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Lattice QCD Activities at CCS

Yoshinobu Kuramashi

Center for Computational Sciences (CCS)

University of Tsukuba

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Contents

§1. Members of Particle Physics Group

　　　 §2. Introduction to Lattice QCD

　　　 §3. PACS-CS Project

PRD79(2009)034503, PRD80(2009)054502,

arXiv:0911.2561

§4. Summary and Future Perspectives

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Members of Particle Physics Group

Staff N.Ishizuka, Y.K., Y.Taniguchi, T.Yoshié PD Y.Namekawa, N.Ukita, T.Yamazaki OB Y.Iwasaki: ex-President of the University of Tsukuba (2004-2009) ex-Director of CCP (1992-1998) A.Ukawa: Executive Advisor to the President ex-Director of CCP and CCS (1998-2007)

Collaborative members S.Aoki, K.Kanaya

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Introduction to Lattice QCD

investigate nonperturbative effects of the strong interaction through

numerical simulations with lattice QCD

strong interaction one of the fundamental forces in Nature 　　　 　　　　　　　　　 (gravity, electromagnetic, strong, weak)

　　　　　　　　　　　 dynamics between quarks and gluons

quark proton neutronnucleon

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6 Flavors of Quarks and Gluons

d s b

u c tcharge +2/3

−1/3s

quark(R,B,G)

gluons

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Various Hadrons

p, n, Δ, Λ, Σ, Σ ＊ , Ξ, Ξ ＊ , Ω, Λc, Ξc, Λc, ...

π, K, K ＊ , ρ, ω, η, φ, a, b, f, D, B, ...

meson (quark and anti-quark)

baryon (3 quarks)

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QCD Lagrangian

determine kinematics and interactions of quarks and gluons

quark mass mq (q=u,d,s,c,b,t) are free parameters

　

Is it possible to quantitatively describe the hierarchical structures with an appropriate tuning of mq ?

quarks hadrons nuclei

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Lattice QCDnonperturbative investigation of strong interactions with respect to QCD Lagrangian

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Path Integral Formalism

numerical integration with Monte Carlo method on discretized 4-dim. space-time lattice

average over the values evaluated on configurations

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History before PACS-CS

1981 first calculation of hadron masses in quenched approx.

(Hamber-Parisi)

demonstrate the possibility of first principle calculations

　　　1996-2000 precision measurements in quenched approx.

(CP-PACS)

　　　　　　　　　 clear deviation from experimental values

　　　　　　　　　　　　 2000-2005 embark on 2+1 flavor QCD simulations

(CP-PACS/JLQCD, MILC, RBC, …)

　　　　　　　　　 attempt of first principle calculations

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2+1 flavor QCD simulations with HMC algoriyhm

CP-PACS/JLQCD project

looks impossible to reach the physical point in near future

CP-PACS/JLQCD

mud=0 mud=∞

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aim to make simulations at the physical point of 2+1 flavor QCD

PACS-CS project

Physicists

S.Aoki, N.Ishizuka, K.Kanaya, Y.K. Tsukuba

Y.Namekawa, Y.Taniguchi, A.Ukawa,

N.Ukita, T.Yamazaki, T.Yoshié

K.-I.Ishikawa, M.Okawa Hiroshima

T.Izubuchi BNL

Computer scientists

T.Boku, M.Sato, D.Takahashi, O.Tatebe Tsukuba

T.Sakurai, H.Tadano

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Parallel Array Computer System for Computational Sciences 2560 nodes, 14.3 Tflops peak, 5.12 TB memory operation started on 1 July 2006 at CCS in U.Tsukuba

PACS-CS

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Tukuba-Tokyo-Kyoto open supercomputer alliance 648 nodes, 95.4 Tflops peak, 20.7 TB memory operation started on 2 June 2008 at CCS in U.Tsukuba

T2K-Tsukuba

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drastic reduction of computational cost thanks to DDHMC algorithm

Algorithmic Improvements

physical point simulations are within reach

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nontrivial curvature = log dependence expected from chiral symmetry

Toward the Physical Point

importance of simulations at smaller ud quark masses

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mπ, mK, mΩ inputs consistent within 2-3 % error bars⇒

Comparison with Experiment

hadron masses extrapolated at the physical point

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Fine Tuning to the Physical Point

reweighting method simulation: (mud,ms) physical point: (m´⇒ ud,m´s)

with mud m´≃ ud and ms m´≃ s

　　　　　　　　　　　

reweighting factors

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mπ/mΩ, mK/mΩ are properly tuned (Δmud<1 MeV, Δms<3MeV)

Comparison with Experiment

hadron masses normalized by mΩ

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Summary and Future Perspective

peak machine target physics 　　　 < 1TF CP-PACS embark on 2+1 flavor QCD

10 TF 　　 PACS-CS physical point simulation

100 TF 　　 T2K-Tsukuba determination of QCD parameters

light nuclei in quenched QCD

(Yamazaki et al., arXiv:0912.1383)

10 PF 　　 NGSC light nuclei in 2+1 flavor QCD

finite temperature and finite density

1 EF NNGSC weak hadron matrix elements w/o OPE

heavy nuclei in 2+1 flavor QCD

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Why Physical Point Simulations?

simulations at heavier quark masses (m>200~300MeV)and extrapolations to the physical point with ChPTcurrent most popular strategy due to computational cost

what’s wrong with cheaper strategy?

・ guiding principle for chiral extrapolation?

ChPT is not always valid for all the physical quantities

polynomial is valid only near the physical point

・ difficult to precisely trace logarithmic curvatures

・ different dynamics at unphysically heavy quark masses

ρ→ππ decay is not allowed

・ final destination is 1+1+1 flavor QCD simulations