Particle Physics Project(A01) Report
Tetsuya Onogi (Osaka University)1Members
T. Onogi (Osaka), Y. Kuramashi (Tsukuba), N. Yamada (KEK)
S. Hashimoto, T. Kaneko, J. Noaki (KEK) ,N. Ishizuka, Y. Taniguchi (Tsukuba),
M. Hayakawa, T. Yamazaki (Nagoya),
Y. Aoki (Riken), N. Ishii (Tokyo),
K.I. Ishikawa (Hiroshima), H. Fukaya (Osaka),
Y. Furui (Teikyo)
T. Izubuchi, E. Shintani (Riken/BNL)

Postdocs
Y. Namekawa (Tsukuba), S.W. Kim (Osaka)

2

Challenge in lattice QCD
1. Towards realistic 3-flavor QCD
1.
2.
3.
4.

Physical quark mass
Large volume
QED corrections
Good chiral symmetry

Configurations will be
useful to A02 group

2. Hadronic interactions and bound states
1. Scattering length
2. Resonance3. Nuclei

Complemantary to the approachby A02 group (nuclear potential)

3. Particle Physics Phenomenology
1. Determination of Low energy constants, form factors
2. Determination of SM parameters
3Are we serious, or notserious enough?
Don’t rush!
Lattice is not a model. It should give a definition ofthe field theory
We should establish reliable calculation based from
1st principles of (lattice) QCD. After establishing thebasis, we can embark on various applications.

4Choice of fermion action• In lattice QCD simulation, multiplying Dirac
operator appears in the most time
consuming part of the calculation.
• Therefore, choice of the fermion is important.
o Staggered fermiono Wilson fermiono Overlap/Domain-wall fermion

cheapest
reasonable
expensive5

Large Scale 2+1-Flavor Lattice QCD Simulations
JLQCD

PACS-CS

overlap fermion

O(a)-improved Wilson fermion
Complementary“Physical point simulation”
Large volume is feasible withreasonable numerical cost.
No need for chiral extrapolation.
Direct test of the hardon spectrum
is possible.

“Exact chiral symmetry”
Large numerical cost but the chiraleffective theory can be reliably applied.

Both approaches are theoretically under control
as long as they are applied to appropriate problems.

6O(a)-improved Wilson
fermion by PACS-CS

7

Highlights from PACS-CS
1.

2+1 flavor QCD near the physical point
Lattice spacing a ~0.1 fm, Physical Size L ~ 3.2 fm
Precise hadron mass spectroscopy2.

1+1+1 flavor QCD+QED at the physical point
Reweighting method
Determination of the quark mass

3. Resonances and Atoms
rho resonance and width
Helium atom from QCD

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Physical point simulation in 2+1 lattice QCD
S. Aoki et al., (PACS-CS collaboration) arXiv:0911.2561[hep-lat]•••

O(a)-improved Wilson fermion with PACS-CS and T2K(Large volume)
Simulations with physical quark masses
tuning of quark masses with reweighting
Comparison of the hadron spectrum : lattice vs experiment
Good agreement within a few percent level.

9Reweighting Method for 1+1+1
Reweighting from Nf=2+1 QCD to Nf=1+1+1 QCD+QED

with (κu*,κd*,κs*) hopping parameters at the physical point

10Quark masses with NP renormalization factor
・NP renormalization factor with Schrödinger functional scheme
PACS-CS, JHEP1008(2010)101
PRD81(2010)074503 [2+1f QCD (1)]
PRD79(2009)034503 [2+1f QCD (2)]・neglect QED corrections to the renormalization factor
・physical inputs: mπ+, mK0, mK+, mΩ−・MS-bar scheme at μ=2GeV
This work
mu [MeV]2.57(26)(07)

md [MeV]3.68(29)(10)

ms [MeV]83.60(58)(2.23)

mud [MeV] 3.12(24)(08)
mu/md0.698(51)ms/mud26.8(2.0)

2+1f QCD (1)2+1f QCD (2)86.7(2.3)

87.7(3.1)

2.78(27)

3.05(12)31.2(2.7)

28.78(40)・possible QED finite size effects: −13.50% for u, +2.48% for d, −0.07% for s
Blum et al., PRD82(2010)094508
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Highlights from PACS-CS“Rho meson decay fromlattice”
can be determined!

12

“Helium Nuclei from lattice” talk by T. Yamazaki• Quenched and Nf= 2+1 QCD• Study of volume dependence• Significant cost reduction in Wickcontraction• Good agreement with experiment13

Highlights from JLQCD
1. Chiral Dynamics
Chiral Condensate
Test of Chiral Perturbation TheoryΠ0γγ
Strange quark content

2. Vacuum Polarization


Sum Rule : S-parameter and pseudo NG –bosonalpha_s from vacuum polarization

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Chiral Condensate
Eigenvalue spectrum of the Dirac operator
Comparison with the resultsfrom lattice QCD in epsilon-regime
and ChPT in epsilon-regime

15

Test of ChPT
Chiral extrapolation•Fit parameter:•NLO fit formula•

NLO gives a good fit forextends the region forconvergence significantly.

Nf=2, a=0.12fm, Q=0

Comparison with ChPT
• ΠV-A(1)• Blue line : fit with CHPT formulaat (aQ)2 =0.038.
• CHPT well describes lattice results
Fit results:
cf. exp. + CHPT: -0.00509(57)c.f. RBC/UKQCD: L10= -0.0057(11)(7)• Other line: linear fit• (aQ)2 > 0.1
CHPT (1-loop) does not work
⇒ need higher order

12/24/201217

Result of Δmπ2

cf. experimental value
1261 MeV2 at physical pion• Fit range: (aQ)2≦2 = Λ2
at zero quark mass
1st error: statistical
2nd error : fit form dependence
3rd error : uncertainty of a6

Solid line : X1,
Dashed line : X2

reasonable value,
but still large systematic error
Other remaining error• finite size
• strange quark mass

12/24/2012

18

7/28/200919

3-point function for A-V-V

20

Nucleon sigma term
Spectrum method (Feynman Hellman theorem)
Direct method (Matrix element)21

Summary
1. Lattice method for 2+1-flavor QCD at present can
successfully describes the hadron dynamics.
2. Approach from O(a)-improved Wilson fermion byPACS-CS is suitable for persue reallistic QCD inlarge volume and physical quark mass. Now readyfor application to nuclear interactions.
3. Overlap fermion by JLQCD is suitable to physics
sensitive to exact chiral symmetry. Application toflavor physics, chiral phase transition, and othernew subjects is expected.
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