Dynamical Anisotropic-Clover Lattice Production for Hadronic Physics

Outline:• Physics requirements• Computational requirements• Production strategies• Resource requirements• Milestones

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

J. Dudek, R. Edwards, B. Joo, H.-W. Lin, N. Mathur, K. Orginos, D. Richards, A. Thomas, JLab

I. Sato, LBLS. Wallace, UMD

J. Juge, U. of PacificG. 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 (Nf=2+1 QCD)

• Spectrum– Pion masses < 200MeV; small scaling violations– Precise isospin, parity and charge conj. (mesons)– High lying excited states: at

-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

=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 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, , m0 on anisotropic lattice• Clover fermion action:

• Previous strategies (CPPACS, Nf=2)– Match sideways potential: Vs(R as) = Vs(R at)– Large volumes - tune via “speed of light’’ (dispersion

relation)– Tree-level values for ct and cs

• New strategy (JLab, Nf=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 Mt(t) and M’t(t) for

sources (wall pion) at t0=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 mq

• Check afterwards: • So, have cs and ct consistent with non-pert. detemination

Anisotropy Tuning Results• Non-perturbatively determine 0, , m0 on anisotropic

lattice• Clover fermion action:

• Example: Nf=3, =3, =5.5, as~0.1fm• Plot of 0, , and M0 versus input current quark mass

00 MM00

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)

0.1fm0.1fm

Nf=0 Spectrum via Group Theory

• Proof of concept: Wilson fermions, Nf=0, 163£ 64, =3, at-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

Nf=2 Spectrum via Group Theory• Compare Wilson Nf=0 with Nf=2 at at

-1 ~ 6 GeV, 163£64, =3• Preliminary analysis of Nf=2 data (Adam Lichtl)• Compare G1g (½+) and G1u (½-)• Interesting! “Roper” appears – mass well below P-wave ½- + • Decay channels open in light quark data – need multi-hadron• Generating 243£64, m=432 MeV, =3 now

Adam Lichtl, PhD 2006

NNff=0, m=0, m=700 MeV=700 MeV NNff=2, m=2, m= 647 MeV= 647 MeV NNff=2, m=2, m= 432 MeV= 432 MeV

Nf=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: at = as/

• 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# Ops HMC HMC costcost

CSD CSD z=1z=1

Step-Step-sizesize

Solver Solver iterationiteration

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 at ~ 0.033fm and Lt ~ 4.0fm, resp.

Anisotropic Clover: dynamical generation

Estimated cost of Nf=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 Q2 ~ 10 GeV2, 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 Nf=3 running at PSC, Wilson Nf=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