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LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END OF 2006) ITEP 7 February 2007

LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END OF 2006) ITEP 7 February 2007. a). Introduction b). Quenched calculations c). Calculations with 2 light dynamical quarks d). (2+1) QCD. INTRODUCTION. Main Problems: starting from Lagrangian. obtain hadron spectrum,

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LATTICE QCD SIMULATIONS, SOME RECENT RESULTS (END OF 2006) ITEP 7 February 2007

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  1. LATTICE QCD SIMULATIONS, SOME RECENT RESULTS(END OF 2006) ITEP 7 February 2007 a). Introductionb). Quenched calculationsc). Calculations with 2 light dynamical quarksd). (2+1) QCD

  2. INTRODUCTION Main Problems: starting from Lagrangian • obtain hadron spectrum, • calculate various matrix elements, • (3) describe phase transitions, and phase diagram • (4) explain confinement of color

  3. INTRODUCTION The main difficulty is the absence of analytical methods, the interactions are strong and only computer simulations give results starting from the first principles. The force between quark and antiquark is 12 tones

  4. INTRODUCTION Methods • Imaginary time t→it • Space-time discretization • Thus we get from functional integral the statistical theory in four dimensions

  5. INTRODUCTION The statistical theory in four dimensions can be simulated by Monte-Carlo methods • The typical multiplicities of integrals are 106-1010 • We have to invert matrices 108 x 108 • The cost of simulation of one configuration is: Improved Wilson fermions

  6. INTRODUCTION Three limits Lattice spacing Lattice size Quark mass Typical values Extrapolation + Chiral perturbation theory

  7. INTRODUCTION Example of extrapolation

  8. INTRODUCTION Fit on the base of the chiral perturbation theory

  9. SU(2) glue;SU(3) glue;2qQCD;(2+1)QCD Numerical results

  10. SU(2) glue SU(3) glue 2qQCD (2+1)QCD 8 Theory of color confinement 8 Theory of chiral symmetry breaking 8 Monopoles 8 Vortices 8 Instantons and calorons 8 Localization of Dirac eigenmodes

  11. SU(2) glue SU(3) glue 2qQCD (2+1)QCD 8 Theory of color confinement 8 Theory of chiral symmetry breaking 8 Monopoles 8 Vortices 8 Instantons and calorons 8 Localization of Dirac eigenmodes

  12. SU(2) glue SU(3) glue 2qQCD (2+1)QCD 8 Theory of color confinement 8 Theory of chiral symmetry breaking 8 Monopoles 8 Vortices 8 Instantons and calorons 8 Localization of Dirac eigenmodes

  13. SU(2) glue SU(3) glue 2qQCD (2+1)QCD 8 Theory of color confinement 8 Theory of chiral symmetry breaking 8 Monopoles 8 Vortices 8 Instantons and calorons 8 Localization of Dirac eigenmodes (Anderson localistion)

  14. SU(2) glueSU(3) glue 2qQCD (2+1)QCD

  15. SU(2) glue SU(3) glue 2qQCD (2+1)QCD • Study of the complicated systems: • Structure of gluon fields inside hadron • Nucleon-Nucleon potential Three body forces!

  16. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Usually the teams are rather big, 5 - 10 -15 people

  17. SU(2) glue SU(3) glue 2qQCD (2+1)QCD The Nuclear Force from Lattice QCD N.Ishii, S.Aoki and T.Hatsuda; nucl-th/0611096;hep-lat/0610002 Phenomenological potential From lattice calculations (six quark matrix element)

  18. SU(2) glue SU(3) glue 2qQCD (2+1)QCD The Nuclear Force from Lattice QCD N.Ishii, S.Aoki and T.Hatsuda; nucl-th/0611096hep-lat/0610002 Lattice calculations with mp/mr=0.595

  19. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Viscosity of quark gluon plasma RHIC result at 1.4<T/Tc<1.8: quark-gluon plasma is not a gas but rather a kind of liquid with low viscosity A. Nakamura, S. Sakai, hep-lat/0510039

  20. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Potential between two B-mesons J. Savage et al. hep-lat/0611038

  21. 2qQCD (2+1)QCD u,d,s virtual quarks

  22. 2qQCD SU(2) glue SU(3) glue 2qQCD (2+1)QCDNew effect: String Breaking Dynamical quarks QQ Glue Qq Qq

  23. SU(2) glue SU(3) glue 2qQCD (2+1)QCDString Breaking (DIK collaboration)MESON

  24. SU(2) glue SU(3) glue 2qQCD (2+1)QCDString Breaking (DIK collaboration)BARYON

  25. SU(2) glue SU(3) glue 2qQCD (2+1)QCD • Partition function of QCD with one flavor at temperature T is: In computer

  26. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Types of Fermions • Wilson • Kogut-Suskind • Wilson improved • Wilson nonperturbatevely improved • Domain wall • Staggered • Overlap 1. Quark mass ->0 2. Fast algorithms

  27. SU(2) glue SU(3) glue 2qQCD (2+1)QCD G. Schierholz (Trento 2006) OLD 2001 2006 NEW 2006

  28. SU(2) glue SU(3) glue 2qQCD (2+1)QCD G. Schierholz (2006) (Trento)

  29. SU(2) glue SU(3) glue 2qQCD (2+1)QCD G. Schierholz (2006) (Trento)

  30. SU(2) glue SU(3) glue 2qQCD (2+1)QCD G. Schierholz (Trento 2006)

  31. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Phase diagram (F.Karsch) Four plenary talks at Lattice 2006! • Color superconductivity in ultra-dense quark matter.Mark G. Alford; hep-lat/0610046 • Lattice QCD at finite density.C. Schmidt;hep-lat/0610116 • Recent progress in finite temperature lattice QCD.Urs M. Heller; hep-lat/0610114 • QCD phase diagram: an overview.M.A. Stephanov; hep-lat/0701002

  32. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Phase diagram THEORY 2-nd or 1-st order for m=0? Di Giacomo –first order (2006) 3 First order (Pisarski, Wilczek)

  33. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Phase diagram: numerical calculations are very difficult, since we have a complex Monte-Carlo weight COMPLEX

  34. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Phase diagram: numerical calculations are very difficult, since we have a complex Monte-Carlo weight Various numerical tricks: analytical continuations, m->im QCD critical point in T-m plane RED – RHIC experiment BLACK – phenomenological models GREEN – Lattice calculations M.A. Stephanov; hep-lat/0701002

  35. Critical temperature, m=0 SU(2) glue SU(3) glue 2qQCD (2+1)QCD • Pure glue SU(3) F. Karsch • Two flavor QCD, clover improved Wilson fermions C.Bernard (2005) DIK collaboration (2005) • Two flavor QCD, improved staggered fermions F.Karsch (2000) • Three flavor QCD, improved staggered fermions! F.Karsch (2000)

  36. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Tc by DIK (DESY-ITEP-Kanazawa) collaboration V.G. Bornyakov, M.N. Chernodub, Y. Mori, S.M. Morozov, Y. Nakamura, M.I. Polikarpov, G. Schierholz, A.A. Slavnov, H. Stüben, T. Suzuki (2006) Russian (JSCC) supercomputer M15000

  37. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Tc by DIK (DESY-ITEP-Kanazawa) collaboration V.G. Bornyakov, M.N. Chernodub, Y. Mori, S.M. Morozov, Y. Nakamura, M.I. Polikarpov, G. Schierholz, A.A. Slavnov, H. Stüben, T. Suzuki (2006)

  38. SU(2) glue SU(3) glue 2qQCD (2+1)QCD DIK RESULTS

  39. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Plasma thermodynamics • Free energy density • energy, entropy, velocity of sound, . pressure

  40. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Plasma thermodynamics, example: pressure F. Karsch (2001-2005)

  41. SU(2) glue SU(3) glue 2qQCD (2+1)QCD Quark condensate F.Karsch et al.

  42. (2+1)QCD JLQCD, CP-PACS The description of the meson mass spectrum is good, but not excellent for lattice QCD with two dynamical quarks

  43. (2+1)QCD JLQCD, CP-PACS The description of the meson mass spectrum is good, but not excellent for lattice QCD with two dynamical quarks f meson mass vs lattice spacing (the mass of the s-quark is fitted from the mass of the K meson)

  44. (2+1)QCD JLQCD, CP-PACS Almost three years of gauge field trajectories generation at Earth Simulator; Lattice spacial volume is (2 fm)^3, a=0.07, 0.1, 0.12 fm

  45. (2+1)QCD JLQCD, CP-PACS RESULTS

  46. (2+1)QCD JLQCD, CP-PACS RESULTS

  47. (2+1)QCD MILC configurations,staggered dynamical fermions, NPLQCD CollaborationHyperon-Nucleon phase shifts (hep-lat/0612026)

  48. Instead of Conclusions I did not discuss a number of important topics Formfactors Heavy-Light mesons Heavy – Heavy mesons and many others

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