NSF Key Project and NSF Key Project and Recent Progress of Recent Progress of Lattice QCD in ChinaLattice QCD in China

Zhongshan (Sun Yat-Sen) University,

Guangzhou, China

stslxq@zsu.edu.cn

http:// qomolangma.zsu.edu.cn

• Xiang-Qian Luo

•Chinese physicists have been involved in the study of lattice gauge theory since early 80's.

•Institute of High Energy Physics, Beijing

•Institute of Theoretical Physics, Beijing

•Peking Uniniversity, Beijing

•Nankai University, Tianjin

•Sichuan University, Chengdu

•Zhejiang University, Huangzhou

•Zhongshan University, Guangzhou

•Beijing

•Tianjin

•Chengdu

•Huangzhou

•Guangzhou

•Most investigations in 80’s were analytical, due to limited computational facilities.

•For review, Guo and Luo, hep-lat/9706017.

•Thanks to (1) rapid development of high performance supercomputers in China in late 90's,

(2) success of the Symanzik improvement program,

(3) support from NSF (National Science Foundation),

more and more Chinese physicists do numerical simulations.

Count Share Rmax Rpeak Procs

USA 228 45.6 % 148696 247700 137736

Germany 71 14.2 % 25468 39590 17778

Japan 47 9.4 % 57902 68619 17331

UK 39 7.8 % 20644 38174 17148

France 22 4.4 % 9644 13341 6543

Italy 16 3.2 % 5525 9040 2664

Korea 9 1.8 % 2569 4554 1284

Netherlands 6 1.2 % 2036 4263 3600

China 5 1 % 1899 3473 960

Sweden 5 1 % 2256 3801 1824

Mexico 5 1 % 1155 2469 1600

Canada 5 1 % 1166 1794 1136

Finland 4 0.8 % 1847 3223 1308

Belgium 4 0.8 % 884 1309 528

Australia 3 0.6 % 1410 2040 720

Taiwan 3 0.6 % 1019 1830 425

Saudi Arabia 3 0.6 % 1098 3390 2768

Norway 3 0.6 % 1006 1497 992

Egypt 3 0.6 % 800 2719 2560

Thailand 3 0.6 % 679 966 416

Brazil 3 0.6 % 589 824 400

Singapore 2 0.4 % 855 1516 400

Hong Kong 2 0.4 % 796 1236 724

Spain 2 0.4 % 410 595 240

South Africa 2 0.4 % 394 541 272

Switzerland 1 0.2 % 736 1331 256

Russian Federation 1 0.2 % 734 1024 768

Portugal 1 0.2 % 393 570 380

New Zealand 1 0.2 % 234 448 132

Austria 1 0.2 % 204 472 160

Total 500 100 % 293058 462357 223053

•Top 500 Supercomputers in the world, 2002

•Top 50 supercomputers in China, 2002

Dawning 3000

Dawning 3000

128 nodes

Rmax: 279.60Gflops

Rpeak: 403.2Gflops

Memory: 168GB

Disk: 3.63TB 。

CPU: Power3-II,

Network: 2D Mesh or Myrinet

Operating system: IBM AIX

•DeepComp 1800

•Legend GroupDeepComp 1800 - P4 Xeon 2 GHz - Myrinet/ 512CPU (NODES)

•Rmax:1.046 TflopsRpeak: 2.048 Tflops

•Location: Beijing, China

•Number 43 of top 500 supercomputers 2002

•The 3rd fastest in Asia?

•http://www.top500.org/lists/2002/11/

•Zhongshan U. self-made PC cluster, 2000

NSFC: National Science Foundation Committee: established in 1986

an organization directly affiliated to the State Council for the management of the National Natural Science Fund.

General project: ~100K yuan for 3 years. (1 Yuan=1/8USD)

NSF project for distinguished young scientists: ~ 80M yuan for 4 years.

Key NSF project: ~100M yuan for 4 years

•Approved NSF Funds in China

•These years, the Chinese lattice physicists received a lot of supports from NSFC and other sources:•T.L. Chen, Nankai U., General project, ~100K yuan

•S.H. Guo, Zhongshan U., Guangzhou, General project, ~100K yuan

•C. Liu, Peking U., Beijing, General project, ~100K yuan

•J.M. Liu, Zhongshan U., General project, ~100K yuan

•X.Q. Luo, Zhongshan U., General project, ~100K yuan

•J.M. Wu, IHEP, Beijing, General project, ~100K yuan

•H.P. Ying, Zhejiang U., Huangzhou, General project, ~100K yuan

•X.Q. Luo, Zhongshan U., NSF project for distinguished young scientists: 80M yuan (1999-2002)

•X.Q. Luo, Q.Z. Chen, Y. Chen, Y.Z. Fang, S.H. Guo, C.Q. Huang,

C. Liu, Z.H. Mei, H.P. Ying, Key NSF project: 120M yuan (2003-2006)

•Structure of Matter

Quantum ChromoDynamics(QCD) ： theory of strong interactions between quarks, mediated by gluons

Lattice Gauge Theory (Wilson, 1974): most reliable non-perturbative tool for strong interactions

Basic Ideas:

Continuum space-time Discretized grid

Derivative Finite difference

)(2

)()( 2

aOa

axax

dx

d

•a) quark field (x)

•b) gauge field U(x,k)

•Advantage: physical quantities can now be calculated by Monte Carlo simulation on a computer

•Disadvantage: O(a) errors are large at large coupling g.

•To reduce the error and keep La > diameter of the hadron, large volume (L>>1) is needed

•It costs a lot of computer time, and high performance parallel computer is necessary

•L: the number of lattice point in one direction

)(12

)2()(8)(8)2( 4

aOa

axaxaxax

dx

d

Improved Lattice QCD

• The most efficient way to reduce the O(a) and finite volume errors

• Improved scalar action (Symanzik, 1983)

• Quark action: Hamber and Wu, Phys. Lett. B133 (1983) 351.

(Sheikholeslami and Wohlert, 1985)

• Improved gluon action (Luscher, Weisz, 1984)

• Tadpole improvement (Lepage, 1996)

• Improved quark Hamiltonian:

Luo, Chen, Xu, Jiang, , Phys. Rev. D50 (1994) 501.

Jiang, Luo, Mei, Jirari, Kroger, Wu, Phys. Rev. D59 (1999) 014501.

• Improved gluon Hamiltonian:

Luo, Guo, Kroger, Schutte, Phys. Rev. D59 (1999) 034503.

Algorithms

• To do numerical simulations with dynamical Wilson fermions ：

Thron, Dong, Liu, Ying ， Phys.Rev. D57 （１９９８） 1642

Ying, Chin. Phys. Lett. 15 (1998) 401.

• To do numerical simulations with Kogut-Susskind fermions in the chiral limit:

Luo, Mod. Phys. Lett. A16 (2001) 1615.

Which extends the following algorithm to QCD:

Azcoiti, Di Carlo, Grillo, Phys. Rev. Lett. 65 (1990) 2239.

Azcoiti, Laliena, Luo, Piedrafita, Di Carlo, Galante, Grillo ， Fernandez, Vladikas, Phys. Rev. D48 (1993) 402.

•To do numerical simulations with clover fermions:Luo, Comput. Phys. Commun. 94 (1996) 119-127.

Jansen and Liu, Comput. Phys. Commun. 99 (1997) 221.

•To do numerical simulations with Ginsparg-Wilson fermions:Liu, Nucl. Phys. B554 (1999) 313.

Problems of standard Langrangian Monte Carlo simulations:

(1)Extremely difficult to study excited states,

(2)Broken done in QCD at finite density.

Hamiltonian formulation of LGT does’t encounter above problem.

Monte Carlo Hamiltonian: to construct effective Hamiltonian from standard Monte Carlo simulations.

Tested in quantum mechanics:Jirari, Kroger, Luo, Moriarty, Phys. Lett. A258 (1999) 6.

Luo, Jiang, Huang, Jirari, Kroger, Moriarty, Physica A281 (2000) 201.

Tested in the scalar model:

Huang, Kroger, Luo, Moriarty, Phys. Lett. A299 (2002) 483.

                                                                     (1)

†M(T)=U D(T)U.

                                       (5)                             

(6)

                                             

Fig. 1. Energy spectrum in a low energy window.

•Fig. 2. Free energy F. Comparison of results from Monte Carlo Hamiltonian (filled circles) with standard Lagrangian lattice calculations (open circles).

Scattering of hadrons using tadpole improved clover Wilson action on coarse anisotropic lattices

Liu, Zhang, Chen, Ma ， Nucl. Phys. B624 (2002) 360 ．

•C ． Liu 

  “Pion scattering length with small anisotropic lattices,” this workshop

•QCD predict the existence of some new particles:

• Glueball: bound state of gluons

• Hybrid meson: bound state of quark, anti-quark and gluons

•Hybrid meson

•Glueball

•Glueball Spectrum•From Hamiltonian lattice QCD:

• Luo, Q. Chen, Mod.Phys.Lett. A11 (1996) 2435.

Nucl. Phys. B(Proc.Suppl.)53 (1997) 243.

•From Improved glunon action:

• C. Liu, Chin. Phys. Lett. 18 (2001) 187.

•D. Liu, Wu, Y. Chen, High Energy Phys. Nucl. Phys. 26 (2002) 222.

Mod.Phys.Lett. A17 (2002) 1419.

•Mei, Luo, 2003, in preparation.•Quantum number JPC

•Construct New Glueball Operators using their relation between lattice and continuum:

•D. Liu, Wu, Y. Chen, High Energy Phys. Nucl. Phys. 26 (2002) 222.

First Calculation for the Mass of the 4++ Glueball

D. Liu, Wu, Mod.Phys.Lett. A17 (2002) 1419.

•Mei, Luo, 2002: Glueball masses from Improved gluon action (compared with Morningstar, Peardon, 1997, 1999)

•MG(0++)=1733MeV

•MG(2++)=2408MeV

•MG(1+-) =2951MeV

•Glueballs can also mix with mesons, and decay (in progress)

•Hybrid meson masses from QCD with improved gluon and quark actions on the anisotropic lattice

Mei and Luo, hep-lat/0206012

•At sufficiently high temperature and density, quarks are no longer confined

•New state of matter: Quark-Gluon Plasma

•Neutron StarNeutron Star

•RHIC (Relativistic Heavy Ion Collider)

•LHC (Large Hadron Collider)

•Lattice QCD at High Temperature can well be investigated by the standard Monte Carlo approach

• At finite density (chemical potential), standard action approach (Hasenfratz, Kasch, 1983) fails: because S is complex, one can not use e-S to generate configurations

• Alternative (Hamiltonian): QCD at finite chemical potential was solved in the strong coupling regime:

Gregory, Guo, Kroger, Luo, Phys. Rev. D62 (2000) 054508.

Luo, Gregory, Guo, Kroger, hep-ph/0011120.

Fang, Luo, hep-lat/0210031.

• There is a first order chiral phase transition at c

• Reasonable results for the

physical quantities are

obtained,

Nature of the chiral phase transition?

Rapp, Schafer, Shuryak, Velkovsky, 1998

Alford, Rajagopal, Wilczek, 1998

Diquark condensation in the high density phase?

Instantons and chaos play an important role?

(1) There is no first principle study in SU(3).

(2) The definition of quantum instantons and quantum chaos are umbiguous.•New Quantum Instantons and Quantum Chaos:

Jirari, Kroger, Luo, Moriarty, Rubin, Phys. Rev. Lett. 86 (2001) 187.

Key Project of National Science Key Project of National Science FoundationFoundation""Large Scale Simulations of Lattice Large Scale Simulations of Lattice Gauge TheoryGauge Theory“, 120M (2003-2006)“, 120M (2003-2006)

• Xiang-Qian Luo (Director, Zhongshan U., Xiang-Qian Luo (Director, Zhongshan U., Guangzou)Guangzou)

• Qi-Zhou Chen (Zhongshan U., Guangzhou)Qi-Zhou Chen (Zhongshan U., Guangzhou)Ying Chen (Institute of High Energy Phys., Ying Chen (Institute of High Energy Phys., Beijing)Beijing)Yi-Zhong Fang (Zhongshan U., Guangzou)Yi-Zhong Fang (Zhongshan U., Guangzou)Shuo-Hong Guo (Zhongshan U., Guangzou)Shuo-Hong Guo (Zhongshan U., Guangzou)Chun-Qing Huang (Zhongshan U. and Foshan Chun-Qing Huang (Zhongshan U. and Foshan U.)U.)Chuan Liu (Peking U., Beijing)Chuan Liu (Peking U., Beijing)Da-Qing Liu (Institute of Theoretical Phys., Da-Qing Liu (Institute of Theoretical Phys., Beijing)Beijing)Zhong-Hao Mei (Zhongshan U., Guangzou)Zhong-Hao Mei (Zhongshan U., Guangzou)He-Ping Ying (Zhejiang U., Huangzhou)He-Ping Ying (Zhejiang U., Huangzhou)

•We plan to do large scale simulations of lattice QCD, using the parallel supercomputing facilities in China. We will develop new numerical methods and study the following hot topics:

•new hadrons such as glueballs and hybrid mesons,

•scattering of hadrons,

•topology of QCD vacuum,

•transition from the quark confinement phase to quark-gluon plasma phase,

•quantum instantons and quantum chaos.