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Tuning for N x =3 Anisotropic-Clover Fermions

Tuning for N x =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. Dynamical Anisotropic-Clover Lattice Production for Hadronic Physics. A. Lichtl, BNL

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Tuning for N x =3 Anisotropic-Clover Fermions

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  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/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)

  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 ctandcs (Manke) • Tadpole improvement factorsus(gauge) andus’ (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 usover a wide range of g2 = 6/ 8

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

  10. 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 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

  11. 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 11

  12. 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 12

  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 13

  14. Nonperturbatively determine γg, γf, m0 on anisotropic lattice Nf = 3,  = 3.5,  = 1.5 arxiv:0803.3960 Plot of γgand γfversus input current quark mass Mild dependence on quark mass; fix γgand γf Nf =3 Nonperturbative Tuning gf gg 0 MeV 175 MeV 0 MeV 175 MeV Huey-Wen Lin — ECT Workshop, May 08 14

  15. Nonperturbatively determine γg, γf, m0 on anisotropic lattice Nf = 3,  = 3.5,  = 1.5 arxiv:0803.3960 Plot of γgandγfversus input current quark mass Mild dependence on quark mass; fixed γgand γf Nf =3 Nonperturbative Tuning PCAC mass measured in SF scheme: mcr = -0.0854(5) 15

  16. Nonperturbatively determine γg, γf, m0 on anisotropic lattice Nf = 3,  = 3.5,  = 1.5 arxiv:0803.3960 Plot ofγgand γfversus input current quark mass Mild dependence on quark mass; fixed γgand γf Nf =3 Nonperturbative Tuning PCAC mass measured in SF scheme: mcr = -0.0854(5) Check NPcs,tcondition in SF scheme 16

  17. 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 17

  18. 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 mπ(MeV) ~ 1600 ~ 660 ~ 1340 ~ 850 ~ 360 Huey-Wen Lin — ECT Workshop, May 08 18

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

  20. λu/d λs 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 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

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