Charmonium II:
Nuclear Collisions
Thomas J. LeCompte
Argonne National Laboratory
1
Review of Yesterday


Charmonium is a bound state of a charmed quark and
antiquark
The attractive force between them has two pieces
 A Coulomb-like part, which dominates at short distances
 A spring-like part, which dominates at long distances

The charmonium wavefunctions
 Are Hydrogen-atom like
 Can be described with H-atom like quantum numbers, e.g. 3S1
 Drive the production properties

Charmonium production
 Is not a simple story
 Cannot be understood without considering the color quantum
numbers
2
Three Kinds of Confinement
1. Uncle Jake’s “two-to-five”
stint in Leavenworth
2. Magnetic Poles: break a magnet in
two, and you still have a N-S pair.
3. Quark confinement – free
quarks seem not to exist, and
only colorless hadrons are seen.
#2 is often used as an analogy for #3
In my opinion, this is a bad analogy
3
Semi-Classical Quark Confinement
Yesterday’s not-too-terrible model of the quark-antiquark force law:
A
F  2  Br
r
A Coulomb-like part
This is just like QED:
  E  4
A spring-like part
This piece comes from the nonAbelian nature of QCD: the fact
that you have 3-gluon and 4-gluon
couplings.
In QED, there is no gg coupling, so
this term is absent
In the interest of full disclosure:
  EQCD  4QCD
The same thing happens with the quark-diquark
forces. [Diquarks are also in a 3bar representation
of SU(3)]
(sometimes called the
“chromoelectric” force)
There are MUCH better potential models than what
I have shown. These models use the quarkonia
spectra to fit their parameters.
4
More Quark Confinement


Start with a quark antiquark
pair
Pull them apart, and the color
lines stretch. Potential energy
increases by ½Br2
 You can think of these color lines
as “strings” connecting the quarks


Eventually, ½Br2 > ~m() and
one can pop an antiquark-quark
pair from the vaccuum
Instead of a free quark, now
you have two colorless hadrons
This is not the way to observe
free quarks – ironically, one of the best things
to do is the reverse. You try and get the quarks
close to each other – so as is small. This is
called “asymptotic freedom” and is the subject
of another talk.
5
Deconfinement

Suppose we repeat the same experiment in an environment
gradually increasing the surrounding energy density
 The additional energy needed to pop a quark-antiquark pair decreases
 It becomes progressively easier to “break the string” holding quarks
together
 The quarks act more and more like free particles
 The other ends of their “color/glue strings” dance from quark to quark
 Having the quark connected to an ensemble of particles (instead of just one)
causes it to behave more like a free quark
 From experience, I can say working for seven bosses is like working for
yourself. It’s the same for quarks.

We have a deconfined state
 a quark gluon plasma
Last talk – the left hand piece of the force law
This talk – the right hand piece
6
Phases of Nuclear Matter
From the Nuclear Physics Wall Chart
(“You don’t have to be a nuclear physicist
to understand nuclear science”)
In a QGP, the coulomb
part of the interaction
dominates; the
confinement part is
overcome by the many
nearby color charges.
7
What Is A Quark-Gluon Plasma?
My recollection of what a QGP was
supposed to be prior to RHIC data,
was a thermally and chemically
equilibrated system of noninteracting quarks and gluons which
were deconfined over distance scales
much larger than a typical hadron. Lanny Ray, University of Texas
… very hot, dense matter can dissolve into
a mass of loosely associated quarks and
gluons known as a quark-gluon plasma, or
QGP, where particles would behave
differently than they do in normal nuclei –
Physical Review Focus
Physicists believe that RHIC collisions
will compress and heat the gold nuclei
so much that their individual protons
and neutrons will overlap, creating an
enormously energetic area where, for
a brief time, a relatively large number
of free quarks and gluons can exist.
This is the quark-gluon plasma. – BNL
Public Web Page
In … ordinary matter … quarks are
never free of other quarks or gluons
… at the heart of these collisions, the
ties that bind quarks and gluons may
have melted, creating a soup-like
plasma of free-floating individual
particles – LBL Public Web Page
Many opinions – but deconfinement is a (the) common thread
8
Reaching the QGP
Two beams of nuclei
traveling towards
each other.
(in the COM frame)
There exist both fixed
target and colliding
beam experiments.
Upon collision, the
pressure and
energy density is
enormous.
If large enough, a
deconfined
state is produced.
As the system
expands and cools,
Hadrons form and
leave the interaction
region.
Detectors measure
these hadrons and
infer the collision
properties.
See S. Bass’ talk
9
Some QGP Questions

Is this actually a phase?
 Is there a phase transition?
 What is the order paramater?
 Is this a 1st order or 2nd order phase transition? Is
there a latent heat?

Or just a “state”?
 An analogy might be a block of glass, a piece of
fiberglass insulation and a pile of sand
 Macroscopically, very different properties, but not
because of properties at the microscopic level

Is QGP an event-wide phenomenon?
 Is it all or nothing within an event? Or is there a
mixed phase?
 With a specific set of initial conditions, do you
always form a QGP, or are there two categories of
an event: events with and without a QGP
 Is there a discontinuity?


What are the exact conditions required to
form a QGP?
How are you sure you’ve made one?
These questions
will occupy the
experimental
programs for
some time to come.
(i.e. I don’t have answers)
The hints that
have been obtained
from the SPS and
RHIC so far
point to a rich and
complex
phenomenon.
10
Charmonium Suppression

Start with a J/y
 This works with other charmonium states
as well
 The J/y is easiest to observe – lamppost
physics


1.
2.
Put it in a sea of color charges
The color lines attach themselves to
other quarks
 This forms a pair of charmed mesons


These charmed mesons “wander off”
from each other
When the system cools, the charmed
particles are too far apart to
recombine
 Essentially, the J/y has melted
Often called Debye screening, in analogy with E&M
3.
c.f. Matsui &
Satz (1986)
11
More on Charmonium Suppression

Another way of looking at it is in terms of energy
density:
 When the energy density is large enough, the color string
between the quark and antiquark pair can break
 This is exactly the same condition that causes quarks in hadrons
to deconfine in a plasma
A simple (simplistic?) view is “All hadrons melt. The J/y is a
hadron.”

The more color charges that can get between the
charmed quark and antiquark, the more the
attraction is disrupted
 It’s easier to “melt” large hadrons than small ones:
The y(2S) is bigger than the J/y
(radial quantum number k = 2 vs. k = 1)
The J/y is bigger than the upsilon family, and so on
 This provides a very interesting prediction that can be tested
experimentally
12
The NA50 experiment
A closed-geometry
muon spectrometer,
like many early
charmonium experiments.
(see yesterday’s talk)
13
The Plot That Got Everyone Excited
From the CERN
NA50 Experiment
This is a complicated
plot: there is a lot of
information in a small
space!
I will spend the next
few slides going
through it.
14
How Excited?
A NEW FORM OF NUCLEAR MATTER has been detected
at the CERN lab in Geneva – Physics News #470
CERN claims quark-gluon first
10 February 2000 physicsweb
First data on the quark-gluon plasma reported at CERN
Europhysics News
'Little Bang' creates cosmic soup – BBC News
Britney Spears set to release second album
- Newsweek
15
The y-axis
 ( AB  J /y )  BF ( J /y   )
 ( AB   DY )

The plot uses the ratio of
the measured numbers of
J/y’s normalized to
Drell-Yan dimuons
A nucleus is a hadron – a big hadron
 It has p.d.f’s, just like nucleons (and mesons too!)
 G(x) for a nucleus may or may not be simply A x G(x) for a nucleon
 Complications: shadowing, anti-shadowing, Cronin effect… [see Dave Soper’s talk]

Normalizing to Drell-Yan is a good idea because
 It tries to compensate for the fact that a nucleon in a nucleus is different
from a free nucleon
 The dimuon final state is similar to the J/y signal – many systematics cancel

Normalizing to Drell-Yan is a bad idea because
 Drell-Yan is an quark-antiquark induced process
 J/y production is a gluon-gluon induced process

Despite the problems this normalization procedure probably does
more good than harm.
16
The x-axis

The x-axis is conceptually simple: the average distance
the J/y travels through the medium
 The amount of J/y dissociation should be proportional to the
distance it travels
 The sudden drop in yield is then interpreted as an increase in
the J/y dissociation probability per unit length

Unfortunately, this is not a directly measured quantity
 It has to be inferred
 Not everyone is happy with the chain of reasoning leading to this
inference
 Averages of distributions can be misleading
F(<x>) may not equal <F(x)>.

Eventually NA50 dropped it
 Later measurements are plotted against more directly measured
quantities
17
The Problem of Impact Parameter
b is large
In a head on or
“central” collision,
there is a lot of
energy transferred –
forming a QGP?
In a glancing blow or
“peripheral” collision,
not much of
excitement happens.
b is small
Impact parameter cannot be measured directly. So experiments
have to use a measured quantity as a proxy for impact parameter:
multiplicity, total transverse energy, etc…
18
Estimating Centrality
Many forward
neutrons:
MID-central collisons
Increasing Multiplicity in Detector
Few forward
neutrons –
EITHER a
peripheral or a
highly central
collision
19
Another Plot that Caused Excitement
Also from the CERN
NA50 Experiment
This is S-U data; it was PbPb that showed the large
J/y suppression
Apology: there was a
lot more going around
CERN at that time
than just the J/y
suppression story.
This is the ratio of the y(2S) production
relative to the J/y. Note that you always
have more y(2S) suppression than J/y
suppression – exactly what you expect in a
QGP
Even though I’m going
to concentrate on one
part of the story,
there’s a lot more
that I am not going to
talk about.
20
The Line on The Plot



Even ignoring the last point, it’s clear
that the J/y yield relative to Drell-Yan
is falling as the nuclei get heavier.
This is called “A-dependence”, and it is
often parameterized as  ~ Aa
What the plot shows is for light nuclei,
there is already some J/y suppression
The point of the NA50 data is not that there
was J/y suppression at all. The point was that
there was too much in Pb-Pb collisions. The
argument was quantitative, not qualitative.
This point often got lost by non-experts trying
to understand and evaluate the NA50 results.
21
J/y A-dependence
DrellYan
1.1
1.05
Open
Charm
a
1
0.95
E-772
0.9
NA-3
NA-38
E-789
0.85
E-537
0.8
10
15
20
25
30
35
40
45
Center of Mass Energy (GeV)
The best fit is something like a ~ 0.92
The y(2S) has a similar A-dependence
(see next slide)
22
y(2S) A-dependence
NA-50

y(2S) measurements are a tough
business
 Yield is only ~2% of the J/y
 In a closed-geometry/high-rate
experiment, resolution smears the J/y
into the y(2S) and you have a
shoulder, not a peak
 In an open-geometry experiment,
you’re fighting the 2% factor.


The [y(2S)]/[J/y] yield
ratio is roughly independent
of target A
 Conclusion: A-dependence is
similar
 Error bars still allow some
difference in the A-dependence
 NUSEA has measured this as
Da ~ 0.02-0.03
A hard choice to make
C. Lourenco
23
Understanding the J/y A-dependence

Drell-Yan has a ~ 1
 Therefore the nuclear quark and antiquark p.d.f’s can’t have
changed by too much
 Sum rules limit how much the gluon can change

Open charm production has a ~ 1
 That tells us we are making about as many charmed quarks as
before – they just aren’t ending up paired as J/y’s.

Inference: we are making as many J/y’s as a = 1 would
predict, but they are disappearing in the medium
 Remaining Hypotheses:
QGP
Absorbtion
Even before we come to the last data
point, there are mysterious goings-on
with charmonium in nuclei.
24
J/y in Nuclear Media

Could it be suppression from Debye screening?
 Note that the word “plasma” never appeared in my discussion
 Are there enough color charges in cold nuclear matter to dissociate a
J/y?
 This is a quantitative question, and the answer appears to be “no”.
 More to the point – this model predicts a rather substantial and
unobserved difference in A-dependence between J/y and y(2S):
 If aJ/y = 0.92, ay(2S) ~ 0.79 [based on relative size of hadrons]

What else can this be?
 If this loss in yield is due to an interaction between the J/y and
nucelons, the cross section inferred is about 6 mb: a little larger than
the J/y itself!
 You will read that the J/y is “blacker than black”: that’s not quite true; many
of the comparisons of cross-section and size drop a factor of .
Nevertheless, the J/y is quite black.
 One would expect the tightly bound J/y to be relatively non-reactive
 An analogy from chemistry: a tightly bound helium atom is also non-reactive
25
Color Octet to the Rescue

From the last talk…
 Color Octet Model suggests that the charm-antiquark pair
forms in a color octet state
 Later this state emits a soft gluon and forms the J/y


The suppression can occur at any time: it does not have
to wait until the J/y is formed
A color-octet state will be very reactive
 To take the helium analogy, He is very non-reactive
 But the He+ ion is VERY reactive: it will oxidize oxygen!
 This can explain the large cross-section
Before the J/y is formed, you have an interacting octet precursor
with a strong A dependence
After the J/y is formed, the relatively inert J/y sails through
26
CoMovers



There’s [at least] one other source of suppression:
co-movers: hadrons moving near the J/y with small relative
velocity.
You might ask “how can something moving slowly impart
enough energy to disrupt a J/y?”
It takes less energy than you think – all you have to do is (for
example) flip the spin of one quark.
 Then you have turned a 3S1 J/y into a 1S0 hc – invisible to the
experiments.
1.
Hadron’s
color field
disrupts
the J/y.
hadron
J/y
Hadron approaches the J/y.
J/y
3.
2.
J/y remnants move apart.27
Three phases of suppression

Before
 Before the J/y formation
 Color-octet precursor interacts strongly, even with cold nuclear
matter
 Gives rise to the observed A-dependence:  ~ A0.92

During
 While the J/y is in the nuclear medium
 This is the Debye screening signature of Matusi and Satz

After
 As the hadrons escape the scene of the crime
 Co-movers can disrupt or destroy J/y’s after they have exited
the nuclear medium
28
Conclusions from
NA50 and Aftermath
Warning: Personal Opinion Here

Charmonium in nuclear media has a very rich phenomenology – richer
than anticipated at the beginning of this enterprise. There is a lot
of interesting physics going on!
 It’s hard to be “simple” and “interesting” at the same time.


The down side of this is that charmonium suppression is no longer
the smoking gun than it was once thought to be. It’s still a powerful
piece of evidence for understanding what is going on in nuclear
matter.
We have – for good or ill – moved past the phase where qualitative
understanding is good enough. We need quantitative modeling of all
three phases - before, during and after – so they can be compared
them with data.
29
More Recent NA50 Data


More data provides
a clearer picture of
what NA50 saw
earlier
The overall picture
is similar, but there
are more data points
 That makes the
transition look less
abrupt.
 See next slide…
L has been dropped in
favor of a more
“experimental” variable.
30
Do We Expect an Abrupt Transition?

There are multiple sources of J/y’s
 8½% come from y(2S) decays
Determined from yield in  channel + branching fractions
 35-40% of them come from c decays
See Talk #1

The Debye screening model says that large
mesons should be destroyed by the QGP more
readily than small ones
 The y(2S) is bigger than the c’s, which are bigger than
the J/y
 Barring overlap, there should be three transitions – not
one
31
Next Steps: RHIC



Our understanding of
charmonium hadroproduction
improved enormously once the
Tevatron collider data entered
the picture
Similarly, heavy-ion physics now
has a colliding beam accelerator,
RHIC (at BNL) available to probe
charmonium in nuclear matter
RHIC
 is a two-ring collider, able to
accelerate nuclei as heavy as gold (A
= 197) to 100 GeV/nucleon
Can (and does) accelerate different
ions in different rings
 has 4 experiments (STAR, PHENIX,
BRAHMS and PHOBOS)
32
The PHENIX Experiment


Large Acceptance Colliding
Beam Detector
Emphasizes Leptons
 Forward and Backward Muon
Spectrometer Arms
 Central 2-Arm high resolution
electromagnetic calorimeter
(for electron identification)
Painful for me to say: I used to be
the physics coordinator for STAR
Probably the detector best suited
for charmonium studies.
The Other RHIC Experiment
33
Calorimeter
Muon Detector
The Real PHENIX
Magnets and Muon Shielding
34
Other RHIC Experiments

STAR
 A 4 solenoidal detector (like
CDF, D0, CMS…)
 Emphasizes hadron
identification
 A calorimeter that is less
capable than PHENIX’s
But with larger coverage
 Tracker is a Time Projection
Chamber (TPC)
These have very slow readout
Makes triggering on the J/y
difficult

BRAHMS & PHOBOS
 Two small acceptance
detectors
STAR probably has the ability to
“confirm” a PHENIX result.
BRAHMS and PHOBOS probably
don’t have the acceptance/yield
35
Life at RHIC is Hard
A picture is worth a
thousand words. I’ll let
the pictures of PHENIX
and STAR Au-Au events
speak for themselves. 36
J/y in d+Au Collisions at PHENIX
 invariant mass
Yield is ~ 1250 events
ee invariant mass
Top: all data
Bottom: wrong sign subtracted
37
Transverse momentum distribution

Rapidity distribution
Physics with J/y’s

With many hundreds of
J/y’s, PHENIX can
measure distributions
 Plots to the left show
kinematics of J/y
production
 PHENIX is already moved
from showing a signal to
making measurements
Thus far, everything
shown is for pp or dAu
collisions
 What about AuAu?
38
Go For The Gold! (Au-Au Collisions)

axes from
present Au-Au run…

PHENIX has a hint of a signal
already of J/y’s in this year’s
Au+Au collisions.
STAR wants very badly to
show a similar plot:
 I expect them to be able to do
this eventually
Once the signals have been established, both experiments will be
investigating the yield of J/y’s, particularly as a function of collision
centrality.
Theoretical predictions can and will be compared with these
measurements as a way of characterizing the properties of the RHIC
collisions: the yield is related to the color charge density.
Stay tuned!
39
Summary

The good news: the phenomenology of charmonium in
nuclear collisions is richer than anyone supposed
 There is enough interesting physics going on to support a few
dozen careers

The bad news: the phenomenology of charmonium in
nuclear collisions is richer than anyone supposed
 Things are not as simple as first supposed

The goal of the field has shifted from “discovering the
quark-gluon plasma” to “characterizing the nuclear
medium under extreme conditions”
 This is a plus – we’ve moved past presupposing how things will
behave and towards measuring and understanding what really
happens
 Charmonium is a critical probe in this wider effort
 RHIC data in Au+Au collisions is right around the corner
40