Charmonium I: Introduction & Production Models

1. Charmonium I:Introduction & Production Models Thomas J. LeCompte Argonne 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 Charmonium is a bound stateof a charmed quark andantiquark. It is “almost nonrelativistic”: b ~ 0.4: Hence the hydrogen atom-likespectrum threshold 3.8 GeV 3S1 y(2S) or y’ 3P2 c2 c1 3P1 Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist. Mass 3P0 c0 J/y 3S1 States can make radiative (E1) transitions to the other column. 3 GeV

4. Review: Quantum Numbers Spin Angular Momentum Means: Quark Spin=1 (3 = 2 x 1 + 1) Quark Orbital Ang. Mom. = 0 Total J/y Spin = 1 Orbital Angular Momentum Means: Total J/y Spin = 1 Parity is Odd Charge Conjugation is Odd Total Angular Momentum

5. An Introduction To Charmonium Charmonium is a bound stateof a charmed quark andantiquark. It is “almost nonrelativistic”: b ~ 0.4: Hence the hydrogen atom-likespectrum threshold 3.8 GeV 3S1 y(2S) or y’ 3P2 c2 c1 3P1 Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist. Mass 3P0 c0 Repeat of the Last Slide J/y 3S1 States can make radiative (E1) transitions to the other column. 3 GeV

6. Quarkonium Potential A not-too-terrible model of the quark-antiquark force law: 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 gg coupling, sothis term is absent A Coulomb-like part This is just like QED:(sometimes called the“chromoelectric” force) 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/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

8. Aside: Why y? Decay is: y(2S) → J/y + p+ + p- Followed by J/y → e+e- It’s very convenient to have the particle nameitself! Mark I (SPEAR) Event Display

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/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.

10. 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) • 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 Together, this is called the “OZI Rule” Strong decays aresuppressed so muchthat EM decaysare competitive

11. 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 p- beam as p+ beam: 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 Muon Detector Examples: CERN NA3, FNAL E-537 DownstreamTracking m+ Target m- Beam HadronAbsorber Magnet This kind of experiment looks only at the muons produced, and thus can tolerate very high rates. Muon Shield

13. J/y Production with p+ and p+ beams

14. Inferences from the Measurement • The cross-section might be 10% or 15% larger for p- 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: p+ and p- 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

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/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…

17. 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 mechanismthat allows gluons to fuse intoa 3S1 state like the J/y

18. 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

19. A 2d Generation Fixed Target Experiment Muon Detector Examples: FNAL E-705, 706/672 DownstreamTracking Calorimeter m+ Target m- Beam g UpstreamTracking Magnet This kind of experiment also looks at particlesproduced in association with the J/y. Muon Shield

20. Selected Results Worse, many experiments saw y(2S) production even when s(b) was small or zero. Strangely, this did not seem to kill the CSM…

21. More Selected Results A typical experiment (E-771)CSM predicts only the right peak is there. CSM Prediction is 0 This ensemble of measurementsis 4.2s different from 0 This STILL did not seem to kill the CSM…

22. A Typical Colliding Beam Experiment m+ Muon detectors Calorimeter:detects c photons & Serves as hadron absorbers for muon detection g Outer tracker: in 1.5-2 T magnetic field m- Silicon vertex detector – for precision track impact parameter measurement Beams-eye view of a typical detector

23. 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!

24. Ingredients of the last plot Start with the J/ycross-section Remove the events that comefrom bottom quark decays

25. 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 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/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.Instead of ggg → J/y, we have gg → J/y + g This is analogous to c production: instead of a singlet c radiating a photonthere is an octet “c” radiating a gluon. The J/y 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 as • For exactly the same reason, the matrix element for the coupling between the octet c-cbar and the J/y + 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/y and y(2S) cross-sectionsA major success of the model!

30. 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 = (sT - 2sL)/(sT + 2sL) • 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.

31. 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 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 COM Alignment Predictions m+ q J/y m- q is the m+ direction withrespect to the J/y directionof motion in the J/y rest frame.(Which technically makes no sense, but you all understand what I mean)

32. Spin Alignment Data It is difficult to characterizethis as good agreementbetween prediction and data. This matches BaBar’s result (they have much smaller uncertainties) when boostingthe measurements into theappropriate frame.

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 a The red-headed stepchild of quarkonium production theories

34. Belle 304M B’s y(2S) Events/10 MeV ? m(J/yp+p-) - m(J/y) 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! 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’s measurement of m(pp) is peaked at large mass. CDF confirms this qualitatively. Belle Belle Belle shows the dipion mass distribution to be peaked at high m(pp) 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(pp) prediction by Yan.Note the D-wave is not so prominent at high mass.

37. What is the cause of all the X-Citement? • Charmonium? • It has to have the right quantum numbers to decay to Ypp 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 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(pp) 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(pp) spectrum, but since the two pions are in a relative l = 2 state, the centrifugal barrier will favor a large m(pp).

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(pp) may be from the decay y + r • But watch out – the kinematics are such that any high mass enhancement looks like a r • 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 pp, but wide on the high mass side, where it decays to KK • Other, more advanced arguments: c.f. Jaffe and Weinstein A new kind ofstrongly interacting matter? Whatever it is, it looks like it will take more data to figure out exactly what is going on.

39. Summary • Many theories have been put forward to explain charmonium hadroproduction • All have their problems • Drell-Yan: p-/p+ 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)