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Lattice QCD (INTRODUCTION)

Lattice QCD (INTRODUCTION). DUBNA WINTER SCHOOL 1-2 FEBRUARY 2005. Main Problems. Starting from Lagrangian. (1) obtain hadron spectrum, (2) describe phase transitions, (3) explain confinement of color. http:// www.claymath.org/Millennium_Prize_Problems/.

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Lattice QCD (INTRODUCTION)

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  1. Lattice QCD(INTRODUCTION) DUBNA WINTER SCHOOL 1-2 FEBRUARY 2005

  2. Main Problems Starting from Lagrangian (1) obtain hadron spectrum, (2) describe phase transitions, (3) explain confinement of color http://www.claymath.org/Millennium_Prize_Problems/

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

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

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

  7. Chiral limit Quark masses Pion mass Exp

  8. Nucleon mass extrapolation Fit on the base of the chiral perturbation theory

  9. Spectrum

  10. Earth Simulator • Based on the NEC SX architecture, 640 nodes, each node with 8 vector processors (8 Gflop/s peak per processor), 2 ns cycle time, 16GB shared memory. – Total of 5104 total processors, 40 TFlop/s peak, and 10TB memory. • It has a single stage crossbar (1800 miles of cable) 83,000 copper cables, 16 GB/s cross section bandwidth. • 700 TB disk space, 1.6 PB mass store • Area of computer = 4 tennis courts, 3 floors

  11. DUBNA 1 FEBRUARYGluon fields inside hadrons on the lattice DESY-ITEP-Kanazawacollaboration V.G.Bornyakov, M.N.Chernodub, H.Ichie, S.Kitahara, Y.Koma,Y.Mori, S.M. Morozov, Y.Nakamura, D.Pleiter, M.I.P., G.Schierholz, D.Sigaev, A.A.Slavnov, T.Streuer, H.Stuben, T.Suzuki, P.Uvarov, A.Veselov hep-lat/0401027, hep-lat/0401026, hep-lat/0401014, hep-lat/0310011, hep-lat/0309176, hep-lat/0309144, hep-lat/0301003, hep-lat/0301002, hep-lat/0212023, hep-lat/0209157, heplat/0111042, …

  12. Simulations • We study QCD with two flavors of non-perturbatively improved Wilson fermions at zero and finite temperature on • 163·8, 243·10 and 243·48 lattices. • Lattice spacings a~0.12 fm • Quark masses mq~100 Mev • Temperatures 0.8<T/Tc<1.28 and T=0. • Abelian variables!

  13. Confining String (Bali, Schlichter, Schilling)

  14. Confining String

  15. Electric field of confining String

  16. Anatomy of Confining String in SU(2) Lattice Gauge TheoryY. Koma, M. Koma, E.-M. Ilgenfritz, T. Suzuki, M.I. P. (2002)

  17. Anatomy of Confining String in Dual Abelian Higgs TheoryY. Koma, M. Koma, E.-M. Ilgenfritz, T. Suzuki, M.I. P. (2002)

  18. Action density of the confining string in Full QCD

  19. Electric field inside the confining string

  20. Monopole currents near the confining string

  21. Check of Maxwell equations

  22. String Breaking QQ Qq Qq Hard to observe at T=0, but at T>0, T<TC it is possible

  23. String BreakingAbelian action densityT>0, T/TC=0.94

  24. String BreakingMonopole actionT>0, T<TC

  25. T/TC=0.94R=0.5 fmR=0.8 fmR=1.3 fm

  26. T/TC=0.94R=0.5 fmR=0.8 fmR=1.3 fm

  27. Profile of the action density in the center of the confining string, T/TC=0.94 R=0.36 fm R=0.85 fm

  28. Analytical description of the profiles R=0.36 fm R=0.85 fm Dipole distribution Lusher-Wiesz fit

  29. Quark-antiquark potential at various temperatures, the Coulomb is subtracted

  30. String tension as the function of the temperatureString breaking distance as the function of temperature

  31. Baryonic system(static potential and string breaking)

  32. Baryon action densityat T=0Y-shape of the string is clearly seen

  33. Mass of material objects is due to gluon fields inside baryon

  34. Sum of ½ meson flux tubes

  35. Y or Delta ? • The baryon action density has a bump in the center, while the superposition of ½ meson flux tubes has a dip • The similar results were also obtained for the Potts model (C. Alexandrou, Ph. de Forcrand and O. Jahn, 2003 )

  36. Baryon action density at T>Tc

  37. RY=r1+r2+r3 Ferma point r2 r1 r3

  38. Baryon potential T=0 T/TC =0.94

  39. Baryon string breaking at T=0

  40. Fitting results String tensions Masses Shaded area: quenched string tension

  41. Electric fields and monopole currents in the chromoelectric string in thebaryon O Electric fields R B G Monopole currents (in perpendicular planes)

  42. Fixed temperature: Action Electric field

  43. Fixed baryon size: Temperatures:

  44. PENTAQUARK

  45. String breakingin 5q systemr=1

  46. r=2

  47. r=3

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