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

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

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

MethodsImaginary time tit

Space-time discretization

Thus we get from functional integral the statistical theory in four dimensions

The statistical theory in four dimensions can be simulated by Monte-Carlo methods

The typical multiplicities of integrals are 106-108We have to invert matrices 106 x 106The cost of simulation of one configuration is:

Three limitsLattice spacingLattice sizeQuark massTypical values nowExtrapolation +Chiral perturbation theory

Chiral limitQuark masses Pion massExp

Nucleon mass extrapolationFit on the base of the chiral perturbation theory

Spectrum

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 storeArea of computer = 4 tennis courts, 3 floors

DUBNA 1 FEBRUARYGluon fields inside hadrons on the lattice

DESY-ITEP-Kanazawa collaboration 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 ,

SimulationsWe study QCD with two flavors of non-perturbatively improved Wilson fermions at zero and finite temperature on 1638, 24310 and 24348 lattices. Lattice spacings a~0.12 fm Quark masses mq~100 Mev Temperatures 0.8

Confining String (Bali, Schlichter, Schilling)

Confining String

Electric field of confining String

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

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

Action density of the confining string in Full QCD

Electric field inside the confining string

Monopole currents near the confining string

Check of Maxwell equations

String Breaking QQQqQq

Hard to observe at T=0, but at T>0, T

String Breaking Abelian action densityT>0, T/TC=0.94

String Breaking Monopole actionT>0, T

T/TC=0.94

R=0.5 fm

R=0.8 fm

R=1.3 fm

T/TC=0.94

R=0.5 fm

R=0.8 fm

R=1.3 fm

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

Analytical description of the profilesR=0.36 fm R=0.85 fmDipole distributionLusher-Wiesz fit

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

String tension as the function of the temperature

String breaking distance as the function of temperature

Baryonic system(static potential and string breaking)

Baryon action densityat T=0

Y-shape of the string is clearly seen

Mass of material objects is due to gluon fields inside baryon

Sum of meson flux tubes

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

Baryon action density at T>Tc

RY=r1+r2+r3Ferma pointr1r2r3

Baryon potentialT=0T/TC =0.94

Baryon string breaking at T=0

Fitting resultsString tensionsMassesShaded area: quenched string tension

Electric fields and monopole currents in the chromoelectric string in the baryonElectric fieldsMonopole currents(in perpendicular planes)BOGR

ActionElectricfieldFixed temperature:

Fixed baryon size: Temperatures:

PENTAQUARK

String breaking in 5q system r=1

r=2

r=3

r=4

Potential

H = HOLLYWOOD