Sept 8-12, 2008ICHIC-Goa School1 Quark-Gluon Plasma – Introduction to Experiments Part - 1 Tapan Nayak VECC, Kolkata [email protected]@veccal.ernet.in.

Sept 8-12, 2008 ICHIC-Goa School 1

Quark-Gluon Plasma – Introduction to Experiments

Part - 1

Tapan NayakVECC, Kolkata

[email protected] [email protected]


The QCD Phase diagramT

empe

ratu

re

baryon density

Neutron stars

Early universe

nucleinucleon gas

hadron gascolour

superconductor

quark gluon plasmaTc

0

critical point ?

vacuum

CFL

High Temperature

High baryon density

DeconfinementChiral symmetry restoration

By increasing the

collision energy


Why do we expect in a phase transition from hadronic phase to quark-gluon plasma?

/T4

Hadronic matter

Quark-gluon plasma

TTC

Hagedorn Limiting Temperature

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 T~TC.


Stephan Boltzman limits for a free Quark Gluon gas

En

erg

y D

ensi

ty/

(Tem

per

atu

re)4

TC ~ 170 15 MeV

C ~ 0.7-1.2 GeV/fm3

0 ~ 0.16 GeV/fm3

F. Karsch, Prog. Theor. Phys. Suppl. 153, 106 (2004)

QCD EoS from Lattice

Recent Lattice results seem to give a value of Tc to be 190 MeV

T/Tc


• Energy Density from experiments: Bjorken estimation

• Temperature from pT spectra of emitted particles (for example: pT spectra of

QCD EoS from Experiments

We can get some idea about the:

(1) Effective degrees of freedom (thermodynamic degeneracy) at a (2) Time () 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


Initial Energy Density – Bjorken estimation

R2

dydz 0

Boost invariant hydrodynamics:

Bjorken 1983

d

dNm

R

dy

dE

R

chT

TBj

2

31

1)(

2

2

: proper timey : rapidity: pseudo-rapdityET: transverse energyNch : Number of charged particlesmT : transverse massR: effective transverse radius


Initial Energy Density and Temperature

d

dNm

R

dy

dE

R

chT

TBj

2

31

1)(

2

2

and T

1. Pseudorapidity distribution of charged particles and photons

3. Rapidity distribution of transverse energy

2a. pT distributions and temperature

2b. Estimation of mean transverse mass, <mT>

4. Source size, R from HBT measurements


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) / (1+v1v/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 (c+v)/(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.

Kinematics: What is Rapidity?


Kinematics: y etc.

Heavy-ion Collision

Target

Projectile

p||

pT

p||

pT

y

dn/dyytarget ybeam

p||

pT

y

dn/dyytarget ybeam

β

z

z

pE

pEy ln

2

1

)/(tanh 1 Epy z

1tanh yy

Pseudorapidity:

)2/tan(ln


Many quantities scale with Npart

or a combination of Npart and

number of collisions, Ncoll:• Transverse Energy• Particle Multiplicity• Particle Spectra

“Spectators”

“Spectators”

“Participants”

Zero-degreeCalorimeter

Detectors at 90o

The collision geometry (i.e. the impact parameter) determines the number of nucleons that participate in the collision

Centrality Selection: participants vs. Spectators


RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

RRelativistic elativistic HHeavy eavy IIon on CCollider (RHIC)ollider (RHIC)Brookhaven National Laboratory (BNL), Upton, NYBrookhaven National Laboratory (BNL), Upton, NY

v = 0.99995c = 186,000 miles/sec Au + Au at 200 GeV

Animation M. Lisa


STAR Experiment at RHIC

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

TPC is at the heart of STAR

PMD


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


Pixel Readout of a Pad Plane Sector

A cosmic ray + deltaelectron

3 sigma threshold


Gold GoldsNN = 130, 200 GeV

(center-of-mass energy per nucleon-nucleon collision)

1000’s of particles

Au on Au Event at RHICTwo-track separation 2.5 cm

Momentum Resolution < 2%

Space point resolution ~ 500 m

Rapidity coverage –1.8 < < 1.8


Time Projection Chamber: 45 padrow, 2 meters (radius), dE/dx)8%, -1<Multi-gap Resistive Plate Chamber TOFr: 1 tray (~1/200), (t)=85ps

Hadron identification: STAR Collaboration, nucl-ex/0309012

Particle ID:


Resonance K*(892) (770) f0(980) (1020) (1232) (1520) (1385)Decay channel K K K p p K

Branching Ratio % ~100 ~100 dominant 49.2 >99 22.5 88.2

Width [MeV] 50.7 150 40 to 100 4.46 ~120 15.6 35.8

Life time [fm/c] 4 1.3 40 ~1.75 13 5.6


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 +


1.Particle Multiplicity and Pseudorapidity distributions


Shapes of dNch/d versus (s = 130)

dN

ch/d

(dN

ch/d)

/(½

Np

art)

0-3%

15-20

35-40

PHOBOS: nucl-ex/0106006

PHOBOS: 3% most central collisions <Nch> = 4200 470

Sept 8-12, 2008 ICHIC-Goa School 21Dec 11, 2007 DAE Nuclear Physics Symposium, Sambalpur 21

Particle production

Number of charged particles as a function of pseudorapidity

=> LHC predictions (Pb+Pb at 5.5TeV): 1100-2000

Extrapolation to LHCAu+Au 0-6% centrality


Particle Density (dN/dvs. s1/2

WA98

WA97/NA57Phobos

NA49

E917/866

STARRESULTS

E877

PHENIX

BRAHMS

Phobos

Top 5% centrality


2a. pT distributions and temperature

2b. Estimation of mean transverse mass, <mT>


p+, p-, K+, K- spectra versus centrality: PRL 92 (2004) 171801

Bose-Einstein fits

mTmAe

/mt exponential fits

K-)1/( / effTmeA

+

Identified Particle Spectra Au+Au @ 200GeV

Jim Thomas

These are color coded by centrality. Make sure they agree with the previous slide. Are they divided by 5 or 10 at each step? Double check with Fuqiang and Raimond.


2

2

1 Ttheff mTT


Pressure, Flow, …

dd = dU + pdV = dU + pdV – entropy; p – pressure; U – energy; V – volume

= kBT, thermal energy per dof

In high-energy nuclear collisions, interaction among constituents and density distribution will lead to: pressure gradient pressure gradient collective flow 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!

Nu Xu


Hadron Spectra from RHICp+p and Au+Au collisions at 200 GeV

sss

ss

uud

ud

Multi-strange hadron spectra are exponential in their shapes. STAR white papers - Nucl. Phys. A757, 102(2005).

mT pT2 m 2

f exp(mT /Tslope )

mor

e ce

ntra

l col

lisio

ns

0-5%

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.

Slope Parameter Systematics

mT pT2 m 2

f exp(mT /Tslope )

Tslope Tthermal m collective

2

STAR: -mesons

200 GeV A+A collisions:- The multi-strange baryons productions , are enhanced in A+A 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


Blast Wave Fits: Tfo vs.

1) 1) , , KK, and , and pp change change smoothly from peripheral smoothly from peripheral to central collisions.to central collisions.

2) At the most central2) At the most central collisions, collisions, TT reaches reaches

0.6c.0.6c.

3) Multi-strange particles 3) Multi-strange particles ,, are found at higher are found at higher TTfofo

and lower and lower TT

light hadrons movelight hadrons move with higher velocitywith higher velocity compared to strangecompared to strange hadronshadrons

STAR: NPA715, 458c(03); PRL 92, 112301(04); 92, 182301(04).

200GeV Au + Au collisions200GeV Au + Au collisions

Nu Xu


-meson Flow: Partonic Flow

“-mesons are produced via coalescence of seemingly thermalized quarks in central Au+Au collisions. This observation implies hot and dense matter with partonic collectivity has been formed at RHIC”

QM2008: J. Chen; X.B. Wang


EoS Parameters at RHIC

In central Au+Au 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

Nu Xu


3. Rapidity distribution of transverse energy


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 incomingnuclei and the rescattering of the produced partons and hadrons.

Transverse phase space is ideal to study the initial conditions after the collision.

Motivation: =>Estimation 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.

=> Study of particle production mechanism

=>Study of Quark-Hadron phase transitions thru fluctuation observables like ET and the ratio of it’s components.

Measurement of Transverse Energy (ET)Raghunath Sahoo: Ph.D. thesis

arXiv:0804.1800 [nucl-ex]

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.


ET Distributions @ 62.4 GeV Au+Au Collisions

Minimum-bias distribution of hadronic transverse energy

Minimum-bias distribution of electromgnetic transverse energy


Minimum-bias distribution of total transverse energy

62.4 GeV Au+Au CollisionsSTAR Preliminary

Transverse energy distribution fordifferent centrality classes.

62.4 GeV Au+Au Collisions

Raghunath Sahoo


STAR Preliminary

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

The excitation function of dET/dy per participant pair from AGS to RHIC.

Raghunath Sahoo


4. Source size, R from HBT measurements


HBT Intensity Interferometry

Intensity interferometry has an intimate relation with Michelson amplitude interferometryAmplitude interferometry measured from detectors 1 and 2 :

| A1 + A2 |2 = | A1|2 + | A2|2 + ( A1* A2 + A1 A2

*)

The later term in the parenthesis is the called the “fringe visibility” .Averaged over,

<V2> = 2 < | A1|2| A2|2> + <A1*2A2

2> + <A12A2

*2> The first term r.h.s above is just twice the correlation of the

intensities landing in the two detectors.<V2> 2<I1I2>

Robert Hanbury Brown and Richard Twiss

p1

“b” source(x)

r1

r2

x1

x2p2

“a” “L”

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.

Interference is a phenomenon associated with the superposition of two or more waves. The two-particle correlations arise from the interference of particle wave-functionsand depend on whether the particles are bosons or fermions

Debasish Das Ph.D. thesis


Probing source geometry through interferometry

2

21

2121 )q(~1

)p(P)p(P)p,p(P

)p,p(C

Measurable!F.T. of pion source

The correlation function is defined as the ratio of the probability for the coincidence of p1 and p2 relative to the probability of observing p1 and p2 separately :

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.

Courtesy of S. Bassp1

“b” source(x)

r1

r2

x1

x2p2

“a” “L”


Qinv (GeV/c)

C2(

Qin

v)

d+AuR ~ 2 fm

Au+AuR ~ 6 fm

p+pR ~ 1 fm

Source geometry p1

“b” source(x)

r1

r2

x1

x2p2

“a” “L”


if a pion is emitted, it is more likely to emit anotherpion with very similar momentum which makes the HBT effect

experimentally measuring this enhanced probability: quite challenging

Measuring the Source geometry


p2

p1

q

R long

Rside

Rout

Rlong – along beam direction

Rout – along “line of sight”

Rside – “line of sight”

Detailed source geometry Debasish Das Ph.D. thesis


Beam energy dependence of pion HBT

Pion rapidity density is proportional to the freezeout volume => Constant Freezeout Volume (freezeout at a constant density).

STAR Debasish Das Ph.D. thesis

Jim Thomas

Get Masashi's latest results from his poster. Use blast wave fits and mean pt.


d

dNm

R

dy

dE

R

chT

TBj

2

31

1)(

2

2

Now finally to Bjorken Energy Density


Compiled by Raghunath Sahoo

Bjorken Energy Density: Excitation function

Bjorken Energy density increases logarithmically with center of mass energy.

= 1

d

dNm

R

dy

dE

R

chT

TBj

2

31

1)(

2

2


Rough Estimation for AuAu 10GeV

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.


END OF LECTURE-1

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 for making an EoS plot

• Work in progress: EoS plot from experimental estimations and

comparison with lattice

SUMMARY

Sept 8-12, 2008ICHIC-Goa School1 Quark-Gluon Plasma – Introduction to Experiments Part - 1 Tapan Nayak VECC, Kolkata [email protected]@veccal.ernet.in.

Documents

limiting temperature

bjorken estimation temperature

value of t c

collision energy slide

p t distributions

ichicgoa school2

ichicgoa school8

ichicgoa school3