1. Lecture 2: Bulk plasma matter ? Lecture 3: Probing the plasma
Modern Nuclear Physics with RHIC: Recreating the Creation of the Universe
Rene Bellwied
Wayne State University
Lecture 1: Why and How ?
Lecture 2: Bulk plasma matter ?
Lecture 3: Probing the plasma

2. Let there be light The Hertzsprung-Russell 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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 K.

9. 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 !

10. 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.

11. The universe is accelerating ???
Based on supernovae measurements
The Hubble Key Project determined in 2000 how fast the universe is expanding. The group
concluded that the universe is expanding at a rate of 74 km/sec/megaparsec (one parcsec is
3.26 light-years) with an uncertainty of 10%.

12. Dark Energy – the new puzzle of physics

13. 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 ?

14. 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

15. 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
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)
3C58
RXJ1856

16. 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)

17. 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.

18. A Cosmic Timeline Age Energy Matter in universe
GeV grand unified theory of all forces
10-35 s GeV 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 MeV nuclei
6*105 years 0.3 eV atoms
Now 3*10-4 eV = 3 K
(15 billion years)

19. 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 seconds. This rapid expansion is called inflation

20. 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 ?) GeV
10-35 s Grand unification scale (strong and electroweak) 1015 GeV
Inflationary period s
10-11 s Electroweak unification scale 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 !

21. The Cosmic Timeline

22. Going back in time

23. 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 m diameter) but it is a finite volume that can be exposed to pressure and temperature

24. 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

25. 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

26. Confinement The strong interaction potential
Compare the potential of the strong & e.m. interaction
Confining term arises due to the self-interaction property of the colour field q1 q2
a) QED or QCD (r < 1 fm)
b) QCD (r > 1 fm) r
QED QCD
Charges electric (2) colour (3)
Gauge boson g (1) g (8)
Charged no yes
Strength

27. 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.
In both QED and QCD the coupling strength depends on distance.
In QED the coupling strength is given by:
where a = a(Q2  0) = e2/4p = 1/137
In QCD the coupling strength is given by:
which decreases at large Q2 provided nf < 16.
em  em
Q2»m2
Q2 = -q2

28. 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 aem 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 as is strongly varying with distance - can’t be ignored.

29. 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:
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.

30. 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.
Note: a phase transition is not expected in binary nucleon-nucleon collisions.
The temperature inside a heavy ion collision at RHIC can exceed
1000 billion degrees !! (about 10,000 times the temperature of the sun)

31. 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.
In the sense that any direction is possible the symmetry is still present.
Below the Curie temperature the underlying rotational symmetry is hidden.
Above the Curie temperature the rotational symmetry is restored.

32. 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

33. 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 = MeV
Results
Shown for B1/4 = 145 MeV and as = 2.2 and ms = 279 MeV
T. deGrand et al, Phys. Rev. D 12 (1975) 2060

34. 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.

35. Estimating the critical parameters, Tc and ec
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

36. Lattice QCD There are two order parameters
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)
(F. Karsch, hep-lat/ )
e/T4
T/Tc
Lattice Results
Tc(Nf=2)=1738 MeV
Tc(Nf=3)=1548 MeV
0.5
4.5 15 35
GeV/fm3 75
T = MeV
e ~ GeV/fm3

37. Lattice QCD: the latest news (critical parameters at finite baryon density)

38. 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.
where m is the quark chemical potential, mq = - mq and b = 1/T.
Taking into account the number of degrees of freedom
Consider two extremes:
1. High temperature, low net baryon density (T > 0, mB = 0).
2. Low temperature, high net baryon density (T = 0, mB > 0).
mB = 3 mq

39. 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:
~ 2-8 times normal nuclear matter density
given pFermi ~ 250 MeV and r ~ 2m3/3p2

40. How to create a QGP ? energy = temperature & density = pressure

41. Let’s collide two heavy nuclei (1)

42. Let’s collide two heavy nuclei (2)

43. Let’s study all phases of the process
Freeze-out
Hadron Gas
Phase Transition
Plasma-phase
Pre-Equilibrium
Hard scattering
In fact we want to understand all processes that are involved in these violent heavy ion collisions. The strategy is to measure as many signals as possible. But here I would like to point out why hard processes are of particular importance.
Looking at a (simplified) Space-time evolution of a RHI collision:
Similarly to the evolution of the Universe, the RHI go through different stages:
If the QGP was formed, it will only live for s !!!!
BUT does matter come out of this phase the same way it went in ???

44. In the beginning quark – gluon
~ 100 s after Big Bang
Nucleosynthesis begins
~ 10 ms after Big Bang
Hadron Synthesis
strong force binds
quarks and gluons in massive objects:
protons, neutrons mass ~ 1 GeV
In the beginning quark – gluon
plasma
time
temperature
STAR
Look at the
In the beginning
Expanded and cooled - Hadron synthesis
Light nuclei
Atoms, stars , galaxies, supernovae explosions
Now (the Thinker) we are looking back trying to solve the mysteries of the early Universe: Why almost massless quarks formed massive hadrons? How did colored objects conspire to bind into colorless matter ? We built RHIC hoping to find the answers of these questions.
In RHIC we can not make time go backward, but we can prepare in the laboratory a system that is as hot as the early Universe.
In our detectors we can not detect the quark-gluon plasma – we see hadrons, leptons and gammas.

45. The RHIC Complex 6 5 3 4 1 2 1. Tandem Van de Graaff
2. Heavy Ion Transfer Line
3. Booster
4. Alternating Gradient Synchrotron (AGS)
5. AGS-to-RHIC Transfer Line
6. RHIC ring 6 5 3 4 1 2

46. The STAR Experiment 450 scientists from 50 international institutions
Conceptual Overview

47. The STAR Experiment construction from 1992-2000 data taking from 2000-2010 (?)
Overview while under construction

48. The STAR Detector Magnet Barrel EM Cal (BEMC) Coils
Central
Trigger
Barrel
(CTB)
ZCal
Time
Projection
Chamber
(TPC)
Barrel EM Cal (BEMC)
Silicon Vertex Tracker (SVT) Silicon Strip Detector (SSD) mVertex Detector
(2006)
FTPC Endcap EM Cal FPD
TOFp, TOFr

49. The STAR Experiment (TPC)
Construction in progress

50. The STAR Experiment (SVT)
Construction in progress

51. The STAR Experiment (SVT)
The happy crew after 8 long years

52. Actual Collision in STAR (1)
Actual STAR data
for a
peripheral collision

53. Actual Collision in STAR (2)
Actual STAR data for a central collision

54. 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, p, K, f, L, r, X, W, d, D, J/y, 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 ?

55. 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’ ?

56. 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

57. 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

58. 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 Gold-Gold 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

59. 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 ?

60. 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.
If things require the fusion of very heavy rare quarks they might be suppressed in a dense medium
Central Au + Au
Peripheral Au + Au
STAR Preliminary ?

61. 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

62. 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)