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Dynamical Chiral Fermions The `Grail’ – dyn. chiral fermions Generation of dyn. chiral fermions configs –RBC on the RIKEN QCDOC – Jan 05 (some %) –UKQCD on the UK QCDOC – Jan 05 (some %) –RBC on the US QCDOC – April 05 (probably some %) Given certain existence of dyn. chiral configs via large scale simulations – NOT AN EXPLORATORY PROJECT Good physics? –Good chiral control – no taste breaking, avoid valence smearing –C. Bernard in May SciDAC : DWF0 < MILC2 in “cost” –A question of when to jump to dyn. chiral ferm. How to leverage off world efforts?

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Which Action?? LHPC/UKQCD - work with B. Joo, A. Kennedy, K. Orginos, U. Wenger Evaluate “cost” of various chiral ferm actions Consider only 5D inverters for use in force term in HMC No projection – have residual mass Decide by a metric – cost for fixed m res Results being presented at RBC/UKQCD meeting Goal: choose a common fermion action within RBC, UKQCD and LHPC for dyn. simulations Coordinate simulations – different lattice sizes??? Each group leverages off other for more resources (like MILC) Share the datasets - early access before public domain

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Results Chiral Fermion Working Group: Results: Of actions tested, standard DWF Shamir is clear loser. Zolotarev Continued Fraction is ``winner’’ (caveats, though). Second is rescaled Shamir DWF via Mobius (tanh) Zolo. DWF actions needed for final decision

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Cost measurements

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Recommendations Chiral Fermion Working Group: Recommendations: Suggest RBC (small) change to Mobius (force term and energy) Big picture – what to have for overlap induced kernel? If Wilson kernel used Cont. Frac - optimal valence action! Nominal sea m res and tiny valence m res (Golterman & Shamir) Cross-over usage by overlap-ers Possible 4D pseudofermion HMC with Cont. Fract. for force term If Shamir kernel used No cross-over to overlap Not optimal inverter Projection problematic??? Recommend Wilson kernel Continue to reduce chiral sym. breaking

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Future Algorithms: Pursue efficacy of projection and smearing 4D pseudofermion HMC Instead 5D HMC via Alternating-Schwarz?? Coordination: Prefer share configs internally. RBC – only available once public? Collaborations: LHPC/UKQCD – Code & analysis development – strong connection Major overlap on hadronic physics – work together?? UKQCD – wait and see LHPC/UKQCD/RBC ?? Many issues raised RBC/UKQCD Only agreed to share Columbia 2K nodes (Asqtad) RBC and UKQCD cases Strong interest generated only from algorithm work

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Allocations Nominally Nuc. Phys. 1/3 of US –By Apr 05 total 8 TFlops in US (currently 0.5 at JLab) –Use some % allocation of NP for dyn. chiral instead of staggered ? –E.g., finish a=0.13fm DWF/Asqtad and do instead dyn. chiral?? Propose a dyn. chiral m =300, 353, 500 MeV, 28^3x32, a=0.11fm –Cost=2.4 TfY for 10k traj – use half (like MILC) – total 1.2 Tflop-Y –Possibly coordinate a 24 3 £32 with RBC or UKQCD? Cost in Tflop-Years of 10K traj., of dyn. chiral ferm generation m (Mev)250300353500 VolumeN5N5 a (fm)Tflop-Y 24 3 £ 3260.111.30.750.460.16 28 3 £ 322.31.30.820.29 32 3 £ 323.82.21.350.47

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Dynamical Fermion - Allocations Propose a dyn. chiral m =300, 353, 500 MeV, 24^3x64, a=0.11fm, L=2.64fm –Cost=2.35 TfY for 5k traj –Possibly coordinate with UKQCD, RBC & U.S. HEP? Cost in Tflop-Years of 5K traj., of dyn. chiral ferm generation m (Mev)250300353 (400)500 24 3 £ 64N 5 =8 Tflop-Y2.21.30.78 (0.54)0.27 m L3.34.04.7 (5.3)6.6

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The Goal Overlap operator on the lattice Choice of H, e.g., H=H w (-M)= 5 D w (-M) We approximate (H) by rational function where P n (H), Q m (H) poly. in H of degree n and m

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Representations Partial Fraction: (``4D Overlap – Inner CG’’) Alternative 5D (N&N) (hybrid of Cont. Frac and gauss int.) Continued Fraction – Euler representation, i determine approx. Equivalence transformations

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Continued Fraction Want solution to Use back-substitution – a 5D algorithm! Equivalent to solving

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Alternative 5D (N&N) Naryanan&Neuberger 5D Operator. Want solution of Solve 5D problem

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5D Domain Wall Domain wall action: 5D Domain wall kernel: with quark mass , and Integrate out L s -1 extra fields to obtain Here P is such that (P -1 ) 1 = q is the light fermion

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Induced 4D action – truncated overlap Core piece of induced kernel: Case of i =1 In general: – Domain wall : H = H T = 5 D w /(2 + a 5 D w ), b 5 -c 5 =a 5 – Overlap: H = H w = 5 D w, b 5 -c 5 =0

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Zolotarev vs. Tanh

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Zoom in – Show approx errors

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Maximum error as approx. range increases

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Maximum error vs. L s

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Comparisons Use RBC Dyn. N f =2 DWF, a=0.11fm, 16 3 £32, m =500 MeV 15 configs. Tune actions to same m - mass renorm. Metric – compare Cost (D_w apps) and rescaled m res Pion mass:

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Operators `CF' = Cont frac. 'M' = Möbius 'Z'=Zolotarev, 'T'=tanh

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Chiral Symmetry Breaking Defect of Ginsparg-Wilson relation Using Overlap operator D(0)=(1/2)(1+ 5 (H)), L measures chiral symmetry breaking Can show usual DWF m res m res just one matrix element of operator L

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M res measurements per config

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Density of Eigenvalues Compare EV’s of L Tanh cumulative error saturates quickly Zolo error can go negative! Densities are what matters Stretching Zolo approx. magnifies errors and m res Can have neg. m res

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Cost measurements

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Conclusions Results: Of actions tested, standard DWF Shamir is clear loser. Zolotarev Continued Fraction is ``winner’’ (caveats, though). Second is rescaled Shamir DWF via Mobius (tanh) Zolo. DWF actions needed for final decision Suspect need test of N&N 5D method (almost ready)

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