Download (March 2004) (ppt-format) - RHIG

Modern Nuclear Physics with STAR @ RHIC:
Recreating the Creation of the Universe
Rene Bellwied
Wayne State University
([email protected])
Lecture 1: Why and How ?
 Lecture 2: Bulk plasma matter ?
 Lecture 3: Probing the plasma

Let there be light

The
HertzsprungRussell
Diagram

Relation
between mass
and
temperature,
light output,
lifetime.
Stars shine
because of
nuclear fusion
reactions in
their core. The
more luminous
they are, the
more reactions
are taking place
in their cores.
Doppler Effect with Stars



A star's motion causes a wavelength shift in its light
emission spectrum, which depends on speed and
direction of motion.
If star is moving toward you, the waves are
compressed, so their wavelength is shorter = blueshift.
If the object is moving away from you, the waves are
stretched out, so their wavelength is longer = redshift.
Relativity and Universe Expansion

The doppler effect tells you about the relative motion
of the object with respect to you.

Important fact:
 The spectral lines of nearly all of the galaxies in
the universe are shifted to the red end of the
spectrum.
 This means that the galaxies are moving away
from the Milky Way galaxy.
 This is evidence for the expansion of the universe.
Uniform Expansion


The Hubble law, speed = Ho × distance, says the
expansion is uniform.
The Hubble constant, Ho, is the slope of the line
relating the speed of the galaxies away from each
other and their distance apart from each other.


It indicates the rate of the expansion.
If the slope is steep (large Ho), then the expansion rate
is large and the galaxies did not need much time to get
to where they are now.
Hubble Law


Hubble and Humason (1931):
 the Galactic recession speed = H × distance,
where H is a number now called the Hubble
constant.
This relation is called the Hubble Law and the
Hubble constant is the slope of the line.
Age of the Universe




Age of the universe can be estimated from the
simple relation of time = distance/speed.
The Hubble Law can be rewritten
 1/Ho = distance/speed.
The Hubble constant tells you the age of the
universe, i.e., how long the galaxies have been
expanding away from each other:
 Age = 1/Ho.
Age upper limit since the expansion has been
slowing down due to gravity.
Evidence for the Big Bang


Galaxies are distributed fairly uniformily across the sky
between a lot of void (Obler’s paradox)
Background radiation was predicted, and has been found,
to be exactly 2.73 K everywhere in the universe. Variations
as measured by a NASA satellite named COBE (Cosmic
Background Explorer) are less than 0.0001 K.
Star Count in the Galaxy
Rough guess of the number of stars in our
galaxy obtained by dividing the Galaxy's
total mass by the mass of a typical star (e.g.,
1 solar mass).
 The result is about 200 billion stars!
 The actual number of stars could be several
tens of billions less or more than this
approximate value.
 All of these numbers are based on luminous
matter !

A Mass Problem



The stars and gas in most galaxies
move much quicker than expected
from the luminosity of the galaxies.
In spiral galaxies, the rotation curve
remains at about the same value at
great distances from the center (it is
said to be ``flat'').
This means that the enclosed mass
continues to increase even though
the amount of visible, luminous
matter falls off at large distances
from the center.

Something else must be adding to the gravity of the
galaxies without shining. We call it Dark Matter !
According to measurements it accounts for 90% of the
mass in the universe.
The universe is accelerating ???
Based on supernovae measurements
The Hubble Key Project determined in 2000 how fast the universe is expanding. The
concluded that the universe is expanding at a rate of 74 km/sec/megaparsec (one pa
3.26 light-years) with an uncertainty of 10%.
Dark Energy – the new puzzle of physics
What is Dark Matter ?
We don’t know (yet)


White dwarfs, brown dwarfs, black holes, massive
neutrinos, although intriguing are very unlikely to account
for most of the dark matter. The dwarfs are generally called
Massive compact halo objects (MACHOS)
New exotic particles or formations are more likely:
 Weakly interacting massive particles (WIMPS)
 Matter based on exotic quark configurations (e.g.
strange Quark matter)
If these states exist somewhere in the universe
wouldn’t they have been produced in the early
universe ?
Where did it all start ?
Witten’s ‘Cosmic Separation of phases’
(Phys.Rev.D 30 (1984) 272) and his idea of
strange quark matter.
 The impact on cosmology might be far reaching
and definitely affected the search for strangeness
enhancement in general and strange quark matter
in particular.
 Strange Quark Matter is still considered a
possibility for stable or metastable matter in the
universe

Two recent examples in astrophysics
Fundamental paper on ‘How to identify a strange star’
by Jes Madsen, PRL 81 (1998) 3311
Recent measurements by Drake et al. and Helfand et al. in
2002 with the Chandra X-ray telescope
3C58
RXJ1856
These two NASA Chandra X-ray Observatory images show two stars - one too small, one too cold that reveal cracks in our understanding of the structure of matter. (AFP)
Did quark matter strike the earth ?
Two anomalous seismic events occurred in 1993, and were
measured independently by 9 monitoring stations.
Strange quark matter should pass through the earth at 400 km/s (40 times the speed
of seismic waves), i.e. search for seismic events not connected with traditional
seismic disturbances e.g. earth quakes. (Herrin et al., SMU, 2002)
What can we do in the laboratory ?
The idea of strange quark matter did not only
initiate strangelet searches but led also to potential
signatures for the QGP phase transition.
Increasing strangeness enhancement as a signal for
QGP and strangeness equilibration as a signal for
thermalization of the particle emitting source were
for years at the forefront of our research.
A Cosmic Timeline
Age
0
10-35 s
Energy
1019 GeV
1014 GeV
Matter in universe
grand unified theory of all forces
1st phase transition
(strong: q,g + electroweak: g, l,n)
10-10 s
102 GeV
2nd phase transition
(strong: q,g + electro: g + weak: l,n)
10-5 s
0.2 GeV
3rd phase transition
(strong:hadrons + electro:g + weak: l,n)
3 min.
0.1 MeV
6*105 years 0.3 eV
Now
(15 billion years)
3*10-4 eV = 3 K
nuclei
atoms
An Inflationary Universe

The universe expanded to a point where the
unified forces of nature started to decouple.
When the strong force decoupled a major
amount of energy was released and the
universe expanded by a factor 1030 in less
than 10-36 seconds. This rapid expansion is
called inflation
Let’s revisit the timelines



The beginning
The universe is a hot plasma of fundamental particles … quarks, leptons, force
particles (and other particles ?)
10-43 s
Planck scale (quantum gravity ?)
1019 GeV
10-35 s
Grand unification scale (strong and electroweak)
1015 GeV
Inflationary period 10-35-10-33 s
10-11 s
Electroweak unification scale
200 GeV
Micro-structure
10-5 s
QCD scale - protons and neutrons form
200 MeV
3 mins
Primordial nucleosynthesis
5 MeV
3105 yrs Radiation and matter decouple - atoms form
1 eV
Large scale structure
1 bill yrs Proto-galaxies and the first stars
3 bill yrs Quasars and galaxy spheroids
5 bill yrs Galaxy disks
Today
Life !
The Cosmic Timeline
Going back in time
Let’s go for the ‘Mini-Bang’



We need a system that is small so that we can
accelerate it to very high speeds.
(99.9% of the speed of light)
But we need a system (i.e. a chunk of matter and
not just a single particle) so that the system can
follow simple rules of thermodynamics and form a
new state of matter in a particular phase.
We use heavy ions (e.g. a Gold ion which is made
of 197 protons and neutrons). It is tiny (about a
10-14 m diameter) but it is a finite volume that can
be exposed to pressure and temperature
What are we trying to do ?

We try to force matter we know (e.g. our Gold
nucleus) through a phase transition to a new state
of matter predicted by the Big-Bang, called a
Quark-Gluon Plasma (QGP)
nucleons
atom
Quarks and
gluons
Quantum Chromodynamics (QCD)
Main features of QCD



Confinement
 At large distances the effective coupling between quarks is large,
resulting in confinement.
 Free quarks are not observed in nature.
Asymptotic freedom
 At short distances the effective coupling between quarks decreases
logarithmically.
 Under such conditions quarks and gluons appear to be quasi-free.
(Hidden) chiral symmetry
 Connected with the quark masses
 When confined quarks have a large dynamical mass - constituent mass
 In the small coupling limit (some) quarks have small mass - current
mass
Confinement

The strong interaction potential

Compare the potential of the strong & e.m. interaction
Vem  

q1q2
c

4 0 r
r
Vs  
c
 kr
r
c, c, k constants
Confining term arises due to the self-interaction property of the
colour field
q1
q2
a) QED or QCD (r < 1 fm)
r
q1
b) QCD (r > 1 fm)
q2
Charges
Gauge boson
Charged
Strength
QED
QCD
electric (2)
g(1)
no
e2
1
em 

4 137
colour (3)
g (8)
yes
 s  0.1  0.2
Asymptotic freedom - the coupling “constant”

It is more usual to think of coupling strength rather than charge
 and the momentum transfer squared rather than distance.
M  initial state mass
W  final state mass
2M  Q2  W 2  M 2

  energy transfer
Q  momentum transfer
In both QED and QCD the coupling strength depends on distance.
e  e
 In QED the coupling strength is given by:
 
em Q2 

1  3  lnQ
2
m
2

Q2»m2
where  = (Q2  0) = e2/4 = 1/137
 In QCD the coupling strength is given by:


 s Q 
 

2 33  2n f 
2
1    
ln Q
s 2
2

 
s
12


 

2

which decreases at large Q2 provided nf < 16.
Q2 = -q2
Asymptotic freedom - summary


Effect in QCD
 Both q-qbar and gluon-gluon loops contribute.
+  The quark loops produce a screening effect analogous to e e loops in QED
 But the gluon loops dominate and produce an anti-screening effect.
 The observed charge (coupling) decreases at very small distances.
 The theory is asymptotically free  quark-gluon plasma !
“Superdense Matter: Neutrons or Asymptotically Free Quarks”
J.C. Collins and M.J. Perry, Phys. Rev. Lett. 34 (1975) 1353
Main points
 Observed charge is dependent on the distance scale probed.
 Electric charge is conveniently defined in the long wavelength limit (r 
).
 In practice em changes by less than 1% up to 1026 GeV !
 In QCD charges can not be separated.
 Therefore charge must be defined at some other length scale.
 In general s is strongly varying with distance - can’t be ignored.
Quark deconfinement - medium effects

Debye screening
 In bulk media, there is an additional charge screening effect.
 At high charge density, n, the short range part of the potential becomes:
r 
1 1
1
V(r)   exp
where rD  3

r
r
n
rD 



and rD is the Debye screening radius.
 Effectively, long range interactions (r > rD) are screened.
The Mott transition
 In condensed matter, when r < electron binding radius
 an electric insulator becomes conducting.
Debye screening in QCD
 Analogously, think of the quark-gluon plasma as a colour conductor.
 Nucleons (all hadrons) are colour singlets (qqq, or qqbar states).
 At high (charge) density quarks and gluons become unbound.
 nucleons (hadrons) cease to exist.
Debye screening in nuclear matter

High (color charge) densities are achieved by
 Colliding heaving nuclei, resulting in:
1. Compression.
2. Heating = creation of pions.
 Under these conditions:
1. Quarks and gluons become deconfined.
2. Chiral symmetry may be (partially) restored.

The temperature inside a heavy ion collision at RHIC can exceed
1000 billion degrees !! (about 10,000 times the temperature of the sun)
Chiral symmetry

Chiral symmetry and the QCD Lagrangian
 Chiral symmetry is a exact symmetry only for massless quarks.
 In a massless world, quarks are either left or right handed
 The QCD Lagrangian is symmetric with respect to left/right handed quarks.
 Confinement results in a large dynamical mass - constituent mass.
 chiral symmetry is broken (or hidden).
 When deconfined, quark current masses are small - current mass.
 chiral symmetry is (partially) restored

Example of a hidden symmetry restored at high temperature
 Ferromagnetism - the spin-spin interaction is rotationally invariant.
Below the Curie
temperature the
underlying rotational
symmetry is hidden.

Above the Curie
temperature the
rotational symmetry
is restored.
In the sense that any direction is possible the symmetry is still present.
Modelling confinement: The MIT bag model


Modelling confinement - MIT bag model
 Based on the ideas of Bogolioubov (1967).
 Neglecting short range interactions, write the Dirac
equation so that the mass of the quarks is small inside the
bag (m) and very large outside (M)
 Wavefunction vanishes outside the bag if M  
and satisfies a linear boundary condition at the bag surface.
Solutions
 Inside the bag, we are left with the free Dirac equation.
 The MIT group realised that Bogolioubov’s model violated
E-p conservation.
 Require an external pressure to balance the internal
pressure of the quarks.
 The QCD vacuum acquires a finite energy density, B ≈ 60
MeV/fm3.
 New boundary condition, total energy must be minimised
wrt the bag radius.
B
Bag model results



Refinements
 Several refinements are needed
to reproduce the spectrum of
low-lying hadrons
e.g. allow quark interactions
 Fix B by fits to several hadrons
Estimates for the bag constant
 Values of the bag constant
range from B1/4 = 145-235 MeV
Results
 Shown for B1/4 = 145 MeV and
s = 2.2 and ms = 279 MeV
T. deGrand et al, Phys. Rev. D 12 (1975) 2060
Summary of QCD input






QCD is an asymptotically free theory.
In addition, long range forces are screened in a dense
medium.
QCD possess a hidden (chiral) symmetry.
Expect one or perhaps two phase transitions connected
with deconfinement and partial chiral symmetry
restoration.
pQCD calculations can not be used in the confinement
limit.
MIT bag model provides a phenomenological description
of confinement.
Estimating the critical parameters, Tc and c

Mapping out the Nuclear Matter Phase Diagram
 Perturbation theory highly successful in
applications of QED.
 In QCD, perturbation theory is only applicable
for very hard processes.
 Two solutions:
1. Phenomenological models
2. Lattice QCD calculations
Lattice QCD
Quarks
and gluons are
studied on a discrete
space-time lattice
Solves the problem of
divergences in pQCD
calculations (which arise
due to loop diagrams)
There
are two order
parameters
1. The Polyakov Loop
2. The Chiral Condensate
0.5
4.5
15
35
L ~ Fq
 ~ mq
75 GeV/fm3
/T4
Lattice Results
Tc(Nf=2)=1738 MeV
Tc(Nf=3)=1548 MeV
(F. Karsch, hep-lat/9909006)
T = 150-200 MeV
 ~ 0.6-1.8 GeV/fm3
T/Tc
Lattice QCD: the latest news
(critical parameters at finite baryon density)
Phenomenology I: Phase transition

The quark-gluon and hadron equations of state
 The energy density of (massless) quarks and gluons is derived
from Fermi-Dirac statistics and Bose-Einstein statistics.
p 3dp
 g  2  bp
2 e  1
1
q 
1

 g 
p3 dp
2 2 e b  p    1
 2T 4
30
7 2T 4  2 T 2  4
 q   q 

 2
120
4
8
where  is the quark chemical potential, q = - q and b = 1/T.
 Taking into account the number of degrees of freedom
 TOT  16 g  12 q   q 

Consider two extremes:
1. High temperature, low net baryon density (T > 0, B = 0). B = 3 q
2. Low temperature, high net baryon density (T = 0, B > 0).
Phenomenology II: critical parameters


High temperature, low density
limit - the early universe
 Two terms contribute to the
total energy density

For a relativistic gas:

For stability:
Low temperature, high density
limit - neutron stars
 Only one term contributes to
the total energy density

By a similar argument:
 qg  37
2
30
T4
1
Pqg   qg
3
Pnet  Pqg  B  0
14
90
Tc   2 B
37 
q 
3
2

 100  170 MeV
4

q
2
c  2 2 B

14
 300  500 MeV
~ 2-8 times normal nuclear matter density
given pFermi ~ 250 MeV and r ~ 23/32
How to create a QGP ?
energy = temperature & density = pressure
Let’s collide two heavy nuclei (1)
Let’s collide two heavy nuclei (2)
Let’s study all phases of the process
Freeze-out
Hadron Gas
Phase Transition
Plasma-phase
Hard
scattering
Pre-Equilibrium
If the QGP was formed, it will only live for 10-21 s !!!!
BUT does matter come out of this phase the same way it went in ???
~ 100 s after Big Bang
Nucleosynthesis begins
~ 10 s after Big Bang
In the beginning
Hadron Synthesis
quark – gluon strong force binds
quarks and gluons in massive objects:
protons, neutrons mass ~ 1 GeV
plasma
STAR
The RHIC Complex
1. Tandem Van
de Graaff
6
2. Heavy Ion
Transfer Line
3. Booster
5
3
4. Alternating Gradient
Synchrotron (AGS)
4
2
1
5. AGS-to-RHIC
Transfer Line
6. RHIC ring
The STAR Experiment
450 scientists from 50 international institutions
Conceptual
Overview
The STAR Experiment
construction from 1992-2000
data taking from 2000-2010 (?)
Overview while
under
construction
The STAR Detector
Magnet
Coils
Central
Trigger
Barrel
(CTB)
Barrel EM Cal
(BEMC)
Silicon Vertex
Tracker (SVT)
Silicon Strip
Detector (SSD)
Vertex Detector
(2006)
ZCal
Time
Projection
Chamber
(TPC)
FTPC
Endcap EM Cal
FPD
TOFp, TOFr
The STAR Experiment (TPC)
Construction
in progress
The STAR Experiment (SVT)
Construction
in progress
The STAR Experiment (SVT)
The happy crew
after 8 long years
Actual Collision in STAR (1)
Actual STAR data
for a
peripheral collision
Actual Collision in STAR (2)
Actual STAR data
for a central
collision
What is going on ?

A Au nucleus consists of 79 protons and 118 neutrons = 197
particles -> 394 particles total

After the collision we measure about 10,000 particles in the
debris!
measured particles: p, , K, f,L,r,X,W, d, D, J/,Y, B
many particles contain s-quarks, some even c- and b-quarks
Energy converts to matter, but does the matter go through a
phase transition ?



What do we have to check ?

If there was a transition to a different phase, then this phase
could only last very shortly. The only evidence we have to check
is the collision debris.

Check the make-up of the debris:
 which particles have been formed ?
 how many of them ?
 are they emitted statistically (Boltzmann distribution) ?
 what are their kinematics (speed, momentum, angular
distributions) ?
 are they correlated in coordinate or momentum space ?
 do they move collectively ?
 do some of them ‘melt’ ?
What do we measure in a collider experiment ?







particles come from the vertex. They have to traverse certain detectors but
should not change their properties when traversing the inner detectors
DETECT but don’t DEFLECT !!!
inner detectors have to be very thin (low radiation length): easy with gas
(TPC), challenge with solid state materials (Silicon).
Measurements:
- momentum and charge via high resolution
tracking in SVT and TPC in magnetic field (and
FTPC)
- PID via dE/dx inSVT and TPC and time of flight
in TOF
- PID of decay particles via impact parameter
from SVT and TPC
particles should stop in the outermost detector
Outer detector has to be thick and of high radiation length (e.g. Pb/Scint
calorimeter)
Measurements:
- deposited energy for event and specific particles
- e/h separation via shower profile
- photon via shower profile
Signatures of the QGP phase
Phase transitions are signaled
thermodynamically by a ‘step function’ when
plotting temperature vs. entropy (i.e. # of
degrees of freedom.
The temperature (or energy) is used to
increase the number of degrees of freedom
rather than heat the existing form of matter.
In the simplest approximation the number of
degrees of freedom should scale with the
particle multiplicity.
At the step some signatures drop
and some signatures rise
How do we know what happened ?


We have to compare to a system that did definitely
not go through a phase transition (a reference
collision)
Two options:
 A proton-proton collision compared to a GoldGold collision does not generate a big enough
volume to generate a plasma phase
 A peripheral Gold-Gold collision compared to a
central one does not generate enough energy
and volume to generate a plasma phase
The idea of two phase transitions
Deconfinement
The quarks and gluons deconfine because energy
or parton density gets too high
(best visualized in the bag model).
Chiral symmetry restoration
Massive hadrons in the hadron gas are massless
partons in the plasma. Mass breaks chiral
symmetry, therefore it has to be restored in the
plasma
What is the mechanism of hadronization ? How do
hadrons get their mass ?
Evidence: Some particles are suppressed

If the phase is very dense (QGP) than certain particles get absorbed
If things are produced in pairs then one
might make it out and the other one not.
Peripheral Au + Au
STAR Preliminary
Central Au + Au
If things require the fusion of very heavy
rare quarks they might be suppressed in a
dense medium
Evidence: Some particles are enhanced

Remember dark matter ? Well, we didn’t find clumps of it yet, but we
found increased production of strange quark particles
What is our mission ?
• Discover the QGP
• Find transition behavior between an excited
hadronic gas and another phase
• Characterize the states of matter
• Do we have a hot dense partonic phase and how
long does it live ?
• Characterize medium in terms of density,
temperature and time
• Is the medium equilibrated (thermal,
chemical)