1. 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

2. 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): (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 Critical need: hybrid meson photo-coupling and baryon spectrum

3. Physics Requirements (N f =2+1 QCD) Spectrum –Pion masses < 200MeV; small scaling violations –Precise isospin, parity and charge conj. (mesons) –High lying excited states: a t -1 ~ 6 GeV !!! –Stochastic estimation: multi-hadron –Fully consistent valence and sea quarks –Several lattice spacings for continuum extrap. –Multiple volumes – finite-V analysis of strong decays –Group theoretical based (non-local) operators Mainly 2-pt correlator diagonalization (Initially) positive definite transfer matrix Simple 3-pt correlators (vector/axial vector current) Anisotropic-Clover satisfies these requirements

4. N f =0 & N f =2 Nucleon Spectrum via Group Theory Compare Wilson+Wilson N f =0 with N f =2 at a t -1 ~ 6 GeV, 24 3 £ 64,  =3 Use variational method: crucial: use displaced operators Classify states according to their Lattice irreps Preliminary analysis of N f =2 data Compare G 1g (½ + ) and G 1u (½ - ) Comparable statistical errors. N f =2 used 20k traj., or ~830 cfgs PRD 76 (2007) N f =0, m  = 490 MeV, a s ~0.10fm N f =2, m  = 400 MeV, a s ~0.11fm

5. Choice of Actions Anisotropic Symanzik gauge action (M&P): anisotropy  =a s /a t Anisotropic Clover fermion action with 3d-Stout-link smeared U’s (spatially smeared only). Choose r s =1. No doublers Tree-level values for c t and c s (Manke) Tadpole improvement factors u s (gauge) and u s ’ (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. Nonperturbative Tuning of the Anisotropy Non-perturbatively determine  g,  f, m 0 on anisotropic lattice Three calculations: 1.Background field in time: PCAC gives M t 2.Background field in space: sideways potential gives  g 3.Antiperiodic in time: dispersion relation gives  f, (m , r 0, etc.) Parameterize anisotropies and PCAC mass linearly: Use space & time BC simulations to fit a’s, b’s, c’s separately Improvement condition: solve 3x3 linear system for each m q Check afterwards: O(a) errors in M t ~ 0 So, have c s and c t consistent with non-pert. determination

7. Non-perturbatively determine  g,  f, m 0 on anisotropic lattice Example: N f =3,  =3.5,  =1.5, a s ~0.12fm Plot of  g and  f versus input current quark mass NOTE: anisotropies independent of quark mass. We fix them! arxiv:0803.3960Results presented in arxiv:0803.3960 Forthcoming scale setting paper to determine a s and m sForthcoming scale setting paper to determine a s and m s Anisotropy Tuning Results gggg ffff 175 MeV 0 MeV

8. Initial prescription for strange quark and lattice spacing –Vary N f =3 quark mass at fixed  –Compute r 0 /a s, set lattice spacing by physical r 0 –Tune quark mass to get physical phi mass –Prescription gives a s ~ 0.2fm Scale Setting and Strange Quark Mass Prescription fails - see significant running of coupling Example: at a fixed m s, see 30% variation in phi mass Instead, use combined chiral extrapolation of K, ,  a s ~0.12fm

9. Use ratio of hadron masses to eliminate lattice spacing Leading order  -PT –Light quark: l  = (9/4) m  2 /m  2 –Strange quark: s  = (9/4) (2m K 2 - m  2 )/m  2 Scale Setting and Strange Quark Mass Better prescription: –Tune N f =3 quark mass to till physical s  achieved Claim: for fixed strange quark, data consistent with horizontal line to physical limit Combined chiral extrapolation of K, , {  a s ~0.12fm Forthcoming scale setting paper to determine a s and m sForthcoming scale setting paper to determine a s and m s

10. Comparison of strange quark mass determinations Leading order  -PT –Light quark: l  = (9/4) m  2 /m  2 –Strange quark: s  = (9/4) (2m K 2 - m  2 )/m  2 More on Strange Quark Mass Aniso-Clover, a s =0.12fm DWF on Asqtad, a=0.125fm DWF on DWF, a=0.116fm

11. N f =2+1 Anisotropic Clover: dynamical generation Scaling based on actual (24 3 ) runs down to ~170 MeV The entries are #traj, location[M-6n-hours](m  L) –Expect ~ 30k traj needed for smaller masses –16 3 & 20 3 proposed for USQCD –24 3 315MeV ORNL runs underway now: ORNL time = 3.5 M-6n –32 3 315MeV only a contingency – not proposed –24 3 250MeV TACC runs start after April 1 –32 3 250MeV available for USQCD allocation Currently, ~3k traj @ 875, 580, ~2k @ 456 MeV (16 3 ): ~5k by July 1 ORNL: 315 MeV (24 3 ), currently 2k traj, get ~1k traj/week a s =0.12fm

12. Spectrum Project Roadmap Phase I – a s =0.12fm lattice spacing, up to 2.4fm boxes –Meson spectrum: Charm hybrid photocoupling using  ~ 875MeV to 315MeV Strange hybrid photocoupling using  ~875 to 580 (threshold) Exploratory light quark excited spectrum to 315MeV –Baryon spectrum: Exploratory light quark excited spectrum  ~ 875 to 315 Exploratory light quark excited transition form-factors –Cost of gauge (to 315MeV) ~ 4.1 (USQCD) + 4.7 (ORNL) M-6n –Cost of valence (to 315MeV) ~ 5 M-6n Phase II – a s =0.12fm up to 2.9fm boxes –Meson spectrum: Light quark photocoupling (stochastic) with  ~ 250MeV –Baryon spectrum: Spectrum for light quarks (stochastic) with  ~ 250MeV Light quark excited state transition FF –Extrapolations: chiral effective theory and/or chiral theory –Cost of gauge (to 250MeV) ~ 22 M-6n Phase III – go to a s =0.10fm –Go to physical light quark for NSF Petaflop project - FY2011