Hadron Structure using Dynamical Chiral Fermions

1. Hadron Structure using Dynamical Chiral Fermions A. Alexandru, B. Bistrovic, J. Bratt, R. Brower, M. Burkardt, T. Draper, P. Dreher, R. Edwards, M. Engelhardt, R. Irwin, G. Fleming, O. Jahn, K.-F. Liu, N. Mathur, J. Negele, K. Orginos, J. Osborn, A. Pochinsky, D. Renner, M. Musolf, D. Richards, D. Sigaev, A. Thomas

2. Proposal Dynamical chiral fermions: • Goal: • Initial dyn. ensemble with small quark (and residual) mass for hadron structure • Test new actions/algorithms • Understand/control mixing effects in hybrid calculations

3. 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 mres • Goal:choose a common 4D/5D fermion action within RBC, UKQCD and USQCD for dyn. simulations • Coordinate simulations – different lattice sizes • Share the datasets - may only be after public release

4. Status • Collaborations with UKQCD • Code & analysis development – strong connection • Completed initial study of fermion actions • Now testing new methods in Nf=2+1 QCD • Intent to produce small quark mass ensemble • UK agreement: • Use of < 10% resources (~ 1 rack) under algorithm devel. • Use in conjunction with USQCD resources and share lattices • Strong interest within UKQCD to pursue improved methods • Clear Edinburgh focused on short-term results • New methods used in a second/later phase of running • RBC: • Interested, but man-power constrained • UK+RBC: • Currently tweaking run-time params for DWF

5. Goal: Overlap operator • Overlap operator on the lattice: • Four dimensional space of algorithms: • Kernel: • Approximation: • Representation (CF – Continued Fraction, PF - Partial Fraction, DWF=CT=Cayley Transform) • Contraint (5D, 4D) • Only 4D operator physically relevant:

6. Kernel • Choice of kernel affects ``physics’’ (cutoff effects) • Wilson kernel • Shamir kernel • Mobius kernel

7. sn(z/M,λ) sn(z,k) Approximations • Two popular approximations • Polar (“tanh”) [induced by DWF] • Zolotarev: (analytic form of my old Remezsolution) • Trick – projection: supplement approx. with exact eigenv.

8. Representations • Continued Fraction – Euler representation, i determine approx. • Partial Fraction: • Cayley Transform:

9. Example: Continued Fraction • Want solution to • Use back-substitution – a 5D algorithm! • Equivalent to solving

10. 5D Operator – Generic Case • Want solution to • Representation for (H) turned into 5D system

11. 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 mres • mresjust one matrix element of operator L • Goal: want small mres for small cost

12. Spectral Flow • Topological charge is deficit of states ofH(-M) • Spectral flow counts zero crossings to find deficit at someM • Dov(0) should have 0 evs when Q != 0 Edwards, Heller, Narayanan 97

13. Overlap(Hw) spectral flow for smooth SU(2) • Spectral flow of overlap Ho(m) = g5 Do(m), H=Hw(-m) • Single instanton, 84, Dirichlet BC, r=1.5, cm = 4.5. • The zero modes after the crossing, m=0.6, 0.7, and 0.8. • The continuum solution

14. DWF Spectral Flow • DWF (and other reps!) should have zero eigenvalues at Q != 0 • Without projection (enforcement of exact -sym), zero evs slowly arise • -sym breaking from nearby zero-crossings (topology change) DWF Projected DWF

15. Spectral flow in SU(3): typical case • Spectral flow of H(m) quenched Wilson b=5.85, 6.0 • 50 configs, 10 evs overlayed • Fill-in by small modes • What about mres? • Two basic scales: (c) (where band stops), (0) • mres affected by: • Dense band below approx region • Evs piling near 0 • Goal: choose approx. below dense band. • Need projection for (0)

16. Tests Chiral Fermion Working Group: • Use Nf=2 DWF ensembles (RBC), m = 500 MeV • Actions (D(0)=(1/2)(1+5(H)) • Mobius : (Rescaled)Shamir (H=HT) and Overlap (H=Hw) • Continued Fraction rep. for (Hw) in 5D form • Different actions with same 4D physics (H) • Reduce mres by better approx. of (x) • Zolotarev (Chebyshev) and tanh approx. to (x)

17. Results– Cost Comparisons • Of actions tested, standard DWF Shamir is least effective. • Zolotarev Continued Fraction (Hw and HT) are candidates

18. Second Moment • Second norm not crazy – shows not wild cancellations in mres • Zolotarev Continued Fraction (Hw and HT) are good candidates

19. Forces in HMC • Comparison of MD forces in Nf=2 DWF [QCDOC] • Forces cancel in combined fermion force term • Gauge force MUCH noisier!! • F*t relevant scale • Can exploit multi-time scale integrators!! • Speed integration since gauge is cheap! • Explains RBC result – no mass dependence on step-size

20. 3-Flavor – DWF Comparison of Nf=2+1 DWF to Cont. Frac. • UKQCD – Iwasaki, =2.2, Nf=3, mf=0.04, a-1 ~ 1.6 – 1.8 GeV, a*m ~ 0.5 • Dyn. calc at Ls=8, mres ~ 0.006 • mres / mf > 10% at large pion mass • Tune Cont. Frac (Hw) to same Ls=8 DWF pion mass

21. 3-Flavor – Continued Fraction Forces in Nf=2+1 HMC, +1 via RHMC • Gauge force noisy. Use improved integrator • Sexton-Weingarten – fine-step integration in gauge action • Combine with new Takaishi-de Forcrand Integrator • Factor of ~ 3 speed-up • Spikes – possible instability or topology change?

22. 3-Flavor – Continued Fraction (Hw) Nf=2+1 Cont. Frac. Chroma – Iwasaki, =2.2, Nf=3, mf=0.024, a*m ~ 0.5 Dyn. calc at • Ls=6, mres*0.04/0.024 = 0.0034(2) • Ls=8, mres*0.04/0.024 = 0.00044(5) • Can achieve small mres via improved approximation!!! • Cost roughly the same UKQCD – Iwasaki, =2.2, DWF, Nf=3, mf=0.04, a*m ~ 0.5, a-1 ~ 1.6 – 1.8 GeV Dyn. calc at • Ls=8, mres ~ 0.006 Valence Ls • Ls=12, mres ~ 0.0025 • Ls=24, mres ~ 0.0004

23. Future • Actions: • For valence calcs – use current improved methods • Very early phase of dyn. fermion development • Can have same physics with different 5D actions • Use improved methods for small quark mass (?) • Algorithms: • Many algorithm tricks to test • Can improve algorithm without changing physics

24. Taste Breaking Effects • Have/producing large Asqtad data sets • Current work (Negele proposal) using DWF on Asqtad • Taste breaking study: • Compare fully chiral physics observables with hybrid calcs • Disentangle taste breaking effects on hybrid calcs • Leverage small allocationto produce low quark mass, high statistics and volume hadronic observables (JLab) • Nucleon structure functions and (generalized) form-factors

25. Code Status • All action tests done in Chroma (JLab, UK IBM’s, BGL) • Valence calcs (spectro, 3pt) in production at JLab • HMC • Nf=2+1 HMC/RHMC in production - 4D even/odd prec, combined force term • Support HMC Mobius, Cont. Frac., Partial Frac - generic H(b5,c5) • Move to use 4D pseudofermions (instead of current 5D) • Stand-alone inverters generically ~25% peak, double prec. • Improve 5D Dirac op – use ``vector’’ dslash calls ~ 35%

26. Machine Status • QCDOC running began ~ May 1, 2005 • 1K Rack UK, 1K US, ~ 1 mother-board (MB) US • BNL QCDOC: • Allocated rack18: still flaky – lost time due to strange unresolved pass-through problems • Most results from UK rack and 1 US MB. • Access to MB’s still tough – since last weekend 6 available. • QOS 2.5.9 memory prevents production on single racks • Disk IO performance, /host, slow – require disk arrays • Network problematic – lost connections (qdaemon). Work around in place. • Nothing unexpected for an alpha user!! • Support staff very helpful! Thanks to Chulwoo J. and Stratos E.

27. Future • Actions: • For valence calcs – use current improved methods • Very early phase of dyn. fermion development • Can have same physics with different 5D actions • Use improved methods for small quark mass (?) • Algorithms: • Many algorithm tricks to test • Can improve algorithm without changing physics