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?

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

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

Cost measurements

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

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

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) VolumeN5N5 a (fm)Tflop-Y 24 3 £ £ £

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) (400) £ 64N 5 =8 Tflop-Y (0.54)0.27 m  L (5.3)6.6

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

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

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

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

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

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

Zolotarev vs. Tanh

Zoom in – Show approx errors

Maximum error as approx. range increases

Maximum error vs. L s

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:

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

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

M res measurements per config

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

Cost measurements

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)