1

2+1 Flavor lattice QCD Simulation on K computer

Y.Kuramashi

U. of Tsukuba/RIKEN AICS

August 2, 2013 @ Mainz

2

Plan of talk

　　 §1. K computer and Strategic Field Program

　　　 §2. Physics Plan

　　　 §3. Simulation Parameters

　　　 §4. Preliminary results

　　　 §5. Summary

3

§1. K computer and Strategic Field Program

Tokyo

KobeTsukuba

KyotoAdvanced Institute for Computational Science(Note: independent of RIKEN-BNL-Columbia Collab.)

RIKEN AICS

Peak=11.28PFlops

Logo

Computer room

4

Strategic Field Program

For strategic use of K computer Government selected 5 strategic fields in science and

technology for importance from national view point For each field, Government also selected a core institute

Each core institute is responsible for organizing research and supercomputer resources in the respective field and its community, for which they receive

− priority allocation of K computer resources

− funding to achieve the research goals

Strategic Field Core Institute

Life Science & Medicine RIKEN

New Materials & Energy ISSP at U. Tokyo

Global Change Prediction JAMSTEC

Next Generation Engineering IIS at U. Tokyo

Matter and Universe CCS at U. Tsukuba

5

§2. Physics Plan

Scientific target • 2+1 flavor QCD 1+1+1 flavor QCD+QED ⇒• Various physical quantities• Investigation of resonances• Direct construction of light nuclei• Determination of baryon-baryon potentials

　　　

6

Light Nuclei in 2+1 Flavor QCD (1)

2+1 flavor QCD, mπ ＝ 0.5 GeV, mN=1.32 GeV

4He 3He NN(3S1) NN(1S0)

Binding energy [MeV] 43(12)(8) 20.3(4.0)(2.0) 11.5(1.1)(0.6) 7.4(1.3)(0.6)

Exp. value [MeV] 28.3 7.72 2.22 0

Successful construction of helium nuclei in 2+1 flavor QCD

Yamazaki-Ishikawa-YK-Ukawa 12Ukawa @this conference

7

Light Nuclei in 2+1 Flavor QCD (2)

NN(3S1) and NN(1S0) channels

Both 3S1 and 1S0 channels are bound at mπ=0.5 GeV|ΔE(3S1)| > |ΔE(1S0)| is observedImportant to investigate quark mass dependence

Target on K computer: construction of nuclei at the physical point

8

Baryon-Baryon Potentials (1)

based on equal-time BS amplitude

Quenched QCD, mN=1.34GeV

Ishii-Aoki-Hatsuda 07Phenomenological model

BS wave function with lattice QCD NN Potential ⇒

9

Baryon-Baryon Potentials (2)

2+1 flavor QCD, lattice size=323×64, mπ ＝ 0.70, 0.57, 0.41 GeV

Attractive phase shift, though the magnitude is just 10% of exp. value(no bound state inconsistency against the direct method)⇒Phase shift becomes smaller, as quark mass decreases

⇒ need direct comparison with exp. values at the physical point

HAL-QCD @FB12

10

Collaboration members

N.Ishii, N.Ishizuka, Y.Kuramashi, Y.Namekawa, TsukubaH.Nemura, K.Sasaki, Y.Taniguchi, N.Ukita

T.Hatsuda, T.Doi RIKEN-Wako

T.Yamazaki Nagoya

S.Aoki Kyoto

Y.Nakamura RIKEN-AICS

K.-I.Ishikawa Hiroshima

HAL QCD Collab. joins to determine baryon-baryon potential

　　　　　　　 　

11

§3. Simulation Parameters

• 2+1 flavor QCD • Wilson-clover quark action + Iwasaki gauge action• Stout smearing with α=0.1 and Nsmear=6 • NP CSW=1.11 determined by SF • β=1.82 a⇒ 〜 0.1 fm• Lattice size=964 (⇒ 〜 9 fm)4 • Hopping parameters: (κud,κs)=(0.126117,0.124790)• Simulation algorithm − (HB)2DDHMC w/ active link for ud quarks, UVPHMC for s quark − Block size=124 (⇒ 〜 1 fm)4

− HB parameters: (ρ1,ρ2)=(0.99975,0.9940)

− Multi-time scale integrator: (N1,N2,N3,N4,N5)=(15,2,2,2,8) − trajectory length: τ=1

− Npoly=310

− Chronological inverter guess: Nchrono=16 − Solver: mixed precision nested BiCGStab　　

12

Performance on K computer

• Kernel (MatVec) performance: >50% • Solver performance: 〜 26% (mixed precision nested BiCGStab)• Weak scaling test − 63×12/node fixed − 16 nodes (V=123×24) 12288 nodes (V=48×72×96⇒ 2)　　

16

256

2048

12288 #node scalability

16 256⇒ 98%

256 2048⇒ 98%

2048 12288⇒ 96%

good weak scaling

B/F=0.5 on K computer

13

Non-Perturbative Determination of CSW (1)

Schördinger functional method − L3×T=83×16 (L3×T=123×24 for volume dependence check) − Choose β such that the lattice spacing becomes around 0.1 fm

Taniguchi @Lattice2012

CSW=1.11 at β=1.82 1/a⇒ 〜 2.1 GeVκC is close to 0.125 at β=1.82

14

Non-Perturbative Determination of CSW (2)

Nsmear dependence of CSW and Kc

CSW monotonically decreases as Nsmear increases κC shows a similar behavior

15

§4. Preliminary results

Meson and baryon effective masses for smeared-local correlatorsSmearing function: Aexp(−Br) − (A,B)=(1.2,0.06) for ud quarks − (A,B)=(1.2,0.12) for s quarks

16

Hadron spectrum

Further tuning to the physical point is planned with reweighting methodClear deviation is already observed for unstable particles (ρ,K*)

Comparison with experiment (normalized by mΩ)

17

ρ Meson Effective Mass

It is hard to find a reasonable plateau (same for Δ baryon effective mass)Analysis of 2×2 correlation matrix (ρ,ππ) is necessary

Decay channel is open: mρ>2√{mπ2+(π/48)2}

mρ=776 MeV

2√{mπ2+(π/48)2}

18

§5. Summary

・ K computer and strategic field program

・ 2+1 flavor QCD simulation at the physical point on ( 〜 9 fm)4 lattice

・ Preliminary results for hadron spectrum