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

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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 BB 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!

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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!”

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

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

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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

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Lattice QCD

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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

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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)

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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)

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Alpha Strong

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CKM projected improvement via Lattice Gauge Before After

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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)

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

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Semi-leptonic Form Factor (prediction)

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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:

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Confinement length vs Pion Compton length ll m -1

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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

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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)

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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

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New fangled Algebraic-Adaptive Multigrid for Disconnected Diagrams

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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 ?)

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

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“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

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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...,

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