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Hadronic Physics at Jefferson Lab
• National program
• Hadronic Physics– Hadron Structure– Spectroscopy
• Algorithmic techniques • Computational Requirements
Robert Edwards Jefferson Lab
ECT, Trento, May 5-9Perspectives and Challenges for full QCD lattice
calculations
Jefferson Laboratory
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
Physics Research DirectionsIn 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
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
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
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
HADRON STRUCTUREHADRON STRUCTURE
• JLabR EdwardsH-W LinD Richards
• William and Mary/JLab K Orginos• Maryland A Walker-Loud • MIT
J Bratt, M Lin, H Meyer, J Negele, A Pochinsky, M Procura
• NMSUM Engelhardt
• YaleG Fleming
• InternationalC AlexandrouPh Haegler B Müsch D RennerW SchroersA Tsapalis
LHP CollaborationLHP Collaboration
Proton EM Form-Factors - I
• LT separation disagrees with
polarization transfer• New exp. at Q2 = 9 GeV2
• Does lattice QCD predict the vanishing of GE
p(Q2) around Q2 ~ 8 GeV2 ?
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
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
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)
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
Nucleon Axial-Vector Charge
Nucleon’s axial-vector charge gA:• 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
• 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, MN
0 ~ 890 MeV
• Covariant-baryon (CB)ChPT resums all orders of
Chiral Extrapolation of GPD’s
Chiral Extrapolation – A20(t,m2)
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
Chiral Extrapolation - hxiqu-d = Au-
d20(t=0)
Focus on isovector momentum fraction
Expt.
LHPC
• Dominates behavior at low mass• gA, f well-determined on lattice
• Colors denote fit range in pion mass
Origin of Nucleon Spin
Quarks have negligible net angular momentum in nucleon
Inventory: 68% quark spin0% quark orbital, 32% gluon
• How is the spin of the nucleon How is the spin of the nucleon divided between quark spin, gluon divided between quark spin, gluon spin and orbital angular spin and orbital angular momentum?momentum?• Use GFFs to compute Use GFFs to compute total total angular momentum carried by angular momentum carried by quarks in nucleonquarks in nucleon
arXiv:0705.4295 [hep-lat]
Old and new HERMES, PRD75 (2007)
• 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
300 MeV pions
550 MeV pions
Extrapolation
Required Measurements
• Measurements required for 3% accuracy at T=10 • May need significantly more
Hadron Structure – Gauge Generation
Possible ensemble of DWF gauge configurations for joint HEP/HadronStructure investigations
LQCD-II
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
HADRON SPECTRUMHADRON SPECTRUM
• University of Pacific
J Juge• JLAB
S Cohen J DudekR EdwardsB JooH-W LinD Richards
• BNLA Lichtl
• YaleG Fleming
• CMUJ Bulava J Foley C Morningstar
• UMDE Engelson S Wallace
• Tata (India)N Mathur
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
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.
a
M5/2 mG2
mH
Spins identified from degeneracies in contiuum limit
S. Basak et al.,PRD72:074501,2005PRD72:094506,2005
• 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
123x48, 200 cfgs,
m~720MeV, as=0.1fm, =3S. Basak et al., PRD72:074501,2005, PRD72:094506,2005
Glimpsing (Quenched) nucleon spectrum
Adam Lichtl, hep-lat/0609012
• Tantalizing suggestions of patterns seen in experiment½+ 5/2+ 3/2- 5/2-3/2+ ½- ½+ 5/2+ 3/2- 5/2-3/2+ ½-
NNff=0, m=0, m= 720 MeV, a= 720 MeV, ass~0.10fm~0.10fm
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
PRD 76 (2007)
NNff=0, m=0, m= 490 MeV, a= 490 MeV, ass~0.10fm~0.10fm
NNff=2, m=2, m= 400 MeV, a= 400 MeV, ass~0.11fm~0.11fm
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
b1 threshold
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
PDGCLEO
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
• 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
A1 0,4...
T1 1,3,4...
T2 2,3,4...
E 2,4...
A2 3...
• Operators can be projected into forms that are transform under the symmetry group of cubic lattice rotations
Variational Method
• Quenched charmonium anisotropic clover, =3, at-1~6 GeV
• Dense spectrum of excited states – how to extract spins?
spin-1spin-2spin-3
dim=1 dim=3 dim=3 dim=2 dim=1
30973097
36863686
37703770
J/ψJ/ψ
ψ’ψ’ψ(3770)ψ(3770)
ψ3ψ3
PRD 77 (2008)
• Can separate spin 1 and 3 (first time)
• 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
Continuum Spin Identification?PRD 77 (2008)
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 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(M†’*M’)1/2 , Gaugespace-space, Gaugespace,time
arxiv:0803.3960
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
AccTime
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 (243) runs down to ~170 MeV
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
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 #
• 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
Temporal Preconditioner
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)
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
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: NPLQCD planning tests of using aniso clover in multi-hadrons