Exploring Qcd With Heavy Ion Collisions

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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.

3

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

4

-5 0

Figure 1.

,/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

5

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

ll.

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.

6

0.16

0.14

0.12

0.08

0.06

0.04 *

+-8 –

+

om +-

P, (GeW

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

model description.

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

separately.

~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

rl

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

7

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

boost-invariance.

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

8

c-2

1

0.5

-=E 8 a0 6

4

0 E895 H NA49 0 WA98

A E866 V NA44 * STAR

*+A + +T+

u)

. I

1.251 , * **+) , , ‘ii , , , , , , , I rr“ 1 i; 2 n

1

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

9

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”.

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