1. Robert Edwards Jefferson Lab Creutz-Fest 2014 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAA 1983 HADRONS

2. Experimental meson spectrum ISOSPIN=1 MESON SPECTRUM Mesons classified by their conserved quantum numbers Spin, isospin, charge-conjugation J PC

3. Experimental meson spectrum ISOSPIN=1 MESON SPECTRUM Mesons classified by their conserved quantum numbers Spin, isospin, charge-conjugation J PC

4. Experimental meson spectrum ISOSPIN=1 MESON SPECTRUM ? Mesons classified by their conserved quantum numbers Spin, isospin, charge-conjugation J PC

5. Experimental meson spectrum ISOSPIN=1 MESON SPECTRUM the constituent quark picture ? n.b. absent: Mesons classified by their conserved quantum numbers Spin, isospin, charge-conjugation J PC

6. Experimental baryon spectrum ISOSPIN=1/2 BARYON SPECTRUM Baryons classified by their conserved quantum numbers Spin, parity, isospin J P

7. Experimental baryon spectrum ISOSPIN=1/2 BARYON SPECTRUM Baryons classified by their conserved quantum numbers Spin, parity, isospin J P Antisymmetric under interchange

8. Experimental baryon spectrum ISOSPIN=1/2 BARYON SPECTRUM Baryons classified by their conserved quantum numbers Spin, parity, isospin J P Antisymmetric under interchange 1S 1P 2S

9. Experimental baryon spectrum ISOSPIN=1/2 BARYON SPECTRUM Some states are “missing” ??? Antisymmetric under interchange 1S 1P 2S ???

10. Patterns in hadron spectrum Observed meson state flavor & J PC systematics: `constituent quarks’  “Exotic” quantum numbers

11. Patterns in hadron spectrum Observed meson state flavor & J PC systematics: `constituent quarks’ Could excited gluonic fields play a role – hybrid mesons ?  Possibly exotic J PC and extra `non-exotic’ states  “Exotic” quantum numbers

12. Patterns in hadron spectrum Observed meson state flavor & J PC systematics: `constituent quarks’ Could excited gluonic fields play a role – hybrid mesons ?  Possibly exotic J PC and extra `non-exotic’ states  “Exotic” quantum numbers However, might lead to extra states Constituent quark picture predicts rich baryon spectrum not all experimentally observed  No exotic J P in hybrid baryons

13. 1977 heavy ‘constituent’ gluon Modeling hybrid mesons Long history of suggestions for gluonic excitations coupled to quarks 1980 1982 excitation in a confining bag 1984 flux-tube oscillation 2008

14. Hybrid baryons 1982 1999 Some suggestions for hybrid baryons in QCD

15. Lattice QCD First-principles numerical approach to the field-theory Use lattice as a regulator (UV & IR) CUBIC LATTICE » in principle recover physical QCD as » large scale computational problem...

16. Lattice QCD First-principles numerical approach to the field-theory Use lattice as a regulator (UV & IR) CUBIC LATTICE » in principle recover physical QCD as » which can get really expensive …

17. People wanted to build computers QCD Teraflop 1 QCD Teraflop 2 … Some not-so-successful national efforts But there were some successes QCDSP

18. (Finally) a national proposal was funded…

19. And it evolved into USQCD QCDOCCLUSTERSBG/QGPU

20. Meson spectrum Range of hadron interpolators → matrix of correlation functions → variational description Monte Carlo stat. uncertainty arXiv:1004.4930. 1309.2608

21. Meson spectrum Range of hadron interpolators → matrix of correlation functions → variational description Patterns similar to experiments - even at artificially heavy pion mass Monte Carlo stat. uncertainty arXiv:1004.4930. 1309.2608

22. Meson spectrum Exotic J PC states are present EXOTIC J PC

23. qq interpretation? Appears to be some qq-like near-degeneracy patterns _ _

24. qq interpretation? “Extra” non-exotic states at same energy scale as lightest exotic? _

25. Meson spectrum Consider the relative size of operator overlaps Suggests we have a hybrid meson super-multiplet

26. Hybrid baryons Lattice QCD spectrum from a large basis of qqq operators qqq ⊗ G ( too small ? ) arXiv:1104.5152, 1201.2349

27. ( too small ? ) hybrid baryon s No exotic quantum numbers for baryons Hybrid baryons qqq ⊗ G Lattice QCD spectrum from a large basis of qqq operators arXiv:1104.5152, 1201.2349

28. A common gluonic excitation scale? Subtract the ‘quark mass’ contribution mesons baryons

29. A common gluonic excitation scale? SU(3) F point Common energy scale of gluonic excitation mesons baryons mesons baryons mesons baryons decreasing quark mass Subtract the ‘quark mass’ contribution

30. What comes next? Results so far suggest a rich spectrum of hadrons in QCD –Suggests a full baryon spectrum, including hybrid mesons and baryons –So far, calculations at artificially heavy quarks –And so far don’t resolve the fact they they should decay (& into what ?)

31. What comes next? Results so far suggest a rich spectrum of hadrons in QCD –Suggests a full baryon spectrum, including hybrid mesons and baryons –So far, calculations at artificially heavy quarks –And so far don’t resolve the fact they they should decay (& into what ?) Need to determine decays –But how? –Finite volume techniques

32. What comes next? Results so far suggest a rich spectrum of hadrons in QCD –Suggests a full baryon spectrum, including hybrid mesons and baryons –So far, calculations at artificially heavy quarks –And so far don’t resolve the fact they they should decay (& into what ?) Need to determine decays –In finite volume, can relate finite volume Euclidean QCD energies to infinite volume Minkowski scattering amplitudes (Luscher originally + others including Lellouch, Christ, Sachrajda, Sharpe extension to matrix elements + others)

33. What comes next? Results so far suggest a rich spectrum of hadrons in QCD –Suggests a full baryon spectrum, including hybrid mesons and baryons –So far, calculations at artificially heavy quarks –And so far don’t resolve the fact they they should decay (& into what ?) Need to determine decays –In finite volume, can relate finite volume Euclidean QCD energies to infinite volume Minkowski scattering amplitudes (Luscher originally + others including Lellouch, Christ, Sachrajda, Sharpe extension to matrix elements + others) Provides a direct connection to the S-matrix of QCD –Complications: truncation to finite number of partial waves, 3-body decays

34. Resonances Most hadrons are resonances –Formally defined as a pole in a partial-wave projected scattering amplitude Can we predict hadron properties from first principles?

35. Isospin=1/2 πK/ηK scattering 73 (real) energies on 3 volumes & momenta Constrain S-matrix in complex plane arXiv:1406.4158

36. Isospin=1/2 πK/ηK scattering 73 (real) energies on 3 volumes & momenta Constrain S-matrix in complex plane Broad resonance in S-wave πK Bound state pole in J P = 1 - Narrow resonance in D-wave πK all at unphysical quark masses… arXiv:1406.4158

37. Can even determine pole locations arXiv:1406.4158 Find S & D-wave poles on unphysical sheets Also presence of a “virtual” bound-state (pole at small –imag axis of momentum plane) RESONANCE POLE POSITION[S]

38. Can even determine pole locations arXiv:1406.4158 Find S & D-wave poles on unphysical sheets Also presence of a “virtual” bound-state (pole at small –imag axis of momentum plane) RESONANCE POLE POSITION[S] Possible because lattice is IR regulator

39. Path forward… A first picture of the highly excited spectrum of QCD: –Suggests another (?) scale in QCD ~ 1.3 GeV –But results are woefully incomplete… Next step – determine decays –(“Finally”) have a connection between QCD, lattice, and S-matrices –Exotics? Hybrids (mesons/baryons)? Scalar sector? Light/charm? Future? –Glue obviously important in QCD –Hard scale should manifest at large Bjorken-x - EIC? Made possible by using lattice as a regulator – thank you Mike! BES III COMPASS GlueX CLAS12 BGO

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42. Backup slides 42

43. Complex plane 43 arXiv:1407.7452

44. Volume dependence: isoscalar mesons Energies determined from single-particle operators: Range of J PC - color indicates light-strange flavor mixing Some volume dependence: Interpretation: energies determined up to a hadronic width arXiv:1309.2608

45. Experimental spectrum of hadrons MESONS J=0,1,2,… Isospin ≤ 1 |strangeness|≤ 1 Hadrons classified by their conserved quantum numbers Spin, isospin, strangeness, charm, … BARYONS J=1/2, 3/2, 5/2, … Isospin ≤ 3/2 |strangeness|≤ 3 QUARKS

46. Experimental baryon spectrum ISOSPIN=3/2 BARYON SPECTRUM Delta baryons classified by their conserved quantum numbers Spin, parity, isospin J P

47. Experimental baryon spectrum ISOSPIN=3/2 BARYON SPECTRUM Delta baryons classified by their conserved quantum numbers Spin, parity, isospin J P Antisymmetric under interchange

48. Experimental baryon spectrum ISOSPIN=3/2 BARYON SPECTRUM Antisymmetric under interchange 1S 2S 1P Delta baryons classified by their conserved quantum numbers Spin, parity, isospin J P

49. Experimental baryon spectrum ISOSPIN=3/2 BARYON SPECTRUM Antisymmetric under interchange 1S 2S 1P ??? Again, seems some states are “missing”

50. Experimental baryon spectrum ISOSPIN=3/2 BARYON SPECTRUM Delta baryons classified by their conserved quantum numbers Spin, parity, isospin J P Need theoretical guidance from QCD

51. Spin identified Nucleon & Delta spectrum arXiv:1104.5152, 1201.2349

52. Spin identified Nucleon & Delta spectrum arXiv:1104.5152, 1201.2349 Full non-relativistic quark model counting Compare mass as well as operator overlaps 4531 23 2 1 221 11

53. Hybrid baryons 53 Negative parity structure replicated: gluonic components (hybrid baryons) [ 70,1 + ] P-wave [ 70,1 - ] P-wave

54. 1 −− operator overlaps Consider the relative size of operator overlaps

55. 1 −− operator overlaps Consider the relative size of operator overlaps

56. 1 −− operator overlaps Consider the relative size of operator overlaps

57. 1 −− operator overlaps Consider the relative size of operator overlaps

58. Isospin=1 (J PC =1 -- ) ππ scattering Breit-Wigner fit to the energy dependence BREIT-WIGNER Reduced width from small phase-space arxiv:1212.0830