Tuning for Nx=3 Anisotropic-Clover Fermions

R. G. Edwards, B. Joo, H.-W. Lin, Jefferson Lab M. Peardon, Trinity College, Dublin

Lattice 2008

Part of larger program for Anisotropic production

Dynamical Anisotropic-Clover Lattice Production for Hadronic Physics

A. Lichtl, BNLJ. Bulava, J. Foley, C. Morningstar, CMU

C. Aubin, K. Orginos, W&MS. Cohen, J. Dudek, R. Edwards, B. Joo,H.-W. Lin, D. Richards, A. Thomas, JLab

S. Wallace, UMDJ. Juge, U. of Pacific

G. Fleming, YaleN. Mathur, Tata Institute

M. Peardon, S. Ryan, Trinity College

Physics Research DirectionsIn 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

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/0506029, 0508018

– Highly excited Nf=0 baryon spectrum• hep-lat/0609019, 0709008

– Highly excited Nf=0 charmonium spectrum• arxiv:0707.4162

– Nf=2 Wilson gauge+Wilson fermions• Nucleon - E. Engelson’s talk • Cascades - N. Mathur’s talk

• Current work:– Nf=3 anisotropic tuning – arXiv:0803.3960 (this

talk)– Nf=2+1 strange quark mass and scales

(M.Peardon)

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

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

Edwards, Heller, Klassen, PRL 80 (1998)

0.1fm0.1fm

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

Nf=0 3d Stout-link Clover

• Another test of 3d Stout-link Clover

• Sanity check: consider Cascade spectrum

• Cascade spectrum sensible

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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/

9

• Nonperturbatively determine γg, γf, m0 on anisotropic lattice

• Three calculations:– Background field in time: PCAC gives Mt

Nf =3 Nonperturbative Tuning

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• 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

Nf =3 Nonperturbative Tuning

Klassen Method: ratio of Wilson loopsWanted: Vs(yas) = Vs(tas/g)

⇨ Condition: Rss(x,y) = Rst(x,t)

Comparison with PBC resultExample:(γg = 4.4, γf = 3.4, m0 = −0.0570, β = 1.5)

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• 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

Nf =3 Nonperturbative Tuning

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• 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

Nf =3 Nonperturbative Tuning

13

• 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

Nf =3 Nonperturbative Tuning

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• Nonperturbatively determine γg, γf, m0 on anisotropic lattice

• Nf = 3, = 3.5, = 1.5 arxiv:0803.3960arxiv:0803.3960

– Plot of γg and γf versus input current quark mass– Mild dependence on quark mass; fix γg and γf

Nf =3 Nonperturbative Tuning

Huey-Wen Lin — ECT Workshop, May 08

gg

175 MeV175 MeV0 MeV0 MeV

ff

175 MeV175 MeV0 MeV0 MeV

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• Nonperturbatively determine γg, γf, m0 on anisotropic lattice

• Nf = 3, = 3.5, = 1.5 arxiv:0803.3960arxiv:0803.3960

– Plot of γg and γf versus input current quark mass– Mild dependence on quark mass; fixed γg and γf

Nf =3 Nonperturbative Tuning

PCAC mass measured in SF scheme: mcr = -0.0854(5)

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• Nonperturbatively determine γg, γf, m0 on anisotropic lattice

• Nf = 3, = 3.5, = 1.5 arxiv:0803.3960arxiv:0803.3960

– Plot of γg and γf versus input current quark mass– Mild dependence on quark mass; fixed γg and γf

Nf =3 Nonperturbative Tuning

PCAC mass measured in SF scheme: mcr = -0.0854(5)

Check NP cs,t condition in SF scheme

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• 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%

Algorithm

Huey-Wen Lin — ECT Workshop, May 08

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• Mass-independent scheme (fixed =1.5 approach)• Scale and masses are defined in chiral limit

(Edwards, Joo, Lin, Peardon, work in progress)

2+1-Flavor Runs

Huey-Wen Lin — ECT Workshop, May 08

mπ (MeV)

~ 1600

~ 660

~ 1340

~ 850

~ 360

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Autocorrelation

• Example: 243×128 volume, with pion mass 360 MeV

• Plaquette history

Huey-Wen Lin — ECT Workshop, May 08

spatial temporal

Autocorrelation

Nf=2+1 Anisotropic Clover - HMC• Nf=2+1, m~360 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

λu

/d λ

s

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. 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