1 Charmonium I: Introduction & Production Models Thomas J. LeCompte Argonne National Laboratory.

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1 Charmonium I: Introduction & Production Models Thomas J. LeCompte Argonne National Laboratory

2 Preliminaries l Thanks to the organizers for inviting me! I had a great time in the Dairy State, and I learned a lot. l I talk too fast – so slow me down by interrupting me with questions! l In this talk, I try to distinguish between what is: nCalculated nMeasured nInferred nJust my opinion l If you can’t tell, speak up!

3 An Introduction To Charmonium 3 GeV 3.8 GeV J/   (2S) or  ’ 3S13S1 3S13S1 3P23P2 3P13P1 3P03P0 22 11 00 Charmonium is a bound state of a charmed quark and antiquark. It is “almost nonrelativistic”:  ~ 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. Mass threshold

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

5 An Introduction To Charmonium 3 GeV 3.8 GeV J/   (2S) or  ’ 3S13S1 3S13S1 3P23P2 3P13P1 3P03P0 22 11 00 Charmonium is a bound state of a charmed quark and antiquark. It is “almost nonrelativistic”:  ~ 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. Mass threshold Repeat of the Last Slide

6 Quarkonium Potential A not-too-terrible model of the quark-antiquark force law: 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, so this term is absent 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/  e + e - annihilation at SPEAR p + Be → e + e - + X at AGS l October, 1974 l Near simultaneous discovery n Ting et al. at BNL AGS nRichter et al. at SLAC SPEAR l Quarks were no longer mathematical objects, but particles that moved in a potential l 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 to have the particle name itself!

9 Homework l #1 – For each quarkonium (i.e. charmonium and bottomonium) state in the PDG, give nQuantum numbers: k, n, L, S (like the Hydrogen atom) nSpin, 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 5n 2 + 1 –3l(l+1). l [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. nThis is ~2/3 of the partial width J/  →  * → hadrons/leptons is allowed nThis is ~30%of the partial width nThere is also a few percent of radiative transitions Together, this is called the “OZI Rule” Strong decays are suppressed so much that EM decays are competitive

11 So How Are J/  ’s Produced? l Theory #1 – Drell-Yan Production nIdea: 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: 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 Downstream Tracking Beam Target Hadron Absorber ++ -- Muon Detector This kind of experiment looks only at the muons produced, and thus can tolerate very high rates. Examples: CERN NA3, FNAL E-537

13 J/  Production with  + and  + beams

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. nThis is true for all energies and all targets çTargets: H, Be, Li, C, Fe, Cu, W, and Pt Drell-Yan cannot be the dominant production mechanism for J/  ’s l Theory #2 – QCD quark-antiquark annihilation nIdea: maybe the production is still initiated by quark-antiquark annihilation, but mediated by gluons rather than photons Prediction:  + and  - production is nearly equal çQuark content has different electrical charge, but the same color charge nPrediction: production from antiproton beams – which contain valence antiquarks - should be substantially (factor of >5-10) larger than production from proton beams çThis difference should be even bigger at low energy

15 Production with p and pbar beams

16 Inferences from the Measurement l Production from pbar beams is larger than from proton beams, and the difference is greatest at lowest energy nTheoretical success? l 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 nIt can be a piece of it, but not a very large piece Conclusion – whatever process produces J/  ’s, it must be gluon induced nProcess of elimination: if it’s not the quarks…

17 The Trouble With Gluons Remember, we know that J/  → gg is forbidden J/  is a 3 S 1 (1 -- ) state nViolates charge conjugation parity çLeft side is C odd, right is C even nIf 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 nInfinitesimal rate There seems to be no mechanism that allows gluons to fuse into a 3 S 1 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. l Therefore, one calculates the production of such a state nThe 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% l 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 Downstream Tracking Beam Target Upstream Tracking ++ -- Muon Detector This kind of experiment also looks at particles produced in association with the J/ . Examples: FNAL E-705, 706/672 Calorimeter 

20 Selected Results ExperimentSqrt(s) (GeV) Fraction of J/  ’s from  ’s E-61020.537% E-672/7063144% E-67318.9-21.631-47% E-7052440% E-7713944% GAMS8.444% HERA-B41.532% R8066247% WA1118.630% 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 ExperimentSqrt(s) (GeV)     Ratio E-61020.50.9 ± 0.4 E-672/706310.57 ± 0.19 E-67318.9-21.60.96 ± 0.64 E-705240.52 +0.57 –0.27 E-77139.53 ±.22 WA1118.61.5 ± 0.6 This STILL did not seem to kill the CSM… A typical experiment (E-771) CSM predicts only the right peak is there. CSM Prediction is 0 This ensemble of measurements is 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 measurement Beams-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 come from 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 CDF but 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? l Maybe it’s because fixed target experiments were at lower p T, so the predictions were thought to be less reliable nBut this complaint was not leveled against Drell-Yan and direct photon experiments at fixed target energies l Maybe a single definitive experiment was more convincing than an ensemble of experiments l Maybe it was lack of theoretical alternatives nHold that thought…coming up is the color evaporation model… l Maybe it was simply better plotsmanship by the collider experiments l 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 nBy the rate, it appears to be the dominant source l Consider the addition of two SU(3) (color) octets n8+8 = 1 + 8 + 8 + 10 + 10bar + 27 nThis allows 8+8 = 8: i.e. two gluons can be in a color octet state nThis is analogous to the three-gluon vertex l Think of this as a two-step process n1. The charm-anticharm pair is produced in a color octet state n2. The octet state radiates a gluon, and becomes colorless 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 photon there is an octet “  ” radiating a gluon. Other octet states also contribute

28 No Free Lunch l 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 çIt must be fit from experiment l All is not lost nThere are only a small number of non-perturbative parameters nWhile they have to be fit from experiment, they have to be consistent across different measurements nThere is at least one other prediction (later in this talk) Strictly speaking, the COM accommodates a large cross section – it doesn’t predict it.

29 Fitting COM Parameters A consistent set of COM parameters can predict reproduce both 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. nPolarization means ≠ 0 Various symmetries force = 0 in J/  production J/  ’s are unpolarized Since the J/  is a vector particle, there are two states that have = 0 nThere is the (0,1,0) state – “transverse” nThere is the (1,0,1) state – “longitudinal” A commonly used convention is  = (  T - 2  L )/(  T + 2  L )  Angular distribution of muons from J/  decay follows 1 +  cos 2 (  )   = 0 is called – incorrectly – “unpolarized” l The correct terminology is “spin alignment” n = 0 does not mean that the density matrix is equally populated nThe 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 p T (near zero),  is or close to zero At high p T (p T >> 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) nProbably 0.5-0.8 is what’s expected Experimentally, high |  | events have one “stiff” (high p T ) muon and one “soft” (low p T ) muon Low |  | events have two muons of similar p T l The measurement revolves around measuring the relative yields of these two classes of events l Not easy: detector geometry and triggering considerations make it easier to get events with muons of nearly equal p T ’s than events with very different p T ’s l Understanding and quantifying this effect is the experimental challenge in this measurement    J   is the  + direction with respect 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 boosting the measurements into the appropriate frame. It is difficult to characterize this as good agreement between prediction and data.

33 Color Evaporation l Basic idea: ncharm-anticharm pairs are produced in a color octet state nThese quarks emit one or more gluons in the process of forming a colorless charmonium meson nNo attempt to understand this microscopic behavior in detail is made çMany theorists find this unsatisfying l Predictions? nNot many – most of the information gets washed out during the color evaporation çMany experimentalists find this unsatisfying nRelative yields of different charmonium states goes as ~(2J+1) çThis 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) l At Lepton-Photon 2003, Belle announced a new charmonium state seen in B decays nYou don’t get a new charmonium state every day nMuch less an unpredicted one!  (2S) m(J/   +  - ) - m(J/  ) Belle 304M B’s Events/10 MeV ? Blow-up of right-hand peak

35 More Joy of X l With a speed uncharacteristic of hadron colliders, both CDF and D0 confirmed this particle nAlso, 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. Belle

37 What is the cause of all the X-Citement? l Charmonium? It has to have the right quantum numbers to decay to  and nIt has to have the wrong quantum numbers to decay to a pair of D- mesons l Options are: h c : ( 1 P 1 ) – mass too low: should be near the center of mass of the  ’s, or 3525 GeV nFirst radial excitation h’ c : 1 P 1 (2P) – okay, so where is the regular h c then?  2 : ( 3 D 2 ): potential models predict this around 3790 MeV çWhy the peak in the wrong spot?  Should also decay to  1 +  : not observed  Prediction exists for the m(  ) spectrum – agreement not great nh 3c : ( 1 F 3 ): potential models predict this around 4000 MeV çAgain, 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 l No charmonium states seem to match the data nIf it’s charmonium, there’s something we don’t understand also going on nThis may be related to the state’s proximity to DD* threshold l Could this be a bound state of a D and an anti-D*? nNaturally explains the mass – just under threshold nWe know hadrons bind – we’re made of bound hadrons! çNot 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  nThere may be precedent with a kaon anti-kaon bound state in the f 0 (980) and it’s isotriplet partner the a 0 (980) çThese are 0 ++ states that fit poorly into the meson nonet  The f 0 is narrow on the low mass side, where it decays to , but wide on the high mass side, where it decays to KK çOther, 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 of strongly interacting matter?

39 Summary l Many theories have been put forward to explain charmonium hadroproduction l All have their problems Drell-Yan:  -/  + cross section ratio nQuark-antiquark: pbar/p cross section ratio Color Singlet: inclusive J/  cross section nColor Octet: spin alignment nColor Evaporation: not very predictive çAll it’s got going for it is agreement with experiment l Still an open issue nMost people seem to feel that the best shot is some variation of the Color Octet picture çEither a more advanced version that predicts a smaller spin alignment çOr maybe the experimental problem will go away with better measurements l Charmonium still has the potential to surprise us nFor example, the mysterious X(3872)

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