While the universe as we know it is well described by the standard model of
particle physics, some important questions remain unanswered. Perturbative
Quantum Chromodynamics (pQCD) – a part of the standard model
– is a very successful description of hard, or short-distance, phenomena l,
where the “strong interaction” becomes weak due to asymptotic freedom.
For example, the production of jets in pp collisions at 1.8 TeV is well described
for jet transverse energies from 10-400 GeV 2. There is, however,
an important set of soft physics phenomena that are not well understood
from first principles in QCD: color confinement, chiral symmetry breaking,
and the structure of the vacuum. These phenomena are important: almost
all of the visible mass of the universe is generated by soft QCD and not
by the direct Higgs mechanism. The current masses of the three valence
quarks make up only about 1% of the mass of the nucleon 3.
In order to study these phenomenon, we seek to separate color charges
by heating matter until a quark-gluon plasma is formed. A conventional
electromagnetic plasma occurs at temperatures of about 104-105 K, corresponding
to the typical ionization energy scale of 1-10 eV. Theoreticalstudies of QCD on the lattice indicate that the typical energy scales of
thermally driven color deconfinement are in the vicinity of 170 MeV, or
2 x 10l2 K. In addition to providing information about the strong interaction,
achieving such temperatures would also provide a window back in
time. The color confinement phase transition is believed to have occurred
within the first few microseconds after the big bang.
In order to achieve such high temperatures under laboratory conditions,
it is necessary to use a small, dynamic system. For instance, experimental
fusion reactors heat a conventional plasma up to temperatures as high as
lo8 K over distance scales of meters and lasting for seconds. By colliding
gold ions at nearly the speed of light, we expect to achieve temperatures of
order 10l2 K over distance scales of order 10 fm and time scales of order 10-
100 ysa. Clearly one of the challenges in this endeavor will be to determine
whether such small and rapidly evolving systems can elucidate the bulk
behavior that we are interested in. Another challenge will be to use some
of the rarer products of the collisions to probe the created “bulk” medium.
The focus of these lectures will be on the results coming out of the Relativistic
Heavy Ion Collider (RHIC) experiments at Brookhaven National
Laboratory (BNL) . Earlier experimental results and some theoretical work
will be mentioned as needed, but a comprehensive review of heavy ion
physics will not be attempted. The RHIC spin physics program using polarized
protons will also not be covered.
2. The Machine and Detectors
The RHIC data described in these lectures were taken during the last three
years of running at RHIC, starting in the summer of 2000, as summarized
in Table 1. The runs were characterized by their species and their6
which is the cm collision energy of one nucleon taken from each nucleus.
For instance, a AuAu collision with 100 x A GeV on 100 x A GeV would
have 6 = 200 GeV. Most of the runs were several weeks in duration,
with two exceptions. The 56 GeV run, not intended as a physics run, was
only 3 hours long and data is only available from a preliminary subsystem
of one experiment (PHOBOS). The 19.6 GeV run was 24 hours long and
usable data were taken by three experiments. For the 130 and 200 GeV
runs, all four detectors participated: two large detectors/collaborations
with 300-400 collaborators each and two small detectors/collaborations
aRecall that one yoctosecond = lo-’* s.
with 50-70 collaborators each. These four detectors complement each other
and have provided a broad range of physics results. The BRAHMS experiment
(Broad RAnge Hadron Magnetic Spectrometer) focuses on tracking
and particle ID at high transverse momentum over a broad range of rapidity
from 0-3. The PHENIX experiment (Pioneering High Energy Nuclear
Interaction experiment) provides a window primarily at mid-rapidity, but
specializes in high rate and sophisticated triggering along with a capability
to measure leptons and photons as well as hadrons. The PHOBOS experiment
(descendant of the earlier MARS experiment) provides nearly 47r
coverage for charged particle detection, good vertex resolution, and sensitivity
to very low p, particles. The STAR experiment (Solenoidal Tracker
At Fthic) provides large solid angle tracking and complete coverage of every
event written to tape. More details concerning the capabilities of the
accelerator and experiments can be found in NIM journal issue dedicated
to the RHIC accelerator and detectors 5 .
Table 1. RHIC running conditions to date.
19.6, 200 GeV
Jan. 2002 200 GeV
Some data will also be shown from lower energy heavy ion collisions,
particularly from the CERN-SPS (Conseil European pour la Recherchk Nu-
Claire – Super Proton Synchrotron) will also be discussed. The top CERN
energy is 6 = 17.2 GeV.
3. Strongly Interacting Bulk Matter
In order to learn anything about QCD from heavy ion collisions, we must
first establish that we have created a state of strongly interacting bulk
matter under extreme conditions of temperature and pressure.
3.1. How Much Matter?
Figure 1 shows the charged particle distribution for central (head-on) AuAu
collisions in the pseudorapidity variable: q G – In tan(Ol2). These data
imply a total charged multiplicity of 1680 f 100 for the 19.6 GeV data and
5060 f 250 for the 200 GeV data 6 . While this number is considerably
,/T& = 19.6, 130, and 200 GeV. Data taken from PHOBOS 6.
Pseudorapidity distributions, dN,h/dq, for central (6%) AuAu collisions at
smaller than Avagadro’s number, it is substantial thermodynamically since
small-system corrections to conventional thermodynamics start to become
unimportant for systems with about 1000 particles or more 7.
The number of particles produced in a given AuAu collision varies widely
due to the variable geometry of the collision. Some collisions are nearly
head-on with a small impact parameter, while most collisions have a larger
impact parameter, with only a partial overlap of the nuclei. These cases
can be sorted out experimentally, using both the number of produced particles
and the amount of “spectator” neutrons seen at nearly zero degrees
along the beam axis. The impact parameter or “centrality” of the collision
is characterized by the number of nucleons from the original ions which
participate in the heavy ion collision, (Npart)o, r the number of binary NN
collisions, (Ncoll). More details can be found in Refs.
3.2. Elliptic Flow: Evidence for Collective Motion
Non-central heavy ion collisions have an inherent azimuthal asymmetry.
The overlap region of two nuclei is roughly ellipsoidal in shape. If there is
collective motion that develops early in the collision, this spatial anisotropy
Figure 2. Left panel: elliptic flow as a function of centrality as seen by STAR (data)
compared to hydrodynamic models (rectangles) lo. Right panel: peak elliptic flow as a
function of collision energy for ultrarelativistic collisions, taken from an NA49 compilation
can be converted to an azimuthal asymmetry in the momentum of detected
particles. This azimuthal asymmetry is characterized by a Fourier decomposition
of the azimuthal distribution:
dN/dr$ = No(l+ 2w1 cos4 + 2212 COS(24)), (1)
where r$ is the azimuthal angle with respect to the reaction planeb. The
left-hand panel of Fig. 2 shows that the elliptic flow parameter is quite
large, nearly reaching the values predicted by hydrodynamic models. These
models assume a limit of local equilibrium with collective motion of the bulk
“fluid”. The right-hand panel of Fig. 2 shows that this asymmetry is the
largest ever seen at relativistic energies.
Elliptic flow, in addition to indicating that there is collective motion,
can provide information about the type of motion. In particular, the p, dependence
of elliptic flow can distinguish between two limits: the low density
limit and the hydrodynamic limit (rapidly expanding opaque source). In
the low density limit, some of the produced particles are absorbed or scattered
once (and usually only once). In this case, for relativistic particles,
v2 is nearly independent of p,. In the hydrodynamic limit, in contrast, we
expect 212 oc p, for moderate values of p,. This effect comes about because
the expansion causes a correlation between normal space and momentum
bThe true reaction plane is defined by the impact parameter vector between the gold ions.
The experimental results shown have been corrected for the reaction-plane resolution,
which would otherwise dilute the signal.
Figure 3. Elliptic flow versus p , for all particles (left panel) lo, and for identified particles
(right panel) from STAR 12. The curves in the right panel refer to a hydrodynamic
space, forcing the highest p, particles to come from the surface, while low
p, particles can come from anywhere in the volume. Data from the SPS
favor the hydrodynamic limit 13. The left-hand panel of Fig. 3 shows a
clear linear relationship between elliptic flow and transverse momentum at
RHIC as well, while the right-hand panel shows that hydrodynamic models
not only describe the overall trend, but even describe the pions and protons
~0.06 I . . . I . . . I . . . I . . . I . * . I . . . I
> PHOBOS Au-AU
01 I . A. I . . . I . . . I . . . ‘ . ‘ . I . . . I ‘ -6 -4 -2 0 2 4 6
Figure 4. Elliptic flow as a function of pseudorapidity from PHOBOS 14.
Finally, elliptic flow can be examined as a function of pseudorapidity.
The expectation was that the elliptic flow would be nearly independent of
pseudorapidity as the basic physics of RHIC were expected to be invariant
under longitudinal boosts. Fig. 4 shows that w2 is strongly dependent on
pseudorapidity, a result which has still not been explained.
Taken together, these results show clear evidence of collective motion
and suggest a system at or near hydrodynamic equilibrium which is rapidly
expanding in the transverse direction and which does not exhibit longitudinal
3.3. Hanbury-Brown Twiss Effect: More Dynamics
Intensity interferometery, or the Hanbury-Brown Twiss effect 15, is a technique
used to measure the size of an object which is emitting bosons (e.g.
photons from a star or pions from a heavy ion collision). Boson pairs which
are close in both momentum and position are quantum mechanically enhanced
relative to uncorrelated boson pairs. Bosons emitted from a smaller
spatial source are correlated over a broader range in relative momentum,
which allows you to image a static source using momentum correlations.
For a given pair of identical particles, we can define their momentum
difference, f, and their momentum average, z. We can further define the
three directions of our coordinate system 16:
0 Longitudinal (Rl) – along the beam direction (S),
0 Outwards (R,) – In the (2, k) plane, I 2,
0 Sidewards (R,) – I i & I i.
For a boost-invariant source, the measured sidewards radius at low pT
will correspond to the actual physical transverse (rms) extent of the source
at freezeout, while the outwards radius will contain a mixture of the spatial
and time extent of the source. Particles emitted earlier look like they are
closer to the observer, which artificially extends the apparent source in the
out direction. In particular,
RZ – R: = iOf.2 – 2/31aZ, + (a: – a:), (2)
where is the transverse velocity associated with z, gT is the “duration
of emission’’ parameter, ox and uv are the geometric size in the out and
side directions, and ox,. is the space-time correlation in the out direction.
In the case of an azimuthally symmetric and transparent source, the
last two terms are taken to be small or zero and we have
Given the assumption of a boost-invariant, azimuthally symmetric and
transparent source, the HBT results from heavy ion collisions have been
-=E 8 a0 6
0 E895 H NA49 0 WA98
A E866 V NA44 * STAR
*+A + +T+
1.251 , * **+) , , ‘ii , , , , , , , I rr“ 1 i; 2 n
Figure 5. HBT parameters as a function of colliding beam energy. 17.
perennially confusing. From Eq. 3, we expect R,/R, 2 4 since most
sources should emit for a time which is of the same order as their size.
Some models of the Quark-Gluon Plasma predict an even larger value for
this ratio as the plasma might need to emit particles over a long time duration
in order to get rid of the entropy Is. However, as can be seen in
Fig. 5, R,/R, is basically unity at RHIC energies, na’ively implying an
instantaneous emission of particles over a moderately large volume.
This situation, along with the modest values of RI, has been termed the
“HBT puzzle”. Primarily, though, these data indicate a need to improve the
modeling of the collision. If you consider a source which is opaque, rapidly
expanding and also not boost invariant, the meaning of RZ – R: changes
since we must use Eq. 2 and not Eq. 3. Opacity reduces the apparent R,
value since you only see the part of the source closest to you in the out
direction. Transverse expansion along with opacity will decrease the ratio
further since particles emitted later are also emitted closer to the viewer,
reducing the magnitude of R,. Finally, a general longitudinal expansion
(not just coasting) must be taken into account since we know that the
source is not boost invariant. This effect would explain the small size of Rl
and has also been shown l9 to reduce the ratio R,/R,.
So, while HBT and elliptic flow have not been successfully described
in full detail by the hydrodynamic models yet, the qualitative message
they provide is very similar. The source is rapidly expanding (probably in
all three dimensions), opaque, and can be described as “hydrodynamically
equilibrated bulk matter”.