Charmonium I:
Introduction & Production Models
Thomas J. LeCompte
Argonne National Laboratory
1
Preliminaries



Thanks to the organizers for inviting me! I had a great
time in the Dairy State, and I learned a lot.
I talk too fast – so slow me down by interrupting me
with questions!
In this talk, I try to distinguish between what is:





Calculated
Measured
Inferred
Just my opinion
If you can’t tell, speak up!
2
An Introduction To Charmonium
DD threshold
3.8 GeV
3S
1
y(2S) or y’
3P
2
Mass
3P
1
3P
0
3S
1
3 GeV
J/y
c2
c1
c0
Charmonium is a bound state
of a charmed quark and
antiquark. It is “almost
nonrelativistic”: b ~ 0.4:
Hence the hydrogen atom-like
spectrum
Only the most important
(experimentally) states
are shown. Many more
with different quantum
numbers exist.
States can make radiative
(E1) transitions to the
other column.
3
Review: Quantum Numbers
Spin Angular
Momentum
2 S 1
J / y  S1
3
LJ
Orbital Angular
Momentum
Total Angular
Momentum
Means:
Quark Spin=1 (3 = 2 x 1 + 1)
Quark Orbital Ang. Mom. = 0
Total J/y Spin = 1
J
PC

1
Means:
Total J/y Spin = 1
Parity is Odd
Charge Conjugation is Odd
4
An Introduction To Charmonium
DD threshold
3.8 GeV
3S
1
y(2S) or y’
3P
2
Mass
3P
1
3P
0
3S
1
3 GeV
J/y
c2
c1
c0
Charmonium is a bound state
of a charmed quark and
antiquark. It is “almost
nonrelativistic”: b ~ 0.4:
Hence the hydrogen atom-like
spectrum
Only the most important
(experimentally) states
are shown. Many more
with different quantum
numbers exist.
States can make radiative
(E1) transitions to the
other column.
5
Quarkonium Potential
A 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
  EQCD  4QCD
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
This will be discussed in more detail in tomorrow’s
talk
There are MUCH better potential models than what
I have shown. These models use the quarkonia
spectra to fit their parameters.
(sometimes called the
“chromoelectric” force)
6
Discovery of the J/y


October, 1974
Near
simultaneous
discovery




Ting et al. at
BNL AGS
Richter et al. at
SLAC SPEAR
Quarks were no
longer
mathematical
objects, but
particles that
moved in a
potential
This work got
the 1976 Nobel
prize in physics
p + Be→ e+e- + X at AGS
e+e- annihilation at SPEAR
c.f. Fred Olness’ talk
7
Aside: Why y?
Decay is:
y(2S) → J/y + + + Followed by J/y → e+eIt’s very convenient to
have the particle name
itself!
Mark I (SPEAR) Event Display
8
Homework

#1 – For each quarkonium (i.e. charmonium and bottomonium) state
in the PDG, give
 Quantum numbers: k, n, L, S (like the Hydrogen atom)
 Spin, parity and charge-conjugation parity



#2 – The J/y is not the charmonium ground state; it’s the first
excited state. Why was charmonium discovered with this state as
opposed to the ground state? (The same is true for bottomonium)
#3 [version for theorists] Assume that the “springy” part of the
force can be treated as a perturbation to the Coulomb potential
(reminder: think “Laguerre polynomials”), and calculate the mass
differences of the y(2S) and c states and of the y(2S) and J/y
states; from this extract values for A and B in the force law (slide
5). Hint: you should get a term like 5n2 + 1 –3l(l+1) .
[version for experimenters] Ask one of your theorist colleagues
what the answer to #3 is.
9
Why is the J/y so Narrow?

J/y → open charm is kinematically
blocked
 m(J/y) < 2m(D)

J/y → gg → hadrons is blocked by
quantum mechanics
 J/y-g-g coupling is zero: more on this
later

J/y → ggg → hadrons is allowed
(but suppressed)
( J /y )  88  5 keV
Together, this
is called the
“OZI Rule”
 But now there are three powers of as.
 This is ~2/3 of the partial width

J/y → g* → hadrons/leptons is
allowed
 This is ~30%of the partial width
 There is also a few percent of radiative
transitions
Strong decays are
suppressed so much
that EM decays
are competitive
10
So How Are J/y’s Produced?

Theory #1 – Drell-Yan Production
 Idea: the electromagnetic decay partial width (~26 MeV) is
about half that of the strong decay partial width (~59 MeV).
Production rates should be comparable, but the input channel of
quark and antiquark is (possibly) more accessible, so maybe this
dominates.
 Prediction: the J/y cross-section should be 4x higher for beam as + beam:
  (Qq )
2
 (  N  J /yX ) Q(u ) 2 (2 / 3) 2


4

2
2
 ( N  J /yX ) Q(d )
(1 / 3)
Aside: this prediction assumes an equal number of u
and d quarks in the target. This is (incorrectly)
called an “isoscalar” target. Even with non-isoscalar
targets, the effect is small: Fe has 5% more d
quarks than u-quarks.
Apology: I am only going to discuss hadroproduction
today. Photoproduction is an interesting story, and
there is some very high-quality data from HERA.
What do the
data show? …
11
A Typical Fixed Target Experiment
Examples: CERN NA3,
FNAL E-537
Downstream
Tracking
Muon
Detector
m+
Target
Beam
mHadron
Absorber
This kind of experiment
looks only at the muons
produced, and thus can
tolerate very high rates.
Magnet
Muon Shield
p /   N  X  J /y  m  m 
12
J/y Production with + and + beams
Pion Beam Charge Comparison
18
16
14
E-331
E-705
nb/nucleon
12
10
negative pions
positive pions
NA3
8
E-444
6
NA3
E-672/706
NA3
4
E-537
2
0
10
15
20
25
30
35
sqrt(s) (GeV)
13
Inferences from the Measurement

The cross-section might be 10% or 15% larger for beam, but it is certainly not a factor of 4.
 This is true for all energies and all targets
Targets: H, Be, Li, C, Fe, Cu, W, and Pt


Drell-Yan cannot be the dominant production mechanism
for J/y’s
Theory #2 – QCD quark-antiquark annihilation
 Idea: maybe the production is still initiated by quark-antiquark
annihilation, but mediated by gluons rather than photons
 Prediction: + and - production is nearly equal
Quark content has different electrical charge, but the same color
charge
 Prediction: production from antiproton beams – which contain
valence antiquarks - should be substantially (factor of >5-10)
larger than production from proton beams
This difference should be even bigger at low energy
14
Production with p and pbar beams
Proton/Antiproton Comparison
18
16
14
nb/nucleon
12
E-705
10
Pbars
Protons
E-444
8
NA-3
E-331
6
4
E-672/706
UA-6
NA-3
E-537
2
0
10
15
20
25
30
35
sqrt(s) (GeV)
15
Inferences from the Measurement

Production from pbar beams is larger than from proton
beams, and the difference is greatest at lowest energy
 Theoretical success?


Instead of being a factor 5-10 difference, it’s (at most)
50%, and more typically 20-25%
Quark-antiquark annihilation cannot be the dominant
production mechanism for J/y’s
 It can be a piece of it, but not a very large piece

Conclusion – whatever process produces J/y’s, it must
be gluon induced
 Process of elimination: if it’s not the quarks…
16
The Trouble With Gluons

Remember, we know that J/y → gg is forbidden
 J/y is a 3S1 (1--) state
 Violates charge conjugation parity
Left side is C odd, right is C even
 If that isn’t bad enough, spin-statistics forces the amplitude to
be zero


That means gg → J/y is also forbidden
ggg → J/y requires a 3-body collision
 Infinitesimal rate
There seems to be no mechanism
that allows gluons to fuse into
a 3S1 state like the J/y
17
The Color Singlet Model (CSM)


A J/y (or any charmonium particle) is a bound state of
a charmed quark and antiquark in a color singlet state.
Therefore, one calculates the production of such a
state
 The TOTAL production rate is the sum of the direct production
rate plus the production rate as the daughter of some other
particle
 Note BF(c1,2 → J/y + g) are 30% and 13%

Predictions:




Virtually all J/ys come from the decays of c’s.
c0:c1:c2 = 15:0:4
This is because gg → c1 is suppressed, but gg → c2 is allowed
Virtually all y(2S)’s come from the decays of b’s
m(y(2S))>m(c), so production from c decay is kinematically blocked
18
A 2d Generation Fixed Target
Experiment
Examples:
FNAL E-705, 706/672
Downstream
Tracking
Calorimeter
Muon
Detector
m+
Target
m-
Beam
Upstream
Tracking
This kind of experiment
also looks at particles
produced in association
with the J/y.
Magnet
g
Muon Shield
p /   N  X (g ?)  J /y  m  m 
19
Selected Results
Experiment
Sqrt(s)
(GeV)
Fraction of J/y’s from c’s
E-610
20.5
37%
E-672/706
31
44%
E-673
18.9-21.6
31-47%
E-705
24
40%
E-771
39
44%
GAMS
8.4
44%
HERA-B
41.5
32%
R806
62
47%
WA11
18.6
30%
Worse, many experiments saw y(2S) production
even when (b) was small or zero.
Strangely, this did not seem to kill the CSM…20
More Selected Results
Experiment
Sqrt(s)
(GeV)
c1:c2 Ratio
E-610
20.5
0.9 ± 0.4
E-672/706
31
0.57 ± 0.19
E-673
18.9-21.6
0.96 ± 0.64
E-705
24
0.52
E-771
39
.53 ± .22
WA11
18.6
1.5 ± 0.6
CSM Prediction is 0
+0.57
–0.27
A typical experiment (E-771)
This ensemble of measurements
is 4.2 different from 0
CSM predicts only the right
peak is there.
This STILL did not seem to kill the CSM…21
A Typical Colliding Beam Experiment
m+
Muon detectors
g
Calorimeter:
detects c photons &
Serves as hadron
absorbers for muon
detection
Outer tracker: in 1.5-2 T
magnetic field
m-
Beams-eye view of a typical detector
Silicon vertex detector
– for precision track
impact parameter
measurement
22
The Plots That Finally Killed the CSM
J/y’s not from c’s or b’s
y(2S)’s not from b’s
Theory and Measurement Disagree by a factor ~50 (red arrows)
Even astronomers would call this poor agreement!
23
Ingredients of the last plot
Start with the J/y
cross-section
Remove the events that come
from bottom quark decays
24
Ingredients of the last plot II
2/3 of the J/y’s are
produced directly.
This is not the few %
predicted by the CSM
From c decay
From y(2S) decay
There are more current and accurate results from D0 and CDF
but they don’t change this picture – just bring it into sharper focus
25
Why Did It Take So Long for the
Color Singlet Model to Die?

Maybe it’s because fixed target experiments were at
lower pT, so the predictions were thought to be less
reliable
 But this complaint was not leveled against Drell-Yan and direct
photon experiments at fixed target energies


Maybe a single definitive experiment was more
convincing than an ensemble of experiments
Maybe it was lack of theoretical alternatives
 Hold that thought…coming up is the color evaporation model…


Maybe it was simply better plotsmanship by the collider
experiments
Maybe this should be the subject of somebody’s
sociology PhD thesis
26
The Color Octet Model

It’s fairly clear that the CSM is missing some source of J/y’s
 By the rate, it appears to be the dominant source

Consider the addition of two SU(3) (color) octets
 8+8 = 1 + 8 + 8 + 10 + 10bar + 27
 This allows 8+8 = 8: i.e. two gluons can be in a color octet state
 This is analogous to the three-gluon vertex

Think of this as a two-step process
 1. The charm-anticharm pair is produced in a color octet state
 2. The octet state radiates a gluon, and becomes colorless
This gets us our third gluon painlessly.
gg  P  S1  g
3
8
2
3
The J/y
Instead of ggg
→ J/y, we have gg → J/y + g
This is analogous to c production:
instead of a singlet c radiating a photon
there is an octet “c” radiating a gluon.
Other octet states also contribute
27
No Free Lunch

The Color Octet Model gives us a third gluon “for free”
 Because it’s soft, there is little penalty for an extra power of as
 For exactly the same reason, the matrix element for the
coupling between the octet c-cbar and the J/y + gluon is nonperturbative
It must be fit from experiment
Strictly speaking, the COM accommodates a large
cross section – it doesn’t predict it.

All is not lost
 There are only a small number of non-perturbative parameters
 While they have to be fit from experiment, they have to be
consistent across different measurements
 There is at least one other prediction (later in this talk)
28
Fitting COM Parameters
A consistent set of COM parameters can predict reproduce
both the measured J/y and y(2S) cross-sections
A major success of the model!
29
Ranting and Raving about Polarization

You may have heard talk of J/y polarization. This is wrong.
 Polarization means <Jz> ≠ 0
 Various symmetries force <Jz> = 0 in J/y production
 J/y’s are unpolarized

Since the J/y is a vector particle, there are two states that
have <Jz> = 0
 There is the (0,1,0) state – “transverse”
 There is the (1,0,1) state – “longitudinal”
 A commonly used convention is a = (T - 2L)/(T + 2L)
 Angular distribution of muons from J/y decay follows 1 + a cos2(q)
 a = 0 is called – incorrectly – “unpolarized”

The correct terminology is “spin alignment”
 <Jz> = 0 does not mean that the density matrix is equally populated
 The literature is chock-full of people using the wrong terminology – only
you can help end this! Make sure your next paper doesn’t do this!
This is just as important as “Deep-Inelastic Scattering” – the
dash, not the space – from George Sterman’s lecture.
30
COM Alignment Predictions


At low pT (near zero), a is or close to zero
At high pT (pT >> m(y): perhaps 20 or 30 GeV) a is large
 Would be 1, but diluted by higher order effects and contamination from
indirect production (e.g. c decay)
 Probably 0.5-0.8 is what’s expected
d
m
 1  a cos2 q
dq
q
m
J/y
q is the m+ direction with
respect to the J/y direction
of motion in the J/y rest
frame.
(Which technically makes no sense, but
you all understand what I mean)





Experimentally, high |a| events have one
“stiff” (high pT) muon and one “soft” (low pT)
muon
Low |a| events have two muons of similar pT
The measurement revolves around measuring
the relative yields of these two classes of
events
Not easy: detector geometry and triggering
considerations make it easier to get events
with muons of nearly equal pT’s than events
with very different pT’s
Understanding and quantifying this effect is
the experimental challenge in this
measurement
31
Spin Alignment Data
It is difficult to characterize
this as good agreement
between prediction and data.
This matches BaBar’s result
(they have much smaller
uncertainties) when boosting
the measurements into the
appropriate frame.
32
Color Evaporation

Basic idea:
The red-headed stepchild of quarkonium
production theories
 charm-anticharm pairs are produced in a color octet state
 These quarks emit one or more gluons in the process of forming
a colorless charmonium meson
 No attempt to understand this microscopic behavior in detail is
made
Many theorists find this unsatisfying

Predictions?
 Not many – most of the information gets washed out during the
color evaporation
Many experimentalists find this unsatisfying
 Relative yields of different charmonium states goes as ~(2J+1)
This actually agrees rather well with the data
 Small or zero spin-alignment parameter a
33
The Joy of X: X(3872)

At Lepton-Photon 2003, Belle announced a new
charmonium state seen in B decays
 You don’t get a new charmonium state every day
 Much less an unpredicted one!
y(2S)
Belle
Events/10 MeV
304M B’s
?
m(J/y
+-)
- m(J/y)
Blow-up of right-hand peak
34
More Joy of X

With a speed uncharacteristic of hadron colliders, both
CDF and D0 confirmed this particle
 Also, they identified that it is produced both promptly and in B
decays
D0
35
Dipion Mass X-perimental Results
Belle
Belle’s measurement of
m() is peaked at large
mass.
Belle
CDF confirms this
qualitatively.
Belle shows the dipion mass
distribution to be peaked at
high m() for the y(2S).
This was explained by Brown
and Cahn (1975) as a
consequence of chiral
symmetry.
I find the paper somewhat
difficult to follow: “by
theorists, for theorists.”
Obscure and under-noticed m() prediction by Yan.
Note the D-wave is not so prominent at high mass.
36
What is the cause of all the
X-Citement?

Charmonium?
 It has to have the right quantum numbers to decay to Y and
 It has to have the wrong quantum numbers to decay to a pair of Dmesons

Options are:
 hc: (1P1) – mass too low: should be near the center of mass of the c’s, or
3525 GeV
 First radial excitation h’c: 1P1(2P) – okay, so where is the regular hc then?
 Y2: (3D2): potential models predict this around 3790 MeV
 Why the peak in the wrong spot?
 Should also decay to c1 + g: not observed
 Prediction exists for the m() spectrum – agreement not great
 h3c: (1F3): potential models predict this around 4000 MeV
 Again, why is the peak in the wrong spot?
 No quantitative prediction exists for the m() spectrum, but since the two
pions are in a relative l = 2 state, the centrifugal barrier will favor a large
m().
37
X-otic possibilities

No charmonium states seem to match the data
 If it’s charmonium, there’s something we don’t understand also going on
 This may be related to the state’s proximity to DD* threshold

Could this be a bound state of a D and an anti-D*?
 Naturally explains the mass – just under threshold
 We know hadrons bind – we’re made of bound hadrons!
 Not only are there nuclei in QCD, there are “hypernuclei”
 The high m() may be from the decay y + 
A new kind of
strongly
interacting
matter?
 But watch out – the kinematics are such that any high mass enhancement looks
like a 
 There may be precedent with a kaon anti-kaon bound state in the
f0(980) and it’s isotriplet partner the a0(980)
 These are 0++ states that fit poorly into the meson nonet
 The f0 is narrow on the low mass side, where it decays to , but wide on the
high mass side, where it decays to KK
 Other, more advanced arguments: c.f. Jaffe and Weinstein
Whatever it is, it looks like it will take more data to
figure out exactly what is going on.
38
Summary


Many theories have been put forward to explain charmonium
hadroproduction
All have their problems





Drell-Yan: -/+ cross section ratio
Quark-antiquark: pbar/p cross section ratio
Color Singlet: inclusive J/y cross section
Color Octet: spin alignment
Color Evaporation: not very predictive
 All it’s got going for it is agreement with experiment

Still an open issue
 Most people seem to feel that the best shot is some variation of the
Color Octet picture
 Either a more advanced version that predicts a smaller spin alignment
 Or maybe the experimental problem will go away with better measurements

Charmonium still has the potential to surprise us
 For example, the mysterious X(3872)
39