Transcript 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.

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
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 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 formfactors 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 weakmatrix elements
– No transfer matrix – problematic for spectrum (at large lattice
spacings)
– Expensive
Physics Requirements (Nf=2+1 QCD)
Hadron Structure
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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
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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 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
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 (W&M) , JLab Users Group Meeting, June
2005
Proton EM Form Factors - II
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•
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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
Generalized Parton Distributions (GPDs): New Insight
into Hadron Structure
D. Muller et al (1994), X. Ji &
A. Radyushkin (1996)
e.g.
X. Ji, PRL 78, 610 (1997)
Review by Belitsky and Radyushkin, Phys. Rep. 418 (2005), 1-387
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
• Hybrid lattice QCD at m
down to 350 MeV
• Finite-volume chiralperturbation theory
LHPC, PRL 96 (2006),
052001
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
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
Expt.
HBChPt
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.
Origin of Nucleon Spin
• 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
Old and new HERMES, PRD75 (2007)
arXiv:0705.4295 [hep-lat]
Quarks have negligible net
angular momentum in nucleon
Inventory: 68% quark spin
0% quark orbital, 32% gluon
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:
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
LQCD-II
Possible ensemble of DWF gauge configurations for joint HEP/Hadron
Structure investigations
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 flavorsinglet quantities
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
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
Wiggles
• 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
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.
mH
M5/2
Spins identified
from degeneracies
in contiuum limit
mG
2
a
S. Basak et al.,
PRD72:074501,2005
PRD72:094506,2005
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
Glimpsing (Quenched) nucleon spectrum
Nf=0, m= 720 MeV, as~0.10fm
Adam Lichtl, hep-lat/0609012
½+
3/2+
5/2+
½-
3/2-
5/2-
½+
3/2+
5/2+
½-
• Tantalizing suggestions of patterns seen in experiment
3/2-
5/2-
Nf=0 & Nf=2 Nucleon Spectrum via Group Theory
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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)
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
bound state
resonance
b1  threshold
Will need multi-volume and
multi-hadron analysis
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
Photocouplings - II
Anisotropic (DWF) study of transitions between conventional mesons, e.g.
PRD73, 074507
S!V
Not used
in the fit
PDG
CLEO
Lattice
lat.
Expt.
Motivated
by this
work,
CLEO-c
reanalyzed
their data
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
A1 0,4...
T1 1,3,4...
T2 2,3,4...
E 2,4...
A2 3...
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)
ψ3
ψ(3770)
3686 ψ’
3770
3097
spin-1
spin-2
spin-3
J/ψ
dim=1
dim=3
dim=3
dim=2
dim=1
Continuum Spin Identification?
PRD 77 (2008)
• Identify continuum spin amongst lattice ambiguities
• Use eigenvectors (orthogonality of states) from variational solution
• 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
• Overlap method crucial for spin assignment besides continuum limit
• Challenge: spin assignment in light quark sector with strong decays
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
Acc
Time
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
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 #
Temporal Preconditioner
• Basic idea (clover):
• HMC: have
• Expect to have smaller cond. #
• Define matrices with projectors P§
• Trick is inversion of “T” with boundaries (ShermanMorrison-Woodbury)
• Consequences: det(CL-1) = det(T2) ~ constant for large Lt
• Application of T-1 reasonable in cost
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
Cond # / Cond # (unprec)
• At larger , both ILU and
3D Schur lower cond. #
• Use ILU due to simplicity
~2.5X smaller than 4D
Schur
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/DiracOp ~ 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 multihadrons