1. Lattice QCD Comes of Age y Richard C. Brower XLIst Rencontres de Moriond March 18-25 2006 QCD and Hadronic interactions at high energy

2. QCD Theory Space! Color Supercond (Dense quarks) Asymptotically Free (UV/Short Distances) String/Gravity Flux Tubes/Spectra (IR/Long Distances) Chiral Restored (High Temp) N color 1/g 2 g2g2 kT BB N = 1, n f = 1 N = 0 * Lattice * Strassler, Katz Orginos Schmidt,Levkova IIB IIA D=11 SGRA HO HEI N = 2 N = 1 M-theory Super String Theory Space!

3. Comparison of Chemistry & QCD : K. Wilson (1989 Capri): “ lattice gauge theory could also require a 10 8 increase in computer power AND spectacular algorithmic advances before useful interactions with experiment...” ab initio Chemistry 1.1930+50 = 1980 2.0.1 flops  10 Mflops 3.Gaussian Basis functions ab initio QCD 1.1980 + 50 = 2030?* 2.10 Mflops  1000 Tflops 3.Clever Multi-scale Variable? * Fast Computers +Rigorous QCD Theoretical AnalysisSmart Algorithms + = ab inition predictions “Almost 20 Years ahead of schedule!”

4. BNL+JLab+FNAL+BG/L= O(10 Tflop/s)

5. USA SciDAC Software Group * Software Coordinating Committee UK Peter Boyle Balint Joo

6. Optimized Dirac Operators, Inverters Level 3 QDP (QCD Data Parallel) Lattice Wide Operations, Data shifts Level 2 QMP (QCD Message Passing) QLA (QCD Linear Algebra) Level 1 QIO Binary Data Files / XML Metadata SciDAC QCD API C/C++, implemented over MPI, native QCDOC, M-via GigE mesh Optimised for P4 and QCDOC Exists in C/C++ ILDG collab

7. Lattice QCD

8. Sources of Error  Wrong “theory” --- no quark loops  solution: Keep Fermionic det & Disconnected diagrams  Finite lattice spacing a  solution: a <.1 fermi + O(a 2 ) asymptotic freedom  Light quark limit m u/d /m s  O(1/20)  solution: Chiral pert. theory + Exact Lattice Chiral Symmetry  Finite space-time volume  solution: Big memory computer  Monte Carlo 1/N 1/2 sampling error  solution: Algorithms + $’s

9. Staggering Results: Role of Determinant (aka Sea Quarks) This is real QCD --- No more excuses (except Staggered Fermion with Det[D] ¼ trick: 4 * ¼ taste loops. Tasteful Chiral perturbation theory to take a  0)

10. Strong Coupling Constant Lattice:  S (M Z ) = 0.1170 (12) Experiment:  S (M Z ) = 0.1187 (20) Lattice (data) vs Perturbation Theory (red/one sigma band)

11. Alpha Strong

12. CKM projected improvement via Lattice Gauge Before After

13. Properties of  and K mesons Rule out m u = 0 by 5 sigma (Strong CP problem not solved!) lattice value is |Vus| = 0.2219±0.0026,experimental results: |Vus| = 0.2262(23)

14. Axial Charge of the Nucleon Lattice g A = 1.226 (84) Experiment g A = 1.295 (29)

15. Semi-leptonic Form Factor (prediction)

16. Multi-scale Algorithms  String Length 1000 Mev ( » 0.2 fm)  Quarks Masses: (197 fm Mev) 2, 8, 100, 1200, 4200, 175,000 Mev  Nuclear: scattering length/effective range a singlet = - 23.714 fm ( » 8 Mev) & r = 2.73 a triplet = 5.425 fm ( » 36 Mev) & r = 1.749 fm  Deuteron Binding = 50 Mev. (» 4 fm)  Finite T, finite  etc Log(m q ) Flavor: u,d,s,c,b,t QCD length scales:

17. Confinement length vs Pion Compton length ll m -1 

18. Quark loops: Multi-time step HMC  Hasenbush Trick:  Rational Hybrid Monte Carlo: In Hybrid Monte Carlo (HMC) simulations, the determinant acts as a potential for molecular evolutions: Equilibrium by “molecular chaos”: Speed up by separating force terms and using multiple step sizes: n times

19. Wilson Fermions with Multi-time step trick (moving the Berlin Wall) Wilson is Almost as efficient as Staggered BUT respects flavor sym (Urbach, Jansen, Shindler, Wegner, hep-lat/0506011)

20. Multi-grid al 1980’s failure point: Universal Autocorrelation:  = F(m l  ) Gauss-Jacobi (Diamond), CG (circle), 3 level (square & star)  = 3 (cross) 10(plus) 100( square

21. New fangled Algebraic-Adaptive Multigrid for Disconnected Diagrams

22. s = 1s = 2s = Ms = L s qLqL qRqR QLQL QRQR qLqL qRqR QRQR QLQL LEFT RIGHT Exact Lattice Chiral Fermions: ( Taking the 5th Dimension Seriously ?)

23. 5-d Flavor Current  4-d Vector/Axial Current Vector: Axial: 4-d Ward-Takahashi Identities via decent relations:

24. “QCD and a Holographic Model of Hadrons” Erlich, Katz, Son, Stephanov, hep-ph/05011 (fit “  qcd, m q,  ”) Remarkably similar to AdS/CFT approach to Flavor Currents * constrained fit

25. Conclusions Not even the Beginning of the End..., perhaps the End of the Beginning”But II. Postdictions  Predictions I. Search for signals  Calibration of Errors Coming of Age for Lattice Field theory: III. To paraphrase W.C. “This is Not the End of Lattice Gauge Theory...,