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1 Lattice QCD: status and prospect An overview including a bit of history Current focus – dynamical 2+1 flavor simulations - A selected topic - lattice pentaquark search - What now? Summary Akira Ukawa Center for Computational Sciences University of Tsukuba XXV Physics in Collision Prague 9 July 2005

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2 Quantum Chromodynamics Quantum field theory of quarks and gluon fields Knowing 1 coupling constant and 6 quark masses will allow full understanding of hadrons and their strong interactions Gross-Wilczek-Politzer 1973 Quark field Gluon field defined over 4-dim space time QCD lagrangian Physical quantities by Feynman path integral

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3 QCD on a space-time lattice Feynman path integral Action Physical quantities as integral averages K. G. Wilson 1974 Space-time continuum Space-time lattice quark fields on lattice sites gluon fields on lattice links Monte Carlo Evaluation of the path integral

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4 Understanding confinement … Random fluctuations of gluon fields cut off correlation at a finite distance A new mechanism of force; not understandable via Yukawa ’ s picture of particle exchange G. Bali and K. Schilling, Phys.Rev. D47 (1993) 661-672

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5 Physical quantities from Euclidean hadron Green functions Hadron masses from 2-point functions Matrix elements from 3-point functions Actual evaluation via Monte Carlo simulation Totally unexpected way to calculate relativistic bound state properties Making it possible to calculate …

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6 Lattice QCD as computation Monte Carlo simulations of lattice QCD Powerful and only general method to calculate the QCD Feyman path integral From computational point of view Relatively simple calculation Uniform mesh Single scale Requires much computing power due to 4-dimensional Problem Fermions (quarks) essential Physics is at lattice spacing a=0 Precision required (
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"name": "6 Lattice QCD as computation Monte Carlo simulations of lattice QCD Powerful and only general method to calculate the QCD Feyman path integral From computational point of view Relatively simple calculation Uniform mesh Single scale Requires much computing power due to 4-dimensional Problem Fermions (quarks) essential Physics is at lattice spacing a=0 Precision required (

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7 Development of lattice QCD simulations (I) lattice size lattice spacing L= 0.8 fm a = 0.1 fm 1981 First lattice QCD simulation VAX ４ ４ ～ ８ ４ lattice quenched approx (no sea quarks) Creutz-Jacobs-Rebbi Creutz Wilson Weingarten Hamber-Parisi Pictures by K. Kanaya

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8 L(fm) a(fm) １９８１ 0.8 0.1 １９８５ 1.2 0.1 １９８８ 1.6 0.1 1980’s Taking advantage of vector supercomputers CRAY-1 1 GFLOPS = one billon flop/sec Development of lattice QCD simulations (II) vector supercomputers

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9 L(fm) a(fm) １９９３ 2.4 0.07 QCDPAX （ JPN ） APE （ Italy ） Columbia （ USA ） GF11 （ USA ） Development of lattice QCD simulations (III) 1990’s QCD dedicated parallel computers vector supercomputers parallel supercomputers

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10 L(fm) a(fm) １９９８ 3.0 0.05 Development of lattice QCD simulations (IV) CP-PACS(JPN)QCDSP(USA) 2000s further development of QCD dedicated computers parallel supercomputers

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11 Progress over the years … 1970 19902000 1980 1995 2005 1985 1975 VAX 1Mfops Crays 100Mflops 2 nd generation 10Gflops QCD-dedicated computers 3 rd generation 1Tfops 4 th generation 10Tfops Lattice size L 0.8fm 1 st spec calculation 1980-81 Weingarten Hamber-Parisi 1.6fm2.4fm 3.0fm 2.4fm #sea quarks Nf Nf=0 quenched Nf=2 u,d Nf=2+1 u,d,s QCDPAX APE100 CP-PACS QCDSP QCDOC 8 3 x16 16 3 x32 24 3 x48 64 3 x118 24 3 x48 Current focus

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12 Impact of lattice QCD LQCD Finite-temperature/ density behavior eta’ meson mass and U(1) problem exotic states glueball, hybrids, penta-quark,… hadronic matrix elements proton spin, sigma term, …. structure functions/form factors Weak interaction matrix elements Hadron spectrum and Fundamental constants of QCD Hadron physics Strong coupling constant Quark masses order of transition critical temperature/density equation of state K meson amplitudes B K K → decays B meson amplitudes f B, B B, form factors Physics of quark-gluon plasma CKM matrix and CP violation Long-standing issues of hadron physics Fundamental natural constants

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13 “ The origins of lattice gauge theory ” recollections by K. G. Wilson at Lattice 2004 The discovery of asymptotic freedom made it clear … that the prefered theory of strong interactions is QCD … … What was I to do, especially I was eager to jump into this research with as little delay as possible? … I knew a lot about lattice theories … … I decided I might find it easier to work with a lattice version of QCD than with the … continuum formulation … Formulating the theory on a lattice turned out to be straightforward … However, the concept of confinement was nowhere in my thinking when I started to construct lattice gauge theory. … When I started to study the strong coupling expansion, I ran into a barrier … … But the situation did eventually become clarified … I was able to write the article … accepted by Physical Review in June 1974 …

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14 Current focus -dynamical 2+1 flavor simulations-

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15 quenched spectrum as a benchmark Sea quark effects ignored General pattern reproduced, but clear systematic deviation of 5-10% e.g., K-K* mass difference too small CP-PACS 1998

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16 QCD simulation with dynamical quarks Spectrum of quarks 3 light quarks (u,d,s)m < 1GeV Need dynamical simulation 3 heavy quarks (c,b,t) m >1GeV Quenching sufficient Dynamical quark simulation (full QCD) costs 100-1000 times more computing power Algorithm for odd number of quarks now available Two-flavor full QCD (since around 1996) u and d quark dynamical simulation s quarkquenched approximation Number of studies: SESAM/UKQCD/MILC/CP-PACS/JLQCD Two+One-flavor full QCD s quark also treated dynamically Extensive studies since around 2000

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17 Nf=2+1 simulations in progress MILC Collaboration and various groups in USA staggered quark action U(1) chiral symmetry “ quartic root ” to deal with the wrong flavor content Joint effort of CP-PACS/JLQCD Collaborations in Japan Wilson-clover quark action Normal spin-flavor content Needs fine-tuning to control chiral symmetry and scaling violation RBC/UKQCD Collaboration across Atlantic domain-wall quark action Chiral symmetry for sufficiently large N5 Computationally much more demanding Starting up using QCDOC at Edinburgh and BNL

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18 KEK U Tsukuba Tokyo Tsukuba 5km KEK Yamada Matsufuru Kaneko Hashimoto U. Tsukuba Ishikawa T. Taniguchi Kuramashi Ishizuka Yoshie Ukawa Baer Aoki Kanaya Iwasaki Kyoto Onogi Hiroshima Ishikawa K. Okawa Now elsewhere Okamoto(FNAL->KEK) Lesk(Imp. Coll.) Noaki(Southampton) Ejiri(Tokyo) Nagai(Zeuthen) Aoki Y.(Wuppertal) Izubuchi(Kanazawa) Ali Khan(Berlin) Manke Shanahan(London) Burkhalter(Zurich) CP-PACS / JLQCD based at U. Tsukuba based at KEK

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19 Use of fully O(a) improved Wilson-clover quark action Lattice spacing errors are O(a 2 ) Polynomial hybrid Monte Carlo algorithm to deal with odd number of dynamical quarks CP-PACS/JLQCD joint effort toward Nf=2+1 strategy JLQCD K. Ishikawa et al PRD C_sw for Nf=3 JLQCD/CP-PACS K. Ishikawa et al Lattice’03

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20 Lattices and computers β=1.90 a ～ 0.10fm 20^3 x 40 8000 trajectory finished β=1.83 a ～ 0.12fm 16^3 x 32 5000 trajectory finished β=2.05 a ～ 0.07fm 28^3 x 56 3000 trajectory in progress Fixed physical volume ～ (2.0fm)^3 Lattice spacing Earth simulator @ Jamstec SR8000/F1 @KEK CP-PACS @Tsukuba SR8000/G1 @Tsukuba VPP5000 @Tsukuba

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21 Meson hyperfine splitting for Nf=2+1 Promising a 1% agreement ….

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22 Light quark masses Sizably small compared to folklore, e.g. mud ～ 5MeV, ms ～ 150MeV

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23 Nf=2+1 simulation in USA pursued by the MILC Collaboration Staggered quark action Three lattice spacings, a ～ 0.12fm, 0.09fm, (0.078fm) Relatively light quark, e.g., mpi ～ 300MeV (500MeV for JLQCD/CP-PACS) Variety of physical quantities by collaborators FNAL, HPQCD,UKQCD, … Quark masses Strong coupling constant D and B meson quantities via NRQCD …

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24 Consistency among heavy/light quantities HPQCD/UKQCD/MILC/FNAL PRL92(2004)022001 Light sector Heavy sector Quenched results Nf=2+1 results Input masses to fix quark masses and lattice spacing

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25 experiment Estimation of HPQCD and UKQCD Collaboration (Q. Mason et al) hep-lat/0503005 Latest lattice QCD result

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26 Attempts to fix CKM matrix elements from semi-leptonic decays FNAL/MILC/HPQCD Phys.Rev.Lett. 94 (2005) 011601 M. Okamoto et al hep-lat/0409116 Further pricision to be pursued

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27 Mass of Bc meson (I) Method Lattice NRQCD for b/FNAL method for c Calculate mass differences Use experimental values for known hadron masses to obtain the Bc mass Error estimations statistical Tuning of heavy quark mass Lattice spacing Heavy quark discretization Allison et al, HPQCD/FNAL/UKQCD Hep-lat/0411027 Check of lattice spacing dependence

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28 Mass of Bc meson (II) Result Comparison with experiment their best estimate CDF ’04 hep-ex/0505076

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29 Lattice pentaquark search Initial studies F. Csikor et al hep-lat/0309090 S. Sasakihep-lat/03010014 Recent studies N. Mathur et alhep-lat/0406196 N. Ishii et alhep-lat/0501022 T. W. Chiu et alhep-lat/0501227 B. G. Lassock et alhep-lat/0503008,0504015 F. Csikor et alhep-lat/0503012 C. Alexandrou et alhep-lat/0503013 T. Takahashi et alhep-lat/0503019 K. Holland et alhep-lat/0504007

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30 Challenges of pentaquark Standard lattice methodology For pentaquark states, Pentaquark state and Nucleon+Kaon scattering states both contribute in the 2-point function Has to disentangle at least two (or more) states Has to disentangle resonance from scattering states Spin-parity is experimentally not known Has to search over large operator space Large time behavior of 2-point correlator yields the ground- state mass

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31 Multi-state analysis methods Multi-state analyses A set of pentaquark operators instead of a single operator Correlator matrix Normalized correlator matrix C. Michael (1985) M. Luescher and U. Wolff (1990) Eigenvalues of the normalized correlator matrix yields masses

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32 Finite volume tests for scattering states Since NK interaction is weak, for non-zero relative momenta, expect a typical L(size) dependence for since wave-function overlap, for the spectral weight, expect

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33 A recent work An extended operator bases Nucleon+Kaon type Diquark-diquark type (Jaffe-Wilczek) F. Csikor et al, hep-lat/0503012 N K N K symmetrically separated by a half-lattice local ud s s local One-link separated on both sides N K anti-symmetrically separated by a quarter-lattice

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34 Multi-state result Lowest two states in the I=0 JP=1/2 － channel F. Csikor et al, hep-lat/0503012 Quenched QCD Wilson quark action Beta=6.0 24^3x60 & 20^3x 60 lattice About 250 configurations “About 0.5Tflops ・ year of computations” according to the authors

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35 Size dependence test for energy F. Csikor et al, hep-lat/0503012 I=0 JP=1/2 － channel I=0 JP=1/2+ channel N+K

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36 Spectral weight test Quenched QCD Overlap quark action Small pion mass ～ 180MeV Lattice spacing a ～ 0.2fm 16^3x28 & 12^3x28 lattice expect: N. Mathur et al, hep-ph/0406196 I=1 JP=1/2+ channel

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37 Spectral weight tests (II) N. Mathur et al, hep-ph/0406196 I=0 JP=1/2 － channel I=0 JP=1/2+ channel

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38 Status of lattice pentaquark search Multi-state and finite-volume analyses crucial for resolving the issue Satisfactory agreement among studies not achieved at present Negative results appear more consistent, however. Is there anything overlooked? Very exotic wave function? Really light quark masses? Sea quark effects? Smaller lattice spacing? …

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39 What now?

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40 Current status of lattice QCD Realistic simulations with three light dynamical quarks (u,d,s) well under way with O(1) Tflops computers Current lattice size L ～ 2-3fm and current lattice spacing a ～ 0.1-0.06fm good enough for calculation of single-hadron properties at a few percent level

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41 With the coming of 10Tflops computers, Time is ripe for: Further advance of Nf=2+1 simulations with realistically light up and down quarks (mpi ～ 200-300MeV) Control of chiral symmetry Determination of fundamental constants Quark masses Strong coupling constant Precision measurements of CKM-related matrix elements at a percent level … Attacking challenging issues K pi+pi decays and direct CP violation Finite temperature/density QCD Nuclear physics from QCD …

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42 One such issue : CP violation parameter ε ’ /ε Small and negative in quenched QCD in disagreement with experiment Possible reasons connected with insufficient enhancement of ΔI=1/2 rule Method of calculation (K → πreduction) may have serious problems A major challenge awaiting further work

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43 Another issue: Phase diagram expected at Tricritical point Second-order D=3 Ising universality D=3 Z(3) Potts universality Where is the physical point? And what happens when μ≠ ０ ?

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44 10 TFLOPS class computers for QCD USA QCDOC Riken-BNLin place and running BNL(SciDAC funded)being installed Large clusters (FNAL and JLAB) Europe QCDOC at Edinburghin place and running ApeNEXT (Italy) Large installation in Italy expected in a year or so? Japan PACS-CS at University of Tsukuba KEK supercomputer upgrade in March 2006 x20 computing power over previous best machines

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45 in USA/UK … 10Tflops QCDOC at RIKEN-BNL Research Center developed by Columbia Group

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46 University of Tsukuba : 25 years of R@D of Parallel Computers 1978 1980 1989 1996 CP-PACS PACS-9 yearnamespeed 1978PACS-97kflops 1980PAXS-32500kflops 1983PAX-1284Mflops 1984PAX-32J3Mflops 1989QCDPAX14Gflops 1996CP-PACS614Gflops PAXS-32 QCDPAX

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47 PACS-CS Successor of CP-PACS for lattice QCD Funded by Special Grant for Research of JPN Government (JFY2005 ～ 2007 ） Installation scheduled in 2 nd quarter 2006 Overall specifications 14.4Tflops of peak speed with 5TBytes of main mamory 2560 nodes connected by a 16x16x10 three- dimensional hypercrossbar network Linux OS with Score and PM-based network driver Parallel Array Computer System for Computational Sciences

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48 A massively parallel system in terms of commodity componets X-switch Z-switch Y-switch Computing node X=16 Y=16 ・・・ Z=10 Communication via single switch communication via multiple switches In the figure Dual link for band width

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49 Detailed design verification system production Begin operation R&D of system software Development of application program Operation by the full system 2048 node system by early fiscal 2006 April 2003April 2004April 2005April 2006April 2007 Basic design Test system builtup and testing April 2008 production schedule 10 years of CP-PACS operation October 2006 R&D in progress Final system by early fiscal 2007 KEK SR800F1 New system Center for Computaitional Sciences PACS-CS

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50 International Research Network for Computational Particle Physics ＳｃｉＤＡＣ Network in USA Edinburgh Glasgow Liverpool Southampton SwanseaDESY/Neumann Berlin/Zeuthen Bielefeld Regensburg LatFor Network in Germany KEK Hiroshima U LFT Forum Network in Japan Future expansion to EU Network Italy, France, Spain, Denmark,… UK core institution: University of Edinburgh Dept. of Physics EPCC Germany core institution: DESY Von Neumann Inst. for computing USA core institution: Fermi National Accelerator Laboratory (FNAL) Japan core institution: University of Tsukuba Center for Computational Sciences Main supercomputer sites International Lattice Data Grid (ILDG) database of QCD gluon configurations at major supercomputer facilities acceleration of research via mutual usage of QCD gluon configurations via fast internet future international sharing of supercomputing and data storage resources Future expansion to Asia/Oceania Kyoto U UKQCD Network in United Kingdom U. Tsukuba Ｗａｓｈｉｎｇｈｏｎ Ｕ BNL/Columbia ＦＮＡＬ ＵＣＳＢ MIT/Boston U JLAB Arizona Utah Indiana St ． Louise JSPS core-to-core program QCDOC x 2 QCDOC APENEXT PACS-CS KEK supercomputer http://www.lqcd.org/ildg/tiki-index.php

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51 Summary Significant progress over the last several years in lattice QCD Inclusion of dynamical effects of all three light quarks (u,d,s) - Quenched approximation is a thing of the past - Beginning of precision calculation of a variety of physical quantities Further progress imminent: Theoretical advances in chirally symmetric lattice quark actions Domain-wall/overlap fermions/Perfect actions New algorithms Coming of 10 Tflops computers for lattice QCD QCDOC/ApeNEXT/PACS-CS/KEK machine

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