Hadronic Physics at Jefferson Lab

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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

• National program
• Hadronic Physics
• Hadron Structure
• Spectroscopy
• Algorithmic techniques
• Computational Requirements

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Jefferson Laboratory
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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 GPDs 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

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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 GPDs
• Initially all for N-N, soon N-? and p-p
• 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

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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

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Physics Requirements (Nf21 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

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Roadmap Hadron Structure

• Phase I (Hybrid approach)
• DWF on MILC Nf21 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 Nf21 DWF of RBCUKQCD(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

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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
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Proton EM Form-Factors - I
EM Form Factors describe the distribution of
charge and current in the proton
Important element of current and future program
projected

• 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 ?

C. Perdrisat (WM) , JLab Users Group Meeting,
June 2005
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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

LHPC, hep-lat/0610007

Leinweber, Thomas, Young, PRL86, 5011
As the pion mass approaches the physical value,
the size approaches the correct value
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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
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Moments of Structure Functions and GPDs

• Matrix elements of light-cone correlation
  functions
• Expand O(x) around light-cone
• Diagonal matrix element
• Off-diagonal matrix element

Axial-vector
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Nucleon Axial-Vector Charge

• Nucleons 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
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Chiral Extrapolation of GPDs

• 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, arxiv0705.4295
• Heavy-baryon (HB)ChPT expands in
• ?? 4? f? 1.17GeV, MN0 890 MeV
• Covariant-baryon (CB)ChPT resums all orders of

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Chiral Extrapolation A20(t,m?2)
Joint chiral extrapolation O(p4) CBChPT (Dorati,
Gail, Hemmert)
LHPC

• Joint chiral extrapolation in m? and t
• CBChPT describes data over wider range

CBChPt
HBChPt
Expt.
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Chiral Extrapolation - hxiqu-d Au-d20(t0)
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.
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Origin of Nucleon Spin
arXiv0705.4295 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)
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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

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300 MeV pions
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550 MeV pions
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Extrapolation
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Required Measurements

• Measurements required for 3 accuracy at T10
• May need significantly more

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

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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

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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 t10
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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 gt 5/2 lie in
representations with lower spins.
Spins identified from degeneracies in contiuum
limit
mH
M5/2
mG2
S. Basak et al., PRD72074501,2005 PRD72094506,20
05
a
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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, as0.1fm, ?3
S. Basak et al., PRD72074501,2005,
PRD72094506,2005
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Glimpsing (Quenched) nucleon spectrum
Nf0, m? 720 MeV, as0.10fm
Adam Lichtl, hep-lat/0609012

• Tantalizing suggestions of patterns seen in
  experiment

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Nf0 Nf2 Nucleon Spectrum via Group Theory

• Compare WilsonWilson Nf0 with Nf2 at at-1 6
  GeV, 24364, ?3
• Mass preconditioned Nf2 HMC, 243 323 x 64,
  m?400 and 540 MeV
• Preliminary analysis of Nf2 data
• Compare G1g (½) and G1u (½-)
• Comparable statistical errors. Nf2 used 20k
  traj., or 830 cfgs
• Next step multi-volume comparisons 243 323

Nf0, m? 490 MeV, as0.10fm
Nf2, m? 400 MeV, as0.11fm
PRD 76 (2007)
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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
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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

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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
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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

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Variational Method
PRD 77 (2008)

• Quenched charmonium anisotropic clover, ?3,
  at-16 GeV
• Dense spectrum of excited states how to extract
  spins?

• Can separate spin 1 and 3 (first time)

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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 Zs for the operators should match in
  continuum
• compatible results found for other operators

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Nf21 Clover - Choice of Actions

• Anisotropic Symanzik gauge action (MP)
  anisotropy ?as/at
• Anisotropic Clover fermion action with
  3d-Stout-link smeared Us (spatially smeared
  only). Choose rs1. No doublers
• Tree-level values for ct and cs (Manke)
• Tadpole improvement factors us (gauge) and us
  (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(MM)1/2 ,
  Gaugespace-space, Gaugespace,time

arxiv0803.3960
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Nf21 Anisotropic Clover - HMC

• Nf21, m?315 MeV, fixed ms, ?3.5, as0.12fm,
  163 128, eigenvalues

• Nf21, fixed ms, ?3.5, as0.12fm, 163 128
• Fixed step sizes (Omeylan), for all masses

Time
Acc
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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

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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 a0.10fm 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

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Algorithmic Improvements Temporal Preconditioner

• Dirac-Op condition increases with ? at fixed as
• Also, HMC forces increase with smaller at
• Quenched Anisotropic Wilson gaugeClover,
  as0.1fm

• Unpreconditioned Clover condition

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Temporal Preconditioner

• 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(CL-1) det(T2) constant for
  large Lt
• Application of T-1 reasonable in cost

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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)
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Temporal Preconditioning - HMC

• Nf21, m?315 MeV, fixed ms, ?3.5, as0.12fm,
  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

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Summary

• Two main directions for JLabs lattice hadronic
  physics program
• Hadronic structure (spin physics)
• Isotropic Nf21 DWF/DWF for twist matrix
  elements (GPDs) in nucleon-nucleon, and new
  systems
• Joint RBCUKQCDLHPC gauge production some UK,
  US, Riken QCDOC DOE Argonne BG/P
• Valence propagators shared
• Spectrum
• Anisotropic Nf21 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