1

Charmonium I:Introduction & Production

Models

Thomas J. LeCompteArgonne National Laboratory

2

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!

3

An Introduction To Charmonium

3 GeV

3.8 GeV

J/

(2S) or ’

3S1

3S1

3P2

3P1

3P0

2

1

0

Charmonium is a bound stateof a charmed quark andantiquark. It is “almostnonrelativistic”: ~ 0.4:Hence the hydrogen atom-likespectrum

Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist.

States can make radiative (E1) transitions to the other column.

Mas

s

thresholdDD

4

Review: Quantum Numbers

JS L12

Total Angular Momentum

Orbital Angular Momentum

Spin Angular Momentum 1

3/ SJ Means: Quark Spin=1 (3 = 2 x 1 + 1) Quark Orbital Ang. Mom. = 0 Total J/ Spin = 1

1PCJMeans: Total J/ Spin = 1 Parity is Odd Charge Conjugation is Odd

5

An Introduction To Charmonium

3 GeV

3.8 GeV

J/

(2S) or ’

3S1

3S1

3P2

3P1

3P0

2

1

0

Charmonium is a bound stateof a charmed quark andantiquark. It is “almostnonrelativistic”: ~ 0.4:Hence the hydrogen atom-likespectrum

Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist.

States can make radiative (E1) transitions to the other column.

Mas

s

thresholdDD

Repea

t of t

he Las

t Slid

e

6

Quarkonium Potential

A not-too-terrible model of the quark-antiquark force law:

Brr

AF

2

A Coulomb-like part

A spring-like part

This piece comes from the non-Abelian nature of QCD: the fact that you have 3-gluon and 4-gluon couplings.

In QED, there is no coupling, sothis term is absentThis is just like QED:

(sometimes called the“chromoelectric”

force)

4 E

QCDQCDE 4

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.

7

Discovery of the J/

e+e- annihilation at SPEAR

p + Be→ e+e- + X at AGS

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

c.f. Fred Olness’ talk

8

Aside: Why ?

Mark I (SPEAR) Event Display

Decay is: (2S) → J/ + + + -

Followed by J/ → e+e-

It’s very convenient tohave the particle nameitself!

9

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/ 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 (2S) and states and of the (2S) and J/ 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.

10

Why is the J/ so Narrow?

J/ → open charm is kinematically blocked m(J/) < 2m(D)

J/ → gg → hadrons is blocked by quantum mechanics J/-g-g coupling is zero: more on this

later

J/ → ggg → hadrons is allowed (but suppressed) But now there are three powers of s. This is ~2/3 of the partial width

J/ → * → hadrons/leptons is allowed This is ~30%of the partial width There is also a few percent of radiative

transitions

Together, thisis called the “OZI Rule”

Strong decays aresuppressed so muchthat EM decaysare competitive

keV588)/( J

11

So How Are J/’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/ cross-section should be 4x higher for - beam as + beam:

2)( qQ 4)3/1(

)3/2(

)(

)(

)/(

)/(2

2

2

2

dQ

uQ

XJN

XJN

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.

What do the data show? …

Apology: I am only going to discuss hadroproduction today. Photoproduction is an interesting story, and there is some very high-

quality data from HERA.

12

A Typical Fixed Target Experiment

Magnet

Muon Shield

DownstreamTracking

Beam

Target

HadronAbsorber

+

-

Muon Detector

This kind of experiment looks only at the muons produced, and thus can

tolerate very high rates. // JXNp

Examples: CERN NA3,FNAL E-537

13

J/ Production with + and + beams

Pion Beam Charge Comparison

0

2

4

6

8

10

12

14

16

18

10 15 20 25 30 35

sqrt(s) (GeV)

nb

/nu

cleo

n

negative pions

positive pions

E-537

E-672/706

NA3

NA3

NA3

E-331

E-444

E-705

14

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/’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

15

Production with p and pbar beams

Proton/Antiproton Comparison

0

2

4

6

8

10

12

14

16

18

10 15 20 25 30 35

sqrt(s) (GeV)

nb

/nu

cleo

n

Pbars

Protons

E-537

NA-3

NA-3E-331

E-444

E-705

E-672/706UA-6

16

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/’s It can be a piece of it, but not a very large piece

Conclusion – whatever process produces J/’s, it must be gluon induced Process of elimination: if it’s not the quarks…

17

The Trouble With Gluons

Remember, we know that J/ → gg is forbidden J/ 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/ is also forbidden ggg → J/ requires a 3-body collision

Infinitesimal rate

There seems to be no mechanismthat allows gluons to fuse intoa 3S1 state like the J/

18

The Color Singlet Model (CSM)

A J/ (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( → J/ + ) are 30% and 13%

Predictions: Virtually all J/s come from the decays of ’s. 0:1:2 = 15:0:4

This is because gg → is suppressed, but gg → is allowed Virtually all (2S)’s come from the decays of b’s

m((2S))>m(), so production from decay is kinematically blocked

19

A 2d Generation Fixed Target Experiment

Magnet

Muon Shield

DownstreamTracking

Beam

Target

UpstreamTracking

+

-

Muon Detector

This kind of experiment also looks at particlesproduced in association with the J/.

/?)(/ JXNp

Examples: FNAL E-705, 706/672 Calorimeter

20

Selected Results

Experiment Sqrt(s) (GeV)

Fraction of J/’s from ’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%

Strangely, this did not seem to kill the CSM…

Worse, many experiments saw (2S) production even when (b) was small or zero.

21

More Selected Results

Experiment Sqrt(s) (GeV)

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 +0.57 –0.27

E-771 39 .53 ± .22

WA11 18.6 1.5 ± 0.6

This STILL did not seem to kill the CSM…

A typical experiment (E-771)

CSM predicts only the rightpeak is there.

CSM Prediction is 0This ensemble of measurementsis 4.2 different from 0

22

A Typical Colliding Beam Experiment

Muon detectors

Calorimeter:detects photons & Serves as hadron absorbers for muon detection

Outer tracker: in 1.5-2 T

magnetic field

Silicon vertex detector– for precision track impact parameter measurementBeams-eye view of a typical detector

+

-

23

The Plots That Finally Killed the CSM

J/’s not from ’s or b’s (2S)’s not from b’s

Theory and Measurement Disagree by a factor ~50 (red arrows)Even astronomers would call this poor agreement!

24

Ingredients of the last plot

Start with the J/cross-section

Remove the events that comefrom bottom quark decays

25

Ingredients of the last plot II

From (2S) decay

From decay

2/3 of the J/’s are produced directly.

This is not the few %predicted by the CSM

There are more current and accurate results from D0 and CDFbut they don’t change this picture – just bring it into sharper focus

26

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

27

The Color Octet Model

It’s fairly clear that the CSM is missing some source of J/’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

gSPgg 138

23

The J/

This gets us our third gluon painlessly.

Instead of ggg → J/, we have gg → J/ + g

This is analogous to production:instead of a singlet radiating a photonthere is an octet “” radiating a gluon.

Other octet states also contribute

28

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 s

For exactly the same reason, the matrix element for the coupling between the octet c-cbar and the J/ + gluon is non-perturbative

It must be fit from experiment

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)

Strictly speaking, the COM accommodates a largecross section – it doesn’t predict it.

29

Fitting COM Parameters

A consistent set of COM parameters can predict reproduceboth the measured J/ and (2S) cross-sections

A major success of the model!

30

Ranting and Raving about Polarization

You may have heard talk of J/ polarization. This is wrong. Polarization means <Jz> ≠ 0

Various symmetries force <Jz> = 0 in J/ production J/’s are unpolarized

Since the J/ 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 = (T - 2L)/(T + 2L)

Angular distribution of muons from J/ decay follows 1 + cos2() = 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.

31

COM Alignment Predictions

At low pT (near zero), is or close to zero

At high pT (pT >> m(): perhaps 20 or 30 GeV) is large Would be 1, but diluted by higher order effects and contamination

from indirect production (e.g. decay) Probably 0.5-0.8 is what’s expected

Experimentally, high || events have one “stiff” (high pT) muon and one “soft” (low pT) muon

Low || 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

J

2cos1d

d

is the + direction withrespect to the J/ direction

of motion in the J/ rest frame.

(Which technically makes no sense, but you all understand what I mean)

32

Spin Alignment Data

This matches BaBar’s result (they have much smaller uncertainties) when boostingthe measurements into theappropriate frame.

It is difficult to characterizethis as good agreementbetween prediction and data.

33

Color Evaporation

Basic idea: 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

The red-headed stepchild of quarkonium production theories

34

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!

(2S)

m(J/ +-) - m(J/)

Belle304M B’s

Eve

nts/

10 M

eV

?

Blow-up of right-hand peak

35

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

36

Dipion Mass X-perimental Results

Belle shows the dipion mass distribution to be peaked at high m() for the (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.”

Belle’s measurement of m() is peaked at large mass.

CDF confirms this qualitatively.

Obscure and under-noticed m() prediction by Yan.Note the D-wave is not so prominent at high mass.

BelleBelle

37

What is the cause of all the X-Citement?

Charmonium? It has to have the right quantum numbers to decay to and It has to have the wrong quantum numbers to decay to a pair of D-

mesons

Options are: hc: (1P1) – mass too low: should be near the center of mass of the ’s,

or 3525 GeV First radial excitation h’c: 1P1(2P) – okay, so where is the regular hc

then? 2: (3D2): potential models predict this around 3790 MeV

Why the peak in the wrong spot? Should also decay to 1 + : 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().

38

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 +

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.

A new kind ofstrongly interacting matter?

39

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/ 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)