1. Hadronic Physics at Jefferson Lab National program Hadronic Physics – Hadron Structure – Spectroscopy Algorithmic techniques Computational Requirements Robert Edwards Jefferson Lab ECT, Trento, May 5-9 Perspectives and Challenges for full QCD lattice calculations

2. Jefferson Laboratory

3. JLab Experimental Program Selected parts of experimental program: Current 6 GeV and future 12GeV program EM Form Factors of Proton and neutron Generalized Parton Distributions: Proton & neutron Soon GPD’s for N-Delta and octets Parity violation/hidden flavor content Baryon spectroscopy Excited state masses and widths Excited state transition form factors (12 GeV) the search for exotic/hybrid mesons

4. Physics Research Directions In broad terms – 2 main physics directions in support of (JLab) hadronic physics experimental program Hadron Structure (Spin Physics): (need chiral fermions) –Moments of structure functions –Generalized form-factors –Moments of GPD’s –Initially all for N-N, soon N-Δ and π-π Spectrum: (can use Clover fermions) –Excited state baryon resonances (Hall B) –Conventional and exotic (hybrid) mesons (Hall D) –(Simple) ground state and excited state form- factors and transition form-factors Critical need: hybrid meson photo-coupling and baryon spectrum

5. Formulations (Improved) Staggered fermions (Asqtad): –Relatively cheap for dynamical fermions (good) –Mixing among parities and flavors or tastes (bad) –Baryonic operators a nightmare – not suitable for excited states Clover (anisotropic): –Relatively cheap (now): –With anisotropy, can get to small temporal extents –Good flavor, parity and isospin control, small scaling violations –Positive definite transfer matrix –Requires (non-perturbative) field improvement – prohibitive for spin physics Chiral fermions (e.g., Domain-Wall/Overlap): –Automatically O(a) improved, suitable for spin physics and weak- matrix elements –No transfer matrix – problematic for spectrum (at large lattice spacings) –Expensive

6. Physics Requirements (N f =2+1 QCD) Hadron Structure –Precise valence isospin, parity and charge conj. (mesons) –Good valence chiral symmetry –Mostly ground state baryons –Prefer same valence/sea – can be partially quenched –Several lattice spacings for continuum extrap. –Complicated operator/derivative matrix elements Avoid operator mixing –Chiral fermions (here DWF) satisfy these requirements Spectrum –Precise isospin, parity and charge conj. (mesons) –Stochastic estimation: multi-hadron –High lying excited states: a t -1 ~ 6 GeV !!! –Fully consistent valence and sea quarks –Several lattice spacings for continuum extrap. –Group theoretical based (non-local) operators (Initially) positive definite transfer matrix Simple 3-pt correlators (vector/axial vector current) –Anisotropic-Clover satisfies these requirements

7. Roadmap – Hadron Structure Phase I (Hybrid approach): –DWF on MILC N f =2+1 Asqtad lattices –20 3 x64 and (lowest mass) 28 3 x64 –Single lattice spacing: a ~ 0.125fm (1.6 GeV) –No continuum limit extrapolation Phase II (fully consistent): –DWF on N f =2+1 DWF of RBC+UKQCD+(now)LHPC –Uses USQCD/QCDOC + national (Argonne BG/P) –Ultimately, smaller systematic errors –Closer to chiral limit –Current lattice spacing: a ~ 0.086fm (0.12fm available) –Need more statistics than meson projects

8. HADRON STRUCTURE JLab R Edwards H-W Lin D Richards William and Mary/JLab K Orginos Maryland A Walker-Loud MIT J Bratt, M Lin, H Meyer, J Negele, A Pochinsky, M Procura NMSU M Engelhardt Yale G Fleming International C Alexandrou Ph Haegler B Müsch D Renner W Schroers A Tsapalis LHP Collaboration

9. Proton EM Form-Factors - I LT separation disagrees with polarization transfer New exp. at Q 2 = 9 GeV 2 Does lattice QCD predict the vanishing of G E p (Q 2 ) around Q 2 ~ 8 GeV 2 ? C. Perdrisat (W&M), JLab Users Group Meeting, June 2005 Important element of current and future program projected EM Form Factors describe the distribution of charge and current in the proton

10. Proton EM Form Factors - II Lattice QCD computes the isovector form factor Hence obtain Dirac charge radius assuming dipole form Chiral extrapolation to the physical pion mass Leinweber, Thomas, Young, PRL86, 5011 As the pion mass approaches the physical value, the size approaches the correct value LHPC, hep-lat/0610007

11. Generalized Parton Distributions (GPDs): New Insight into Hadron Structure e.g. D. Muller et al (1994), X. Ji & A. Radyushkin (1996) Review by Belitsky and Radyushkin, Phys. Rep. 418 (2005), 1-387 X. Ji, PRL 78, 610 (1997)

12. Moments of Structure Functions and GPD’s Matrix elements of light-cone correlation functions Expand O(x) around light-cone Diagonal matrix element Off-diagonal matrix element Axial-vector

13. Nucleon Axial-Vector Charge Nucleon ’ s axial-vector charge g A : Fundamental quantity determining neutron lifetime Benchmark of lattice QCD LHPC, PRL 96 (2006), 052001 Hybrid lattice QCD at m  down to 350 MeV Finite-volume chiral- perturbation theory

14. Covariant Baryon Chiral P.T. gives consistent fit to matrix elements of twist-2 operators for a wide range of masses [Haegler et.al., LHPC, arxiv:0705.4295] Heavy-baryon (HB)ChPT expands in   = 4  f  » 1.17GeV, M N 0 ~ 890 MeV Covariant-baryon (CB)ChPT resums all orders of Chiral Extrapolation of GPD’s

15. Chiral Extrapolation – A 20 (t,m  2 ) Joint chiral extrapolation O(p^4) CBChPT (Dorati, Gail, Hemmert) Joint chiral extrapolation in m  and “t” CBChPT describes data over wider range Expt. LHPC HBChPt CBChPt

16. Chiral Extrapolation - h x i q u-d = A u-d 20 (t=0) Focus on isovector momentum fraction Expt. LHPC Dominates behavior at low mass g A, f  well-determined on lattice Colors denote fit range in pion mass

17. Origin of Nucleon Spin Quarks have negligible net angular momentum in nucleon Inventory: 68% quark spin 0% quark orbital, 32% gluon How is the spin of the nucleon divided between quark spin, gluon spin and orbital angular momentum? How is the spin of the nucleon divided between quark spin, gluon spin and orbital angular momentum? Use GFFs to compute total angular momentum carried by quarks in nucleon Use GFFs to compute total angular momentum carried by quarks in nucleon arXiv:0705.4295 [hep-lat] Old and new HERMES, PRD75 (2007)

18. Signal to noise degrades as pion mass decreases Due to different overlap of nucleon and 3 pions also have volume dependence: Statistics for Hadron Structure

19. 300 MeV pions

20. 550 MeV pions

21. Extrapolation

22. Required Measurements Measurements required for 3% accuracy at T=10 May need significantly more

23. Hadron Structure – Gauge Generation Possible ensemble of DWF gauge configurations for joint HEP/Hadron Structure investigations LQCD-II

24. Hadron Structure - Opportunities Isovector hadron properties to a precision of a few percent: form factors, moment of GPDs, transition form factors… –High statistics, smaller a, lower m , full chiral symmetry Calculation of previously inaccessible observables: –Disconnected diagrams, to separately calculate proton and neutron observables –Gluon contributions to hadron momentum fraction and angular momentum (Meyer-Negele) –Operator mixing of quarks and gluons in flavor- singlet quantities

25. HADRON SPECTRUM University of Pacific J Juge JLAB S Cohen J Dudek R Edwards B Joo H-W Lin D Richards BNL A Lichtl Yale G Fleming CMU J Bulava J Foley C Morningstar UMD E Engelson S Wallace Tata (India) N Mathur

26. 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

27. Lattice “PWA” Do not have full rotational symmetry: J, J z ! , Has 48 elements Contains irreducible representations of O, together with 3 spinor irreps G 1, G 2, H: R.C.Johnson, PLB114, 147 (82) Note that states with J >= 5/2 lie in representations with lower spins. a M 5/2 mG2mG2 mHmH Spins identified from degeneracies in contiuum limit S. Basak et al., PRD72:074501,2005 PRD72:094506,2005

28. Why anisotropic? COST!! Lower cost with only one fine lattice spacing instead of all 4. Correlation matrix: Diagonalize Mass from eigenvalue Basis complete enough to capture excited states Small contamination as expected: Anisotropic? Demonstration of method 12 3 x48, 200 cfgs, m  ~720MeV, a s =0.1fm,  =3 S. Basak et al., PRD72:074501,2005, PRD72:094506,2005

29. Glimpsing (Quenched) nucleon spectrum Adam Lichtl, hep-lat/0609012 Tantalizing suggestions of patterns seen in experiment ½+½+ 5/2 + 3/2 - 5/2 - 3/2 + ½-½- ½+½+ 5/2 + 3/2 - 5/2 - 3/2 + ½-½- N f =0, m  = 720 MeV, a s ~0.10fm

30. N f =0 & N f =2 Nucleon Spectrum via Group Theory Compare Wilson+Wilson N f =0 with N f =2 at a t -1 ~ 6 GeV, 24 3 £ 64,  =3 Mass preconditioned N f =2 HMC, 24 3 & 32 3 x 64, m  =400 and 540 MeV Preliminary analysis of N f =2 data Compare G 1g (½ + ) and G 1u (½ - ) Comparable statistical errors. N f =2 used 20k traj., or ~830 cfgs Next step: multi-volume comparisons 24 3 & 32 3 PRD 76 (2007) N f =0, m  = 490 MeV, a s ~0.10fm N f =2, m  = 400 MeV, a s ~0.11fm

31. bound state resonance Lattice QCD: Hybrids and GlueX - I GlueX aims to photoproduce hybrid mesons in Hall D. Lattice QCD has a crucial role in both predicting the spectrum and in computing the production rates Only a handful of studies of hybrid mesons at light masses – mostly of 1 -+ exotic Will need multi-volume and multi-hadron analysis b 1  threshold

32. Hybrid Photocouplings Lattice can compute photocouplings Guide experimental program as to expected photoproduction rates. Initial exploration in Charmonium Good experimental data Allow comparison with QCD-inspired models Charmonium hybrid photocoupling – useful input to experimentalists

33. 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

34. Simple interpolating fields limited to 0 -+, 0 ++, 1 --, 1 +-, 1 ++ Extension to higher spins, exotics and excited states follows with use of non-local operators We chose a set whose continuum limit features covariant derivatives Excited Charmonium A1A1 0,4... T1T1 1,3,4... T2T2 2,3,4... E2,4... A2A2 3... Operators can be projected into forms that are transform under the symmetry group of cubic lattice rotations

35. Variational Method Quenched charmonium anisotropic clover,  =3, a t -1 ~6 GeV 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) Can separate spin 1 and 3 (first time)

36. Identify continuum spin amongst lattice ambiguities Use eigenvectors (orthogonality of states) from variational solution Overlap method crucial for spin assignment besides continuum limit Challenge: spin assignment in light quark sector with strong decays E.g. lightest states in PC=++ –consider the lightest state in T 2 and E –the Z’s for the operators should match in continuum –compatible results found for other operators Continuum Spin Identification? PRD 77 (2008)

37. N f =2+1 Clover - Choice of Actions Anisotropic Symanzik gauge action (M&P): anisotropy  =a s /a t Anisotropic Clover fermion action with 3d-Stout-link smeared U’s (spatially smeared only). Choose r s =1. No doublers Tree-level values for c t and c s (Manke) Tadpole improvement factors u s (gauge) and u s ’ (fermion) Why 3d Stout-link smearing? Answer: pragmatism (cost) –Still have pos. def. transfer matrix in time –Light quark action (more) stable –No need for non-perturbative tuning of Clover coeffs HMC: 4D Schur precond: monomials: log(det(A ee )), det(M † ’*M’) 1/2, Gauge space-space, Gauge space,time arxiv:0803.3960

38. N f =2+1 Anisotropic Clover - HMC N f =2+1, m  ~315 MeV, fixed m s,  =3.5, a s ~0.12fm, 16 3 £ 128, eigenvalues N f =2+1, fixed m s,  =3.5, a s ~0.12fm, 16 3 £ 128 Fixed step sizes (Omeylan), for all masses Acc Time

39. Spectroscopy – Gauge Generation First phase of ensemble of anisotropic clover lattices Designed to enable computation of the resonance spectrum to confront experiment Two lattice volumes: delineate single and multi-hadron states Next step: second lattice spacing: identify the continuum spins Scaling based on actual (24 3 ) runs down to ~170 MeV

40. 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

41. Algorithmic Improvements – Temporal Preconditioner Dirac-Op condition # increases with  at fixed a s Also, HMC forces increase with smaller a t Quenched: Anisotropic Wilson gauge+Clover, a s =0.1fm Unpreconditioned Clover condition #

42. Basic idea (clover): HMC: have Expect to have smaller cond. # Define matrices with projectors P § Trick is inversion of “T” with boundaries (Sherman- Morrison-Woodbury) Consequences: det(C L -1 ) = det(T 2 ) ~ constant for large L t Application of T -1 reasonable in cost Temporal Preconditioner

43. Temporal Preconditioner (tests) Considered 2 choices: –3D Schur: can 3D even-odd prec. - messy –ILU: Comparison with conventional 4D Schur (Quenched) comparison with conventional 4D Schur At larger , both ILU and 3D Schur lower cond. # Use ILU due to simplicity ~2.5X smaller than 4D Schur Cond # / Cond # (unprec) m  (MeV)

44. Temporal Preconditioning - HMC N f =2+1, m  ~315 MeV, fixed m s,  =3.5, a s ~0.12fm, 24 3 £ 128 Two time scales, all Omelyan integrators –Shortest: temporal part of gauge action –Longest: each of 1 flavor in RHMC + space part of gauge –Time integration step size is  smaller than space 16 coarse time steps (32 force evaluations) ILU ~ 2X faster in inversions – flops/Dirac- Op ~ 25% overhead, so 75% improvement Scaling improved (fixed 3D geometry) – go down to 2 £ 2 £ 1 £ 128 subgrids

46. Summary Two main directions for JLab’s lattice hadronic physics program Hadronic structure (spin physics): –Isotropic N f =2+1 DWF/DWF for twist matrix elements (GPD’s) in nucleon-nucleon, and new systems –Joint RBC+UKQCD+LHPC gauge production: some UK, US, Riken QCDOC + DOE Argonne BG/P –Valence propagators shared Spectrum: –Anisotropic N f =2+1 Clover: light quark excited meson & baryon spectrum, also E.M. transition form-factors. –Multi-volume analysis Future: NPLQCD planning tests of using aniso clover in multi- hadrons