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