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Hadronic Physics at Jefferson Lab

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

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Hadronic Physics at Jefferson Lab

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

  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 (Nf=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: at-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 Nf=2+1 Asqtad lattices • 203x64 and (lowest mass) 283x64 • Single lattice spacing: a ~ 0.125fm (1.6 GeV) • No continuum limit extrapolation • Phase II (fully consistent): • DWF on Nf=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 EM Form Factors describe the distribution of charge and current in the proton • LT separation disagrees with polarization transfer • New exp. at Q2 = 9 GeV2 • Does lattice QCD predict the vanishing of GEp(Q2) around Q2 ~ 8 GeV2 ? Important element of current and future program projected C. Perdrisat (W&M) , JLab Users Group Meeting, June 2005

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

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

  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 gA: • Fundamental quantity determining neutron lifetime • Benchmark of lattice QCD • Hybrid lattice QCD at m down to 350 MeV • Finite-volume chiral-perturbation theory LHPC, PRL 96 (2006), 052001

  14. Chiral Extrapolation of GPD’s • 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, MN0 ~ 890 MeV • Covariant-baryon (CB)ChPT resums all orders of

  15. Chiral Extrapolation – A20(t,m2) Joint chiral extrapolation O(p^4) CBChPT(Dorati, Gail, Hemmert) LHPC • Joint chiral extrapolation in m and “t” • CBChPT describes data over wider range CBChPt HBChPt Expt.

  16. Chiral Extrapolation - hxiqu-d = Au-d20(t=0) Focus on isovector momentum fraction • Dominates behavior at low mass • gA, f well-determined on lattice • Colors denote fit range in pion mass LHPC Expt.

  17. Origin of Nucleon Spin arXiv:0705.4295 [hep-lat] • 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 Quarks have negligible net angular momentum in nucleon Inventory: 68% quark spin 0% quark orbital, 32% gluon Old and new HERMES, PRD75 (2007)

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

  19. 300 MeV pions

  20. 550 MeV pions

  21. Extrapolation

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

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

  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. Wiggles 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

  27. Lattice “PWA” • Do not have full rotational symmetry: J, Jz!,  • Has 48 elements • Contains irreducible representations of O, together with 3 spinor irreps G1, G2, H: R.C.Johnson, PLB114, 147 (82) Note that states with J >= 5/2 lie in representations with lower spins. Spins identified from degeneracies in contiuum limit mH M5/2 mG2 S. Basak et al., PRD72:074501,2005 PRD72:094506,2005 a

  28. Anisotropic? Demonstration of method • 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: 123x48, 200 cfgs, m~720MeV, as=0.1fm, =3 S. Basak et al., PRD72:074501,2005, PRD72:094506,2005

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

  30. Nf=0 & Nf=2 Nucleon Spectrum via Group Theory • Compare Wilson+Wilson Nf=0 with Nf=2 at at-1 ~ 6 GeV, 243£64, =3 • Mass preconditioned Nf=2 HMC, 243 & 323 x 64, m=400 and 540 MeV • Preliminary analysis of Nf=2 data • Compare G1g(½+)and G1u(½-) • Comparable statistical errors. Nf=2 used 20k traj., or ~830 cfgs • Next step: multi-volume comparisons 243 & 323 Nf=0, m= 490 MeV, as~0.10fm Nf=2, m= 400 MeV, as~0.11fm PRD 76 (2007)

  31. bound state • resonance b1 threshold 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

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

  34. Excited Charmonium • 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 • Operators can be projected into forms that are transform under the symmetry group of cubic lattice rotations

  35. ψ3 • ψ(3770) 3770 • ψ’ 3686 spin-1 spin-2 spin-3 • J/ψ 3097 dim=1 dim=3 dim=3 dim=2 dim=1 Variational Method PRD 77 (2008) • Quenched charmonium anisotropic clover, =3, at-1~6 GeV • Dense spectrum of excited states – how to extract spins? • Can separate spin 1 and 3 (first time)

  36. Continuum Spin Identification? PRD 77 (2008) • 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 T2 and E • the Z’s for the operators should match in continuum • compatible results found for other operators

  37. Nf=2+1 Clover - Choice of Actions • Anisotropic Symanzik gauge action (M&P): anisotropy =as/at • Anisotropic Clover fermion action with 3d-Stout-link smeared U’s (spatially smeared only). Choose rs=1. No doublers • Tree-level values for ctandcs (Manke) • Tadpole improvement factorsus(gauge) andus’ (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(Aee)), det(M†’*M’)1/2 , Gaugespace-space, Gaugespace,time arxiv:0803.3960

  38. Nf=2+1 Anisotropic Clover - HMC • Nf=2+1, m~315 MeV, fixed ms, =3.5, as~0.12fm, 163£ 128, eigenvalues • Nf=2+1, fixed ms, =3.5, as~0.12fm, 163£ 128 • Fixed step sizes (Omeylan), for all masses Time Acc

  39. Spectroscopy – Gauge Generation Scaling based on actual (243) runs down to ~170 MeV 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

  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 as • Also, HMC forces increase with smaller at • Quenched: Anisotropic Wilson gauge+Clover, as=0.1fm • Unpreconditioned Clover condition #

  42. Temporal Preconditioner • Basic idea (clover): • HMC: have • Expectto have smaller cond. # • Define matrices with projectorsP§ • Trick is inversion of “T” with boundaries (Sherman-Morrison-Woodbury) • Consequences: det(CL-1) = det(T2) ~ constant for large Lt • Application of T-1reasonable in cost

  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 • Nf=2+1, m~315 MeV, fixed ms, =3.5, as~0.12fm, 243£ 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

  45. Summary • Two main directions for JLab’s lattice hadronic physics program • Hadronic structure (spin physics): • Isotropic Nf=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 Nf=2+1 Clover: light quark excited meson & baryon spectrum, also E.M. transition form-factors. • Multi-volume analysis • Future:NPLQCDplanning tests of using aniso clover in multi-hadrons

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