1. R L Jaffe DIS05 Madison Life and Death among the Hadrons R. L. Jaffe DIS05 Madison April 2005 R. L. Jaffe DIS05 Madison April 2005 Update on the Theta Diquark correlations in QCD

2. R L Jaffe DIS05 Madison Postmortem on the Theta The is in trouble. It may survive, but it is not too early to look at the consequences of its demise should it occur

3. R L Jaffe DIS05 Madison Positive sightings of the Theta Dzierba, Meyer, Szczepaniak hep-ex/0412077

4. R L Jaffe DIS05 Madison Negative non-sightings of the Theta Dzierba, Meyer, Szczepaniak hep-ex/0412077

5. R L Jaffe DIS05 Madison Very recent results -- first of a second generation Reported by R. De Vita for CLAS at APS Tampa 4/17/05

6. R L Jaffe DIS05 Madison More detail

7. R L Jaffe DIS05 Madison Same reaction, Phys. Lett. B572 (2003)

8. R L Jaffe DIS05 Madison Implication s SU(3) Chiral Soliton Models (Diakonov, Petrov, Polyakov) Strong prediction asserted: M=1540 MeV, = 15 MeV Apparently the model is unreliable, why? ?Truncation of chiral effective lagrangian? ?Adiabatic (rigid) excitation? ?Perturbative implimentation of SU(3) violation? Dynamical balance Assume that rotational excitations neither deform soliton nor mix with radial excitations. No separation of scales. No justification to ignore ?Perhaps baryons are not chiral solitons in the first place!

9. R L Jaffe DIS05 Madison Implication s Quark models, Large N c (a la Jenkins/Manohar), Never could accommodate narrow width No prediction because absolute mass scale of could not be determined Absence of Theta limits the strength of the correlation (diquark) that has other important spectroscopic and dynamical implications ? ? ? ? ? ?

10. R L Jaffe DIS05 Madison Lessons There really are no (light, narrow) exotics in QCD Phenomenological models should not be taken very quantitatively, especially for overall scale (eg. mass of lightest state in sector, or lightest glueball) Lattice QCD has not yet progressed to the stage that it can be decisive Comments do not apply to heavy quark (c and b) exotics, where different issues apply. See (e.g.) Stewart, Wessling & Wise, hep-ph/0402076. Not covered here/ lack of time. A happy accident: the saga of the Theta has reminded us of the importance of diquark correlations in QCD

11. R L Jaffe DIS05 Madison Diquarks correlations in QCD Color, flavor, spin antisymmetric diquark dominates Spectroscopic consequences Exotics in general Pentaquarks and related states Spectroscopic consequences Exotics in general Pentaquarks and related states Diquarks in deep inelastic processes ? Phenomenological evidence for diquark correlations Defining diquarks Spectroscopy in color non-singlet sectors! Conclusions

12. R L Jaffe DIS05 Madison Correlations and classification Confinement correlations ? Color, flavor, spin antisymmetry Chiral symmetry breaking

13. R L Jaffe DIS05 Madison Classification Fermi statistics – Parity + Parity Color Leaves only two diquarks in the low energy spectrum

14. R L Jaffe DIS05 Madison Diquarks Flavo r ColorSpin -8 8/3 “Good” “Bad”

15. R L Jaffe DIS05 Madison Condensation in quark matter at high density condenses in flavor antisymmetric channel generating color-flavor locked superconductivity Long history in QCD, but never in the mainstream (D. Lichtenberg) Phenomenological evidence for diquarks Certain regularities in spectroscopy Absence of Systematic analysis of baryon and meson resonances. More later -- A. Selem & F. Wilczek in preparation Systematic analysis of baryon and meson resonances. More later -- A. Selem & F. Wilczek in preparation rule in nonleptonic weak decays dominance gives good description of non- perturbative effects. Systematic study by Neubert, Stech & collaborators in late 1980’s.

16. R L Jaffe DIS05 Madison Diquark regularities in DIS Baryon parton distribution function regularities follow from Regularities in fragmentation ratios in to hadrons Fragmentation ratios measured at LEP (Delphi) Fragmentation ratios measured at LEP (Delphi) Known since 1960’s Recent JLab results nucl-ex/0308011 Recent JLab results nucl-ex/0308011

17. R L Jaffe DIS05 Madison Good diquark, strange Formally define color antitriplet diquarks in the presence of an infinitely heavy spectator quark (or Polyakov line) Awaiting lattice calculations, estimate from charm and strange systems: Characterizing diquarks Good diquark, non- strange Bad diquark, strange Bad diquark, non- strange Bad diquark, doubly strange

18. R L Jaffe DIS05 Madison Other estimates from charm sector Good - bad mass difference decreases with quark mass. Diquark -- heavy quark spin interaction decreases with heavy quark mass and with light quark mass Conclude: charm baryon masses allow estimate of diquark masses in a heavy quark background. Correlation is ~ 200 MeV. Not huge, but important

19. R L Jaffe DIS05 Madison Most important: Diquark correlations explain the total (so far) absence of exotics in the light quark spectrum. Spectroscopic consequences Next: Diquark correlations “explain” supernumerary nonet of light scalar mesons as dominantly states Qualitative regularities in the meson and baryon spectra Suggest possible exotics in the heavy quark spectrum.

20. R L Jaffe DIS05 Madison Spectra Baryons Fermi statistics kills the singlet and allows only one octet which is a mixture of good and bad diquark except for and Mesons No Exotics ! Lightest multiplet is 0 ++ nonet

21. R L Jaffe DIS05 Madison Scalar mesons: a supernumerary nonet

22. R L Jaffe DIS05 Madison Spectra Pentaquarks Negative parity, non- exotic, s-wave Positive parity, possibly exotic, p-wave Only possible exotic Exotic requires diquarks in an antisymmetric space state (bose statistics) -- heavier, less stable Dibaryons Only s-wave is the SU(3)- singlet dihyperon: Made heavier by Pauli blocking

23. R L Jaffe DIS05 Madison Spectra Summary Generically, no exotics among light (u,d,s) Marginal cases: Pentaquark Dibaryon Scalar mesons: Ground state is a nonet of 0 ++ mesons resembling known light nonet. Heavy quark exotics should be explored more thoroughly

24. R L Jaffe DIS05 Madison In Deep Inelastic Processes Structure function regularities, especially as Fragmentation functions If diquarks are strongly correlated, baryon fragmentation functions should not be dramatically smaller than meson f.f. Data on two particular baryons... Good [u,d] diquark in s-wave Good [u,d] diquark in p- wave

25. R L Jaffe DIS05 Madison

26. Limits on diquarks from higher twist... A. Vainshteyn & RLJ (unpublished) “But aren’t strong correlations in QCD ruled out by the absence of large twist-four corrections to DIS?” “How pointlike can diquarks be?” “But aren’t strong correlations in QCD ruled out by the absence of large twist-four corrections to DIS?” “How pointlike can diquarks be?” corrections to DIS are known to be small, and limit non-perturbative scales in QCD beyond These limits constrain diquarks because twist-four operators include ones sensitive to diquark correlations...

27. R L Jaffe DIS05 Madison Leading twist However: “Good” diquark is spinless and does not contribute at twist four ! Dimension-6, spin-2 ⇒ twist-4, but only if quarks are coupled to maximum spin. Twist four -- diquark operator

28. R L Jaffe DIS05 Madison QCD spectroscopy in color non-singlet sectors Neutralize with spectator Wilson line (= infinitely heavy quark) (Or with uniform color background charge (how?)) Compare with bottom hadron spectroscopy And with phenomenological models Neutralize with spectator Wilson line (= infinitely heavy quark) (Or with uniform color background charge (how?)) Compare with bottom hadron spectroscopy And with phenomenological models Mesons Baryon s Tetraquark mesons Pentaquark baryons Even color sextet light quark states Study correlations in QCD by studying color non-singlet spectroscopy! The “ affair” suggests that correlations in QCD can be studied by studying color non- singlet light quark systems neutralized by heavy quark spectator. Study correlations in QCD by studying color non-singlet spectroscopy!

29. R L Jaffe DIS05 Madison Example: Classification of ground state “Exotics” with unique SU(3) assignments. “Exotics” mixed by SU(3) violating interactions. Total J=3/2 states with (Ignore for simplicity -- dynamics?)

30. R L Jaffe DIS05 Madison “Exotics” with unique SU(3) assignments. “Exotics” mixed by SU(3) violating interactions. Non-exotics, mix with single quark states. Total J=1/2 states with (Ignore for simplicity -- dynamics?)

31. R L Jaffe DIS05 Madison Color triplet spectroscopy 1/21+1[15] 1/23/20[15] 1/21[15] + [6] 1/2 -2[15] 1/20+1[6] * This representation only occurs when qq are coupled to 6

32. R L Jaffe DIS05 Madison Conclusions The Theta may have died* CSM takes a hit Quark model, large N c and other phenomenological models remain as limited as before. Jury is still out on heavy quark analogues The Theta may have died* CSM takes a hit Quark model, large N c and other phenomenological models remain as limited as before. Jury is still out on heavy quark analogues The “Theta affair” re-focused attention on diquarks Lots of phenomenological evidence for diquarks Important spectroscopic consequences, especially absence of exotics and scalar mesons Role in DIS --- qualitative --- fragmentation functions and higher twist A systematic study of correlations in QCD: light quark spectroscopy in the color non-singlet sectors The “Theta affair” re-focused attention on diquarks Lots of phenomenological evidence for diquarks Important spectroscopic consequences, especially absence of exotics and scalar mesons Role in DIS --- qualitative --- fragmentation functions and higher twist A systematic study of correlations in QCD: light quark spectroscopy in the color non-singlet sectors *Resurrection?