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Lattice QCD Comes of Age y

Lattice QCD Comes of Age y. Richard C. Brower. XLIst Rencontres de Moriond March 18-25 2006 QCD and Hadronic interactions at high energy. Super String Theory Space!. D=11 SGRA. N = 2. HO. IIA. N = 1. M-theory. M?. IIB. HE. I. QCD Theory Space!. String/Gravity. Strassler, Katz.

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Lattice QCD Comes of Age y

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

  2. Super String Theory Space! D=11 SGRA N = 2 HO IIA N = 1 M-theory M? IIB HE I QCD Theory Space! String/Gravity Strassler, Katz N = 1, nf = 1 N = 0 Flux Tubes/Spectra (IR/Long Distances) Asymptotically Free (UV/Short Distances) Ncolor QCD g2 Orginos 1/g2 *Lattice* B kT Schmidt,Levkova Color Supercond (Dense quarks) Chiral Restored (High Temp)

  3. Comparison of Chemistry & QCD : K. Wilson (1989 Capri):“lattice gaugetheory could also require a 108 increase in computer power ANDspectacular algorithmic advances before useful interactions with experiment ...” • ab initio Chemistry • 1930+50 = 1980 • 0.1 flops  10 Mflops • Gaussian Basis functions • ab initio QCD • 1980 + 50 = 2030?* • 10 Mflops  1000 Tflops • Clever Multi-scale Variable? “Almost 20 Years ahead of schedule!” *Fast Computers + Smart Algorithms + Rigorous QCD Theoretical Analysis = ab inition predictions

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

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

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

  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(a2) asymptotic freedom • Light quark limit mu/d/ms O(1/20) • solution: Chiral pert. theory + Exact Lattice Chiral Symmetry • Finite space-time volume • solution: Big memory computer • Monte Carlo 1/N1/2 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 (data) vs Perturbation Theory (red/one sigma band) Lattice: S(MZ) = 0.1170(12) Experiment: S(MZ) = 0.1187(20)

  11. Alpha Strong

  12. CKM projected improvement via Lattice Gauge Before After

  13. Properties of  and K mesons Rule out mu = 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 Experiment gA = 1.295 (29) Lattice gA = 1.226 (84)

  15. Semi-leptonic Form Factor (prediction)

  16. Multi-scale Algorithms QCD length scales: Log(mq) • 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 asinglet = - 23.714 fm ( » 8 Mev) & r = 2.73 atriplet = 5.425 fm ( » 36 Mev) & r = 1.749 fm • Deuteron Binding = 50 Mev. (» 4 fm) • Finite T, finite  etc Flavor: u,d,s,c,b,t

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

  18. Quark loops: Multi-time step HMC 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: • Hasenbush Trick: • Rational Hybrid Monte Carlo: 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. Exact Lattice Chiral Fermions: (Taking the 5th Dimension Seriously ?) s = 1 s = 2 s = M s = Ls qL QL qR QR RIGHT LEFT qR QR QL qL

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

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

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

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