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

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

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

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 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)

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

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

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

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

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

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

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

Nf =3 Nonperturbative Tuning Nonperturbatively determine γg, γf, m0 on anisotropic lattice Nf = 3,  = 3.5,  = 1.5 arxiv:0803.3960 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

Nf =3 Nonperturbative Tuning Nonperturbatively determine γg, γf, m0 on anisotropic lattice Nf = 3,  = 3.5,  = 1.5 arxiv:0803.3960 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 = -0.0854(5) 15 15

Nf =3 Nonperturbative Tuning Nonperturbatively determine γg, γf, m0 on anisotropic lattice Nf = 3,  = 3.5,  = 1.5 arxiv:0803.3960 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 = -0.0854(5) Check NP cs,t condition in SF scheme 16 16

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

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

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

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

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

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