# Presentation: 564165

## Hadronic Physics at Jefferson Lab

**Hadronic Physics at Jefferson Lab**

** ****National program**
-  **Hadronic Physics**
-  Hadron Structure
-  Spectroscopy
** ****Algorithmic techniques **
** ****Computational Requirements**

- Robert Edwards
- Jefferson Lab
- ECT, Trento, May 5-9
***Perspectives 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 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

## 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 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

**Proton EM Form-Factors - I**

**LT separation disagrees with polarization transfer**
**New exp. at Q****2**** = 9 GeV****2**
**Does lattice QCD predict the vanishing of ****G****E****p****(Q****2****) ****around     ****Q****2**** ~ 8 GeV****2**** ?**

**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

**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

## Moments of Structure Functions and GPD’s

**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 Axial-Vector Charge **

***Nucleon’s axial-vector charge g******A******:***
*** ******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, MN0 ~ 890 MeV

Covariant-baryon (CB)ChPT resums all orders of 

- 		[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 of GPD’s**

## Chiral Extrapolation – A20(t,m2)

**Chiral Extrapolation – A****20****(t,m********2****)**

- 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

**Origin of Nucleon Spin**

**Quarks have negligible net angular momentum in nucleon**
**Inventory: 68% quark spin**
**0% quark orbital, 32% gluon**

-  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

**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: 

- 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/Hadron
- Structure 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 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
- 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, J****z**** ****!**** ********, ******
**Has 48 elements**
**Contains irreducible representations of O, together with ****3 spinor irreps G****1****, G****2****, 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.,***
***PRD72:074501,2005***
***PRD72:094506,2005****** ***

## 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: 

- 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, =3

**S. Basak *****et al., PRD72:074501,2005,   PRD72:094506,2005****** ***

## Glimpsing (Quenched) nucleon spectrum

**Adam Lichtl, hep-lat/0609012**

-  Tantalizing suggestions of patterns seen in experiment

- Nf=0, m= 720 MeV, as~0.10fm

## Nf=0 & Nf=2 Nucleon Spectrum via Group Theory

**N****f****=0 & N****f****=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 (1⁄2+)  and G1u (1⁄2-)
-  Comparable statistical errors. Nf=2 used 20k traj., or ~830 cfgs
-  Next step: multi-volume comparisons 243 & 323

**PRD 76 (2007)**

- Nf=0, m= 490 MeV, as~0.10fm

- Nf=2, m= 400 MeV, as~0.11fm

## Lattice QCD: Hybrids and GlueX - I 

**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

## Hybrid Photocouplings

**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

- PDG

- CLEO

**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

- 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?

- 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

- 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 *T**2* 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

- Acc

- Time

## 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

*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

- 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

## Slide 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: NPLQCD planning tests of using aniso clover in multi-hadrons