase
transition at TTC.
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QCD EoS from Lattice
Stephan Boltzman limits for a free Quark Gluon
gas
Energy Density/ (Temperature)4
T/Tc
F. Karsch, Prog. Theor. Phys. Suppl. 153, 106
(2004)
Recent Lattice results seem to give a value of Tc
to be 190 MeV
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QCD EoS from Experiments

• Energy Density from experiments Bjorken
  estimation
• Temperature from pT spectra of emitted
  particles (for example pT spectra of f

We can get some idea about the (1) Effective
degrees of freedom (thermodynamic degeneracy) at
a (2) Time (t) at which matter comes to
approximate thermal equilibrium and starts to
behave like a hydrodynamic fluid.
Problems arise in accessing Initial conditions
Initial Energy densities Initial Temperatures
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Initial Energy Density Bjorken estimation
Bjorken 1983
Boost invariant hydrodynamics
t proper time y rapidity h
pseudo-rapdity ET transverse energy Nch Number
of charged particles mT transverse mass R
effective transverse radius
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Initial Energy Density and Temperature
and T
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Kinematics What is Rapidity?
In non-relativistic physics the Galileo law of
summation of velocities is valid v2 v1 v
(non-rel), where v1 and v2 are the velocities
measured in reference frames one of which moves
at a velocity v with respect to the other. In
relativistic physics instead of the above, the
Einstein law of summation of velocities is
valid v2 (v1 v) / (1v1v/c2)
(relativistic) This is non-additive one. This is
inconvenient as difference in velocities of two
particles depends on the choice of the moving
reference frame. To retain the property of
additivity a new kinematic quantity the
rapidity (y) is introduced in relativistic
kinematics . By definition y ½ ln
(cv)/(c-v) And with this, one can show that
y2 y1 y (relativistic) Thus the
difference yA yB in rapidities of two
particles in same in all moving reference frame.
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Heavy-ion Collision
Kinematics y, h etc.
Before
After
ytarget
ybeam
dn/dy
y
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Centrality Selection participants vs. Spectators
The collision geometry (i.e. the impact
parameter) determines the number of nucleons
that participate in the collision
Spectators
Spectators
Participants

• Many quantities scale with Npart
• or a combination of Npart and
• number of collisions, Ncoll
• Transverse Energy
• Particle Multiplicity
• Particle Spectra

Detectors at 90o
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Relativistic Heavy Ion Collider (RHIC)Brookhaven
National Laboratory (BNL), Upton, NY
v 0.99995?c 186,000 miles/sec Au
Au at 200 GeV
Animation M. Lisa
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STAR Experiment at RHIC
Not Shown pVPDs, ZDCs, and FPDs
PMD
4.2 meters
TPC is at the heart of STAR
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TPC Gas Volume Electrostatic Field Cage

• Gas P10 ( Ar-CH4 90-10 ) _at_ 1 atm
• Voltage - 28 kV at the central membrane
  135 V/cm over 210 cm drift path

Self supporting Inner Field Cage
Al on Kapton using Nomex honeycomb
0.5 rad length
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Pixel Readout of a Pad Plane Sector
A cosmic ray delta electron
3 sigma threshold
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Au on Au Event at RHIC
Two-track separation 2.5 cm Momentum Resolution
lt 2 Space point resolution 500 mm Rapidity
coverage 1.8 lt h lt 1.8
1000s of particles
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Particle ID
Time Projection Chamber 45 padrow, 2 meters
(radius), s(dE/dx)?8, -1lt?lt1 Multi-gap Resistive
Plate Chamber TOFr 1 tray (1/200), s(t)85ps
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Particle ID using Topology Combinatorics
Secondary vertex Ks ? p p? L ? p p? X
? L p? W ? L K g ??? ee-
Ks ? p p - f ? K K - L ? p
p - r ? p p -
kinks K?? ?? ?
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1. Particle Multiplicity and Pseudorapidity
   distributions

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Shapes of dNch/dh versus h (Ös 130)
PHOBOS 3 most central collisions ltNchgt 4200
? 470
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Particle production
Number of charged particles as a function of
pseudorapidity
gt LHC predictions (PbPb at 5.5TeV) 1100-2000
Dec 11, 2007
DAE Nuclear Physics Symposium, Sambalpur
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Particle Density (dN/dh) vs. s1/2
Top 5 centrality
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2a. pT distributions and temperature
2b. Estimation of mean transverse mass, ltmTgt
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Identified Particle Spectra
AuAu _at_ 200GeV
p, p-, K, K- spectra versus centrality PRL 92
(2004) 171801
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Pressure, Flow,
Nu Xu

• tds dU pdV
• s entropy p pressure U energy V
  volume
• t kBT, thermal energy per dof

• In high-energy nuclear collisions, interaction
  among constituents and density distribution will
  lead to
• pressure gradient ? collective flow
• ? number of degrees of freedom (dof)
• Equation of State (EOS)
• The thermalization is not required pressure
  gradient only depends on the density gradient and
  interactions.
• ? Space-time-momentum correlations!

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Hadron Spectra from RHICpp and AuAu collisions
at 200 GeV
0-5
more central collisions
Multi-strange hadron spectra are exponential in
their shapes.
STAR white papers - Nucl.
Phys. A757, 102(2005).
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Freeze-out Systematic
At freeze-out The temperature parameters Tfo
seem to be around 100 -140 MeV. v2 continuously
rise with beam energy. A clear increase in
averaged velocity parameters ?r - increase of the
pressure in the system at RHIC. When v2
crosses zero, a plateau appears for Tfo and ?r at
beam energy 5 GeV.
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Slope Parameter Systematics
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STAR ?-mesons

• 200 GeV AA collisions
• The multi-strange baryons productions ?, ? are
  enhanced in AA collisions
• The ?-meson productions are also enhanced, but
  may be with different trends
• The enhancements are NOT due to Canonical
  Ensample Suppression!
• PRL. 98 (2007) 062301
  (nucl-ex/0606014) PRL in print, nucl-ex/
  0703033 nucl-ex/ 0705.2511

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Blast Wave Fits Tfo vs. ?bT?
Nu Xu

• 1) p, K, and p change
• smoothly from peripheral
• to central collisions.
• 2) At the most central
• collisions, ??T? reaches
• 0.6c.
• 3) Multi-strange particles ?,
• ? are found at higher Tfo
• and lower ??T?
• ? light hadrons move
• with higher velocity
• compared to strange
• hadrons
• STAR NPA715, 458c(03) PRL 92, 112301(04) 92,
  182301(04).

200GeV Au Au collisions
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? -meson Flow Partonic Flow
QM2008 J. Chen X.B. Wang
?-mesons are produced via coalescence of
seemingly thermalized quarks in central AuAu
collisions. This observation implies hot and
dense matter with partonic collectivity has been
formed at RHIC
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EoS Parameters at RHIC
Nu Xu
In central AuAu collisions at RHIC -
partonic freeze-out Tpfo 165 10 MeV
weak centrality dependence vpfo 0.2 (c) -
hadronic freeze-out Tfo 100 5 (MeV)
strong centrality dependence vfo 0.6 0.05
(c) Systematic study are needed to understand
the centrality dependence of the EoS
parameters Thermalization assumed
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3. Rapidity distribution of transverse energy
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Measurement of Transverse Energy (ET)
Raghunath Sahoo Ph.D. thesis arXiv0804.1800
nucl-ex
Transverse energy (ET) is the energy produced
transverse to the beam direction. This is
generated due to the initial scattering of
partonic constituents of the incoming nuclei and
the rescattering of the produced partons and
hadrons.
Transverse phase space is ideal to study the
initial conditions after the collision.
Motivation gtEstimation of the Bjorken energy
density of the produced fireball
thru the estimation of ET on an event by
event basis to verify if a
condition for deconfinement does exist.
gt Study of particle production
mechanism gtStudy of
Quark-Hadron phase transitions thru fluctuation
observables like ET and the
ratio of its components.
The hadronic transverse energy (EThad) is
measured thru the TPC reconstructed tracks (PID
and momentum information). The electromagnetic
transverse energy (ETem) is measured thru the
calorimeter tower hits after correcting for the
hadronic contaminations.
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ET Distributions _at_ 62.4 GeV AuAu Collisions
Minimum-bias distribution of electromgnetic
transverse energy
Minimum-bias distribution of hadronic
transverse energy
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Minimum-bias distribution of total transverse
energy
Transverse energy distribution for different
centrality classes.
62.4 GeV AuAu Collisions
62.4 GeV AuAu Collisions
Raghunath Sahoo
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The excitation function of dET/dy per
participant pair from AGS to RHIC.
Raghunath Sahoo

• The EKRT model (based on final state Gluon
  saturation) underestimates the final transverse
  energy.

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4. Source size, R from HBT measurements
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Robert Hanbury Brown and Richard Twiss

HBT Intensity Interferometry
Intensity interferometry has an intimate relation
with Michelson amplitude interferometry Amplitude
interferometry measured from detectors 1 and 2
A1 A2 2 A12 A22 ( A1 A2
A1 A2) The later term in the parenthesis is
the called the fringe visibility . Averaged
over, ltV2gt 2 lt A12 A22gt ltA12A22gt
ltA12A22gt The first term r.h.s above is just
twice the correlation of the intensities landing
in the two detectors. ltV2gt ? 2ltI1I2gt
Debasish Das Ph.D. thesis
Interference is a phenomenon associated with the
superposition of two or more waves. The
two-particle correlations arise from the
interference of particle wave-functions and
depend on whether the particles are bosons or
fermions
The goal of intensity interferometry is to
extract the space-time information of the
heavy-ion collision source from the momentum
spectra which are the only measureable
quantities making use of quantum statistical
correlations between the pairs of identical
particles.
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Probing source geometry through interferometry
Correlation function constructed
experimentally,
C2 (q) A (q) / B (q)
(normalized to unity at large q), A (q) ? is
the pair distribution in momentum difference q
p2 - p1 for pairs of particles from the same
event. B (q) ? is the corresponding distribution
for pairs of particles from different events.
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Source geometry
C2(Qinv)
Qinv (GeV/c)
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Measuring the Source geometry
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Detailed source geometry
Debasish Das Ph.D. thesis
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Beam energy dependence of pion HBT
STAR
Debasish Das Ph.D. thesis
Pion rapidity density is proportional to the
freezeout volume gt Constant Freezeout Volume
(freezeout at a constant density).
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Now finally to Bjorken Energy Density
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Bjorken Energy Density Excitation function
t 1
Bjorken Energy density increases logarithmically
with center of mass energy.
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Bjorken Energy Density for different
centralities
Bjorken Energy density is unique for given
centrality and beam energy and can be used as an
estimator for different physics topics.
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SUMMARY

• What did we try to learn today
• Measurement of charged particle multiplicity and
  rapidity distributions
• Measurement of pT spectra and extraction of
  effective temperature
• Radial flow and estimation of thermal
  temperature
• Source sizes from HBT parameters
• Estimation of energy density
• Work in progress Use of f for making an EoS
  plot
• Work in progress EoS plot from experimental
  estimations and comparison with lattice

END OF LECTURE-1