Dynamical Anisotropic-Clover Lattice Production for Hadronic Physics Outline: Physics requirements Computational requirements Production strategies Resource requirements Milestones A. Lichtl, BNL J. Bulava, C. Morningstar, CMU J. Dudek, R. Edwards, B. Joo, H.-W. Lin, N. Mathur, K. Orginos, D. Richards, A. Thomas, JLab I. Sato, LBL S. Wallace, UMD J. Juge, U. of Pacific G. Fleming, Yale

Physics Research Directions In broad terms – 2 main physics directions in support of JLab (hadron physics) experimental program Spectrum: (can use Clover fermions) –Excited state baryon resonances (Hall B) –Conventional and exotic (hybrid) mesons (Hall D) –Simple 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 photocoupling and baryon spectrum

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 state ID Disconnected contributions –Fully consistent valence and sea quarks –Several lattice spacings for continuum extrap. –Multiple volumes – finite-V analysis of strong decays –Non-local group theoretical based operators Mainly 2-pt correlator diagonalization (Initially) positive definite transfer matrix Simple 3-pt correlators (vector/axial vector current) Anisotropic-Clover satisfies these requirements

Choice of Actions Conventional anisotropic Wilson gauge action: 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 not needed – factors close to 1. 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

Anisotropic Tuning Non-perturbatively determine  0,, m 0 on anisotropic lattice Clover fermion action: Previous strategies (CPPACS, N f =2) –Match sideways potential: V s (R a s ) = V s (R  a t ) –Large volumes - tune via “speed of light’’ (dispersion relation) –Tree-level values for c t and c s New strategy (JLab, N f =3) –Basic idea: impose Ward identities – rotational sym. and PCAC –Use small volumes - Schroedinger Functional –Fixed boundaries on fermion and gauge action –Sideways potential still valid in background field –Separate time and space boundary condition (BC) calculation More details in appendix of proposal. Paper forthcoming (Edwards, Lin, Joo)

Nonperturbative Tuning of the Anisotropy Translationally invariant O, we have (PCAC) if parameters tuned to non-pert. values Define temporal current mass M t (t) and M’ t (t) for sources (wall pion) at t 0 =0, t  =T, resp. Similarly for space. Parameterize: have renormalized gauge anisotropy, and spatial and temporal current quark mass 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: So, have c s and c t consistent with non-pert. detemination

Anisotropy Tuning Results Non-perturbatively determine  0,, m 0 on anisotropic lattice Clover fermion action: Example: N f =3,  =3,  =5.5, a s ~0.1fm Plot of  0,, and M 0 versus input current quark mass 0000 M0M0M0M0

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 Edwards, Heller, Klassen, PRL 80 (1998) 0.1fm

N f =0 Spectrum via Group Theory Proof of concept: Wilson fermions, N f =0, 16 3 £ 64,  =3, a t -1 ~ 6 GeV Crucial: use displaced operators Classify states according to their Lattice irreps Apply variational method in nucleon sector at m  ' 700 MeV Adam Lichtl, PhD 2006

N f =2 Spectrum via Group Theory Compare Wilson N f =0 with N f =2 at a t -1 ~ 6 GeV, 16 3 £ 64,  =3 Preliminary analysis of N f =2 data (Adam Lichtl) Compare G 1g (½ + ) and G 1u (½ - ) Interesting! “Roper” appears – mass well below P-wave ½ - +  Decay channels open in light quark data – need multi-hadron Generating 24 3 £ 64, m  =432 MeV,  =3 now Adam Lichtl, PhD 2006 N f =0, m  =700 MeV N f =2, m  = 647 MeV N f =2, m  = 432 MeV

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

Scaling of Anisotropic Lattice Generation Cost of producing (independent) configs (lattice units) USQCD projects only count cost of producing traj. – no critical slowing down. Improved algorithms – no step-size cost. Take anisotropy into account: a t = a s /  Based on actual timings (QCDOC, clusters), cost is Message: cost higher than isotropic calcs. – a dimension taken to (near) continuum limit! Benefit is additional physics # Ops HMC cost CSD z=1 Step- size Solver iteration

Production Goals Expected lattice sizes and anisotropies needed for the project Large volumes needed for large physical states Lattice sizes for each physical size and lattice spacing. Not all lattice sizes are needed at each pion mass The temporal lattice spacing and extent are held to a t ~ 0.033fm and L t ~ 4.0fm, resp.

Anisotropic Clover: dynamical generation Estimated cost of N f =2+1 production (in TFlop-yrs) for 7K traj Phase I – initial production at a=0.1fm – –Hybrid photo-couplings – –cost = 2.7 TF-yr + 10% analysis Phase II – all of Phase I + 4.0fm – –Baryon spectra – –cost = 10 TF-yr + 50% analysis Phase III – add a=0.125fm – –Spectra at light pion mass and 2 lattice spacing for cont. limit – –cost = 16 TF-yr + 50% analysis Phase IV – add a=0.08fm – –Full continuum limit – –cost ~ 42 TF-yr + 50% analysis

Project Milestones - Spectrum Spectrum project (anisotropic Clover) –Phase I – a=0.1fm lattice spacing, 2.4fm to 3.2fm boxes Smallest pion mass is 220 MeV Result: first full QCD calculation of  1 (1 -+ ) hybrid photo- coupling and exotic meson masses Cost of production = 2.7 TF-yr + 10% analysis –Phase II – a=0.1fm at 2.4fm, 3.2fm, and 4.0fm boxes Smallest pion mass is 181 to 200 MeV Result: several (more than 2 or 3) low-lying excited baryon resonance masses with decay widths, nucleon form-factors, strange FF in nucleon Cost of production = 10 TF-yr + 50% analysis –Phase III – add a=0.125fm lattice on 2.4fm, 3.2fm and 4.0fm boxes Smallest pion mass is 181 MeV Result: first continuum limit of resonance masses, nucleon form-factors Q 2 ~ 10 GeV 2, N-  and Roper transition FF, strange FF in nucleon Cost of production = 16 TF-yr + 50% analysis

Summary and Current Status Anisotropic-Clover production supports JLab (and hadronic physics) experimental program Different project requirements result in different lattice formulations –Aniso-Clover for spectra and simple FF’s, DWF for spin physics –Different approaches optimize science output – most science per dollar of computing infrastructure Realistically, a multi-year program – (2011+) Have INCITE 2007 award: ~ 1 TF-yr. ORNL XT3 currently turned off (upgrade to XT4) Clover N f =3 running at PSC, Wilson N f =2 running on QCDOC Were asked to move QCDOC allocation??? Obvious HMC algorithm improvements underway (~2X?)

Backup slides Slides afterwards are backups:

Limitations on Anisotropic-Clover: dynamical generation Problem: lack of full chiral symmetry: –Unprotected fluctuations of smallest Dirac eigenvalue –Large fluctuations in fermionic force & propagators Result: recent study of large volumes (Luescher): –Empirical bound on smallest eigenvalue implies stability of integration when Smallest obtainable pion masses Upshot: physics requires large m  L, smallest mass not an issue All this discussion ignores Stout-ing: stabilizes operator Luescher, et.al., JHEP (2006)

Unsuitability of Chiral Fermions for Spectrum Chiral fermions - no pos. def. transfer matrix Unphysical excited states. Obscures true excited states Unphysical masses ~ 1/a, so separate in continuum limit Shown is the Cascade effective mass of DWF over Asqtad Upshot: chiral fermions not suited for high lying excited state program at currently achievable lattice spacings Source at t=10 Wiggles