1. Tuning for Nx=3 Anisotropic-Clover Fermions
R. G. Edwards, B. Joo, H.-W. Lin, Jefferson Lab
M. Peardon, Trinity College, Dublin
Part of larger program for Anisotropic production
Lattice 2008

2. Dynamical Anisotropic-Clover Lattice Production for Hadronic Physics
A. Lichtl, BNL
J. Bulava, J. Foley, C. Morningstar, CMU
C. Aubin, K. Orginos, W&M
S. Cohen, J. Dudek, R. Edwards, B. Joo,
H.-W. Lin, D. Richards, A. Thomas, JLab
S. Wallace, UMD
J. Juge, U. of Pacific
G. Fleming, Yale
N. Mathur, Tata Institute
M. Peardon, S. Ryan, Trinity College

3. Physics Research Directions
In broad terms – 2 main physics directions in support of
(JLab) hadronic physics experimental program
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
Hadron Structure (Spin Physics): (use chiral fermions)
Moments of structure functions
Generalized form-factors
Moments of GPD’s
Initially all for N-N, soon N-Δ and π-π
Critical need: hybrid meson photo-coupling and baryon spectrum

4. Excited State Spectrum and Structure
Access highly excited states via anisotropic lattices
Previous (and on-going) work:
Development of group theoretical baryon ops
hep-lat/ ,
Highly excited Nf=0 baryon spectrum
hep-lat/ ,
Highly excited Nf=0 charmonium spectrum
arxiv:
Nf=2 Wilson gauge+Wilson fermions
Nucleon - E. Engelson’s talk
Cascades - N. Mathur’s talk
Current work:
Nf=3 anisotropic tuning – arXiv: (this talk)
Nf=2+1 strange quark mass and scales (M.Peardon)

5. 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
Still have pos. def. transfer matrix in time
Light quark action (more) stable
No need for non-perturbative tuning of Clover coeffs
Claim: can verify Clover coeffs. consistent with non-pert. tuning

6. Clover Scaling Studies
Clover – small scaling violations
Positive def. transfer matrix
Shown is a plot of clover scaling compared to various actions
Scaling holds for anisotropic lattices
Stout and non-stout clover scaling identical
Sanity check: charmonium hyperfine splitting:
82(2) MeV (Manke coeffs)
87(2) MeV (FNAL coeffs)
65(8) MeV (3d-Stout: Manke)
3d-Stouting not unreasonable
0.1fm
Edwards, Heller, Klassen, PRL 80 (1998)

7. Nf=0 3d Stout-link Clover
Another test of 3d Stout-link Clover
Sanity check: consider Cascade spectrum
Cascade spectrum sensible

8. Tadpole Factors and Stout Smearing
Stout parameter study for Nf=3 Aniso-Clover and Symanzik glue
one-loop (Foley et al.) numerical
Conservative choices: nρ = 2 and ρ = 0.14 (< 1/2d)
Padé approximation for us over a wide range of g2 = 6/ 8 8

9. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Three calculations:
Background field in time: PCAC gives Mt 9 9

10. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Three calculations:
Background field in time: PCAC gives Mt
Background field in space: sideways potential gives g
Klassen Method: ratio of Wilson loops
Wanted: Vs(yas) = Vs(tas/g)
⇨ Condition: Rss(x,y) = Rst(x,t)
Comparison with PBC result
Example:
(γg = 4.4, γf = 3.4, m0 = −0.0570, β = 1.5) 10 10

11. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Three calculations:
Background field in time: PCAC gives Mt
Background field in space: sideways potential gives g
Antiperiodic in time: dispersion relation gives f 11 11

12. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Three calculations:
Background field in time: PCAC gives Mt
Background field in space: sideways potential gives g
Antiperiodic in time: dispersion relation gives f 12 12

13. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Three calculations:
Background field in time: PCAC gives Mt
Background field in space: sideways potential gives g
Antiperiodic in time: dispersion relation gives f
Parameterize anisotropies and PCAC mass linearly:
Use space & time BC simulations to fit a’s, b’s, c’s separately
Improvement condition: solve 3×3 linear system for each mq,
with  = as/at = 3.5 13 13

14. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Nf = 3,  = 3.5,  = 1.5 arxiv:
Plot of γg and γf versus input current quark mass
Mild dependence on quark mass; fix γg and γf gg
175 MeV
0 MeV gf
175 MeV
0 MeV
Huey-Wen Lin — ECT Workshop, May 08 14 14

15. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Nf = 3,  = 3.5,  = 1.5 arxiv:
Plot of γg and γf versus input current quark mass
Mild dependence on quark mass; fixed γg and γf
PCAC mass measured in SF scheme: mcr = (5) 15 15

16. Nf =3 Nonperturbative Tuning
Nonperturbatively determine γg, γf, m0 on anisotropic lattice
Nf = 3,  = 3.5,  = 1.5 arxiv:
Plot of γg and γf versus input current quark mass
Mild dependence on quark mass; fixed γg and γf
PCAC mass measured in SF scheme: mcr = (5)
Check NP cs,t condition in SF scheme 16 16

17. Huey-Wen Lin — ECT Workshop, May 08
Algorithm
Rational Hybrid Monte Carlo (RHMC)
Multi-scale anisotropic molecular dynamics update
Even-odd preconditioning for the clover term
Stout-link smearing in fermion actions
Split gauge term
Three time scales
δt1: Omelyan integrator for and
δt2: Omelyan integrator SG,(S)
δt3: Omelyan integrator SG,(T)
Choice: δt1 = δt2
Time-link step size 3X smaller than space
Acceptance rate: ~75%
Huey-Wen Lin — ECT Workshop, May 08 17 17

18. Huey-Wen Lin — ECT Workshop, May 08
2+1-Flavor Runs
Mass-independent scheme (fixed  =1.5 approach)
Scale and masses are defined in chiral limit
(Edwards, Joo, Lin, Peardon, work in progress)
mπ (MeV)
~ 1600
~ 660
~ 1340
~ 850
~ 360
Huey-Wen Lin — ECT Workshop, May 08 18 18

19. Huey-Wen Lin — ECT Workshop, May 08
Autocorrelation
Example: 243×128 volume, with pion mass 360 MeV
Plaquette history
spatial temporal
Autocorrelation
Huey-Wen Lin — ECT Workshop, May 08 19 19

20. Nf=2+1 Anisotropic Clover - HMC
Nf=2+1, m~360 MeV, fixed ms, =3.5, as~0.12fm, 163£ 128, eigenvalues
λu/d λs
Nf=2+1, fixed ms, =3.5, as~0.12fm, 163£ 128
Fixed step sizes (Omeylan), for all masses
Time
Acc

21. 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

22. Spectroscopy - Roadmap
First stage: a ~ 0.12 fm, spatial extents to 4 fm, pion masses to 220 MeV. Initial runs at 140MeV.
Spectrum of exotic mesons
First predictions of 1 photocoupling
Emergence of resonances above two-particle threshold
Second stage: two lattices spacings, pion masses to 140 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
Spectrum computation - 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