1. Prospects for Spectroscopy Robert Edwards Jefferson Lab Exascale Computing January 2009 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

2. Private outline/notes What do we want? Use the requested bullets Current spectroscopy – iso –Actions? Chiral ferms bad – wiggles Clover good? Anisotropic program –Chiral ferms still bad –Operators and variational technology –Charmonium spectrum Excited Spectrum Overlaps – nature kind at dim=5 Excited transtion FF –Baryon spectrum –Costs Gauge Valence – overtaking gauge? Contractions not trivial Aniso switch over to Iso – want fine lattices Magic –No chiral ferms – can use clover –Can do magic of OPE w/o OPE – weak matelems (HEP) –Dist amps & sum-rules (structure) –Possibly do QCD light-cone directly (NP), qcdsf/detmold/keh-fei –Synergy HEP/NP –Costs – gauge (valence still expensive)

3. Physics Goals Exotic and excited state meson spectrum –Future JLab Hall D & GSI/Panda experiments –Photo-couplings & electromagnetic transition form-factors –Isoscalar spectrum –Also heavy quark spectrum – cross-over to HEP Baryon spectrum –Light quark and strange quarks E.g., many cascade states unknown parity –NP2012: Masses along with ground state and excited state transition form-factors up to 7 GeV 2 These are the simplest examples of views NOTE: spectrum & structure division arbitrary –Also consider 3D structure view of (excited) hadrons

4. Requirements Dynamical quarks: –Light quarks (u,d) – can be degenerate –Strange quark –Charm? Chiral extrapolation: problematic ! physical limit Multi-volume/decays Continuum extrapolation Disconnected contributions: –Isosinglets –3pt & 4-pt –Annihilation diagrams

5. Strange Quark Mass Decouple strange quark mass & lattice spacing “a” determinations Consider strange quark determination understood! Chiral PT extendable in (l_X, s_X) SU(3) stable hadron for scale X Physics observables (l_X, s_X) BMW, HadSpec 2008

6. Continuum Extrapolation Clover action - small discretization effects Chiral PT works well in ratio method BMW 2008 Ratio methoda @ phys limit

7. Some Ground State Masses Some of the ground state masses Missing negative parity octet and decuplet – much more to do! BMW Collab, Science (2008)

8. Decays ½ mass from effective range expansion: finite box QCDSF 2008 2¼, n=100 2¼, n=110 2¼, n=111 m ¼ =250 MeV m ¼ =390 MeV physical ½

9. Decays ½ mass QCDSF 2008

10. More complicated decays Exotic 1 -+ : cascading decays as mass decreases:

11. More complicated decays Exotic 1 -+ : cascading decays as mass decreases : first 1 -+ ! b 1 ¼ S-wave [Dominant decay in flux-tube models]

12. More complicated decays Exotic 1 -+ : cascading decays as mass decreases : first 1 -+ ! b 1 ¼ S-wave [Dominant decay in flux-tube models] second b 1 ¼ ! !¼¼ S-wave

13. More complicated decays Exotic 1 -+ : cascading decays as mass decreases : first 1 -+ ! b 1 ¼ S-wave [Dominant decay in flux-tube models] second b 1 ¼ ! !¼¼ S-wave

14. More complicated decays Exotic 1 -+ : cascading decays: Also 1 -+ ! ½¼ P-wave [P-wave suppressed in flux-tube models] L=1 L=2.0fm Need multiple volumes Theory not well developed Will get to cost…

15. Nucleon spectrum (Experimental) NP2012 milestone: Spectrum & E&M transitions up to Q 2 = 7 GeV 2 Challenges/opportunities: –Compute excited energies –Compute decays ½+½+ 5/2 + 3/2 - 5/2 - 3/2 + ½-½- N¼¼ or ¢¼ N¼ or N´ or N(1440)¼ N¼¼ or ¢¼

16. Strange Quark Baryons Strange quark baryon spectrum poorly known Future: Narrow widths: easy(er) to extract (?) ¥ &  : unknown spin & parities Widths are small

17. Simple interpolating fields ( à C ¡ à ) ¡Ã limited to ½ +, ½ -, 3/2 +, 3/2 - Non-local operators: higher spins and excited states Extend to: ¡ D i à ¡ D j à ¡ D k à Excited Baryons Lattice Continuum G1G1 1/2, 7/2,… G2G2 5/2, 7/2,… H3/2, 7/2,... Operators: cubic lattice symmetries a M 5/2 m G2 mHmH Nature is kind! Action: chiral breaking dim=5, Lorentz invariant Masses possibly O(a) Splittings ~ O(a 2 ) Precocious scaling

18. Correlation matrix: Diagonalize Mass from eigenvalue Basis complete enough to capture excited states Small contamination as expected: Variational Method Luscher,Wolff; HadSpec PRD72:074501,2005, PRD72:094506,2005

19. Noisy signals – go anisotropic [Hadron Spectrum Collaboration] Why? COST!! Lower cost with only one fine lattice spacing instead of all 4. Anisotropic Lattice m  ~720MeV, a s =0.1fm,  =3 HadSpec PRD72:074501,2005, PRD72:094506,2005

20. N f =2 Nucleon Spectrum via Group Theory HadSpec 2009 N f =2, m  = 416 MeV, a s ~0.11fm N f =2, m  = 572 MeV

21. N f =2 Nucleon Spectrum via Group Theory Possible 5/2 - state HadSpec 2009 N f =2, m  = 416 MeV, a s ~0.11fm N f =2, m  = 572 MeV

22. Nucleon Spectrum Possible 5/2 - state: pattern similar to exp: Future: –As expected, most states decaying –Multiple volumes for decay analysis –Cost???

23. Nucleon Radiative Transition Exploratory: P11->Nucleon transition

24. Nucleon Radiative Transition Excited transition: large “pion cloud” effects ! small mass arXiv:0810.5141 m ¼ = 480, 720, 1100 MeV

25. Mesons New experimental efforts in meson spectroscopy GlueX aims to photoproduce hybrid mesons in Hall D. –CD4 in 2015 Compass (CERN) Panda (GSI) Lattice QCD: crucial role –Predict the spectrum –Compute production rates

26. Hybrid Photocouplings Compute photocouplings : gives rates Test in charmonium: useful in own right

27. Photocouplings at Q 2 = 0 Experimental & theoretical programs (e.g., EBAC) need form-factors as input Beyond Photocouplings pn °¤°¤ p n °¤°¤ ¼ ½ F ¼½ ( Q 2 ) or

28. Covariant derivatives operators: Excited Mesons Lattice Continuum A1A1 0,4... T1T1 1,3,4... T2T2 2,3,4... E2,4... A2A2 3... Operators: cubic lattice symmetries a M2M2 mEmE m T2 Splittings ~ O(a 2 )

29. Motivation J PC state: wavefunction –Short distance: sufficient derivatives – nonzero overlap –Long distance: different structure R Ã(R) 0

30. Charmonium Spectrum Dense spectrum of excited states – how to extract spins? spin-1 spin-2 spin-3 dim=1dim=3 dim=2dim=1 3097 3686 3770 J/ψ ψ’ ψ (3770) ψ3ψ3 ψ3ψ3 PRD 77 (2008) Separate spin 1 and 3 (first time)

31. Variational method: gives eigenvectors Challenge: spin assignment in light quark sector with strong decays Lightest states in PC=++ –consider T 2 and E –Z’s for the operators should match in continuum Continuum Spin Identification? PRD 77 (2008)

32. Strategy for Excited Decays Variational results: use in 3-pt Excited sink: p=0 Ground source: p  0 Q2Q2  v (n)

33. Excited state decays Excited 0th 1st 2nd4th HadSpec 2009 Q2Q2 E1(Q 2 )

34. Hybrid decay Excited/exotic decays possible: go to light quarks

35. Light quarks N f =2+1: m ¼ = 580 MeV

36. Scalar mesons Long standing puzzle – 2-quarks, 4-quarks, molecules…?? Difficult experimentally Opportunity/challenge for lattice –Need N f =2+1 : ´ ’s prominent –Need disconnected, multi-hadron operators

37. Multi-hadrons Meson and baryon excited state energies obtainable 2-pt correlators: e.g., 2-mesons Different than in 3-pt Inversions on multiple time-slices/sources – Big cost: > 10x ??

38. Message so far Fine lattices (a < 0.04fm) crucial for u,d,s quark highly excited state spectroscopy, transitions, decays Current approach is anisotropic Not optimal for hadronic structure studies (light-cone interpretation) Go to fine lattice spacing isotropic What about costs? How does it help??

39. Small “a” – transformational ? OPE without OPE (Rome/Southampton/Washington) Weak-matrix elements need Small a -> compute Wilson coeffs in pert. theory Solve for renormalized operators –Avoid operator mixing & power divergent term [Rossi/Testa & Sharpe]: –a -1 ~ 8 GeV, so a ~ 0.025fm –Can use simple clover formulation – no chiral fermions –Avoid problems with heavy quarks in PT of c i

40. Synergy with Hadron Structure Hadron structure: also need OPE for hadronic tensor Variants: –Direct extraction and/or non-pt Wilson coeffs (QCDSF) –Connect with QCD sum-rules (QCDSF) –Fictitious heavy quark (Detmold/Lin)

41. Small ``a’’ – synergy of projects Isotropic lattices: a ~< 0.04fm –Potentially only need simple Clover formulation for HEP & NP –No chiral fermions – lower cost (10x ??) –Suitable for charm quarks - possibly bottom quarks??? –Light quarks (u,d,s): Current anisotropic program, a ~ 0.033fm Excited spectrum and transition FF’s –Suitable for hadron structure –Nuclear interactions: Helps with signal/noise – still need big/huge boxes

42. Scaling of costs Isotropic: m ¼ L = 4.2. Current aniso

43. Costs Physical limit: box sizes > 6fm ! m ¼ L > 4.2 Valence costs > gauge generation Number trajectories: dependent on problem (see Orginos) Lower bounds: (ignore future algorithm improvements): Anisotropic gauge: physical limit (6fm) ~ 0.1 PF-yr Isotropic gauge: physical limit (6fm): –a ~ 0.06fm: ~ 1 PF-yr –a ~ 0.04fm: ~ 10 PF-yr Overall factors: –Above only 10K traj (1K configs): need > 10x?? (baryons) –Valence inversions: need > 10x?? Summary: easily 10 PF-yr to 100 PF-yr

44. Backup slides Afterwards are backup slides

45. Spectroscopy - Roadmap First stage: a ~ 0.12 fm, spatial extents to 4 fm, pion masses to 220 MeV –Spectrum of exotic mesons –First predictions of  1 photocoupling –Emergence of resonances above two-particle threshold Second stage: two lattices spacings, pion masses to 180 MeV –Spectrum in continuum limit, with spins identified –Transition form factors between low-lying states Culmination: Goto a=0.10fm computation at two volumes at physical pion mass –Computation of spectrum for direct comparison with experiment –Identification of effective degrees of freedom in spectrum * Resources: USQCD clusters, ORNL/Cray XT4, ANL BG/P, NSF centers, NSF Petaflop machine (NCSA-2011)/proposal

46. Unsuitability of Chiral Fermions for Spectrum Chiral fermions lack a positive definite transfer matrix Results in unphysical excited states. Unphysical masses ~ 1/a, so separate in continuum limit Shown is the Cascade effective mass of DWF over Asqtad Upshot: chiral fermions not suited for high lying excited state program at currently achievable lattice spacings Source at t=10 Wiggles

47. PDG CLEO Photocouplings - II Anisotropic (DWF) study of transitions between conventional mesons, e.g. S !  V PRD73, 074507 Not used in the fit lat. Lattice Expt. Motivated by this work, CLEO-c reanalyzed their data