Niels Bohr Institute

1
????????????????????

• Niels Bohr Institute
• (???????????)
• ?? ??
• for JLQCD collaboration

HF T.Onogi, Phys.Rev.D70,054503 (2004) JLQCD
collaboration, Phys.Rev.D74,094505 (2006) JLQCD
collaboration, Phys.Rev.Lett.98,172001 (2007)
2
JLQCD collaboration
KEK S. Hashimoto,H.Ikeda T. Kaneko, H.
Matsufuru, J. Noaki, M. Okamoto, E.
Shintani, K.Takeda, N.Yamada RIKEN -gt Niels Bohr
H. Fukaya Tsukuba S. Aoki, N.Ishizuka, T.
Kanaya, Y. Kuramashi, Y. Taniguchi,
A. Ukawa, T. Yoshie Hiroshima K.-I. Ishikawa,
M. Okawa YITP H. Ohki, T. Onogi (TWQCD
T-W.Chiu, K.Ogawa )
KEK BlueGene (10 racks, 57.3 TFlops)
3
1.Introduction - ????????? -

• ?????? ??0????????? ??????????
• ???????
• ??????(?)????????????
  ?
• ???????? ???Nf?????????????????????? ??????
• ? ???????? ??????????
• ( ?????????????)
• ????????? ?????? ????????????
• ????????????? Nambu 1961
• ???????????????????????
• ?????????????????

4
1.Introduction - ????????? -

• ???????????
• ????????????????????
• ? ???????????
• ???? constituent ?? ????????MeV???????????
  ???etc.???1GeV????????????
• ??????????????
• (?)Nambu-Goldstone boson ?????????????????(?????
  ??Weinberg 1979)???????? ? ?????????????????????
  ???
• ?????????????????
• ???????????????
• ? ????????? ? ?????????? ! (??????)

5
1.Introduction - ????????? -

• ??????
• ????????????Dirac???????????????
• ??????????????????????????????

??????????????????????????????????? ?????????
?????????????????????
6
Contents

• Introduction - ????????? -
• ????QCD??????????????
• ??QCD?????????????????
• JLQCD collaboration ????????????
• ???

7
2. ????QCD??????????????

• ???????(??QCD)
• ??????????????????????????
• ??????????????????????
• ???????????????????
• Nielsen-Ninomiya ?? 1981
• ???????????(?????)?
• ? ??????????????????????????
• ??? ?????? ? ?????????????
• ????????????????? naive fermion
• ??? ???????? ????????Wilson
  fermion
• Ginsparg-Wilson ??? 1982
• ??????????????????????????????????????
• ?????Dirac????
• ????????? (??????????????????????)

8
2. ????QCD??????????????

• Overlap Dirac ???Neuberger 1998
• 1998??????????????????Ginsparg-Wilson
  ??????????
• ??????????Dirac ??????????
• Wilson Dirac ???
• Overlap Dirac ????????????????? Luescher 1998
• ?? ???
• ???????
• ?????????
• ? ????????????
• ?????????
• ?????????Hasenfratz 1998
• ? ?????????????????????!

???? ???,???(2006?11??), ???????????(2008?4??)
9
2. ????QCD??????????????

• Overlap Dirac ?????????
• overlap ?????Wilson ?????? ? ????????????????
• ?????(7-8?)?????O(100)????????
• Topology ???( ?0???????0????????????
• ?????)???fermion ????????
• ? ????????????????
• ?????????????
• (?????????????????????
• ??????S???????????)
• ???O(10)????????

Q1
Q0
??????????????????????????? (?????GW???????domain
wall fermion????????????????????????????????residu
al ????MeV?????)
10
3. ??QCD?????????????????

HF T.Onogi, Phys.Rev.D70,054508(2004) JLQCD,
Phys.Rev.D74,094505(2006)

• ???? 1. ???????????????????????
• 2. ?????????????????????

1. ??????????????????????????? ???????????????????
???????????????????????????
Q1
Q0
11
3. ??QCD?????????????????

• 2. ??????????????????????????
• ??????? ????????
• Vafa -Witten ???1984 ???
• ????????????????
• ?(fixed Q)eta-prime ????2(4)??????????

S.Aoki, HF, S.Hashimoto, T.Onogi
Phys.Rev.D76,054508(2007) JLQCDTWQCD,
arXiv0710.1130(2007)
12
3. ??QCD?????????????????

• 2. ??????????????????????????
• ????????
• ??????????(???????)????????????????????
• ? fixed topology ??????0 ???????????????????
  ????(???????????one-matrix Model???)?
• ?????????????????????????????????????????????????
  ??
• ?????? Q0 ????????

• HF T.Onogi, Phys.Rev.D70,054508 (2004)
• JLQCD collaboration, Phys.Rev.D74,094505
  (2006)???
• ??????????????????????????????????????????????
• ????????????????????????? overlap Dirac
  ?????????????????????
• ??????????????????????????????
• ??????????
• ? ???? overlap fermion ??????

13
4. JLQCD collaboration ????????????

• Overlap fermion ????????
• ?????O(100)??Dw???
• ???????????????????????????O(10)?
  O(1000)? ? Wilson fermion ?
• ????
• ?????????fermion??????????? 10? ??
• KEK?BlueGene (??????57TFlops)?? 50?
• ??????????????
• (multimass solver, mass preconditioning etc.)
  10? or more

• - Iwasaki (beta2.3,2.35) Q stabilizing action
• - Q0 topological sector (No topology change.)
• The lattice spacings a is calculated from
• quark potential (Sommer scale r0).
• - Eigenvalues are calculated by Lanzcos
  algorithm.
• (and projected to imaginary axis.)
• - 400 4600 HMC trajectories (460confs).

L3T163 32 (L1.8fm) 2-flavor QCD ??????????
3MeV ??????????!
14
4. JLQCD collaboration ????????????

• Banks-Casher ???1980

15
4. JLQCD collaboration ????????????

• Dirac spectrum ? Q,V,m ??
• ?????????? (Q0) ???
• ???? (V 1.8fm)
• ???? (m3MeV) ????
• ????(????????????) Damgaard Nishigaki,2001 ?
• ??????

S
S
???? ??????????2007?2???30
16
4. JLQCD collaboration ????????????

• m3MeV, Q0, V(1.8fm)4 ???
• ?? Banks-Casher ????????
• low mode ????
• ??????S(240MeV)3?consistent?
• ????0??????????????
• 1. ?????????????
• m, Q, V??????
• 2. RI/MOM?????????
• ??????????
• 3. ????????????
• ?????
• ???????????

17
4. JLQCD collaboration ????????????

• ????????
• ?????????????
• Overlap Dirac ???????????? O(a) ???????????
• O(a2)?(???)????
• ???????????????
• m3MeV ????????????? (S1/3 ?QCD250MeV????)
• ???????????
• LO??????????????????????
• NLO???????????????????10-13 ??????????

18
4. JLQCD collaboration ????????????

• ?????????????? - ????????????-
• Pseudo-scalar correlator ??axial vector
  correlator ??
• (partially quenched) ????????????????NLO???
• P.H.Damgaard HF, Nucl.Phys.B793160-191,2008,
  F.Bernardoni P.Hernandez, JHEP0710(2007)033
• ????
• ? ???????consistent?????????JLQCD,
  arXiv0711.4965 to appear in PRD.
• (? ?????????????????????(0-mode)????????????????
• ??????????????????????????????????????)

19
4. JLQCD collaboration ????????????

• ?????????????? -?????????????????-
• ?????????? ?????in p-regime?

JLQCD TWQCD, arXiv0711,1130
Q0
Instanton ????? Pure YM???QCD ? QCD with light
quarks ?? ??????? ????? ! T??????
20
5. ???

• ????????????? overlap Dirac ??????????
  ??????????????
• L2 fm ???????????3MeV????
• ?????? Banks-Casher ???????? consistent ?
• ??????????????????????????????????????????????????
  ?????????????????
• ?????(???????????????????????????)??????????????

• ??????????????????????????????
• ???????????????QCD????????????

21
5. ???

• Talks by JLQCD collaboration
• Overview (?? 24pZC)
• Meson spectrum (?? 24pZC)
• Pion form fator (?? 24pZC)
• S-parameter (?? 24pZC)
• Nucleon Sigma term (??? 24aZC)

22
5. ???

• ?????
• ???????????????????????????????MeV????????????????
  ???????????
• Overlap fermion ?????O(a)?????????????????????
• ?????????????????????????
• ????????????????????
• ???????? L4-5fm ????? (m3MeV???) !
• ??????????????????????????
• ( Partially quenched ) ??????? in finite
  volume????
• Pseudo-scalar and scalar correlators
  P.H.Damgaard HF,Nucl.Phys.B793160(2008)
• Pion decay constant P.H.Damgaard,
  T.DeGrand,HF,JHEP12(2007)060
• Axial and vector currents F.Barnerdoni,
  P.H.Damgaard, HF, P.Hernandez, in preparation.
• Kaon physics P.H.Damgaard, T.DeGrand, HF, in
  progress.

23
Appendix

• ?????S???
• ??????????3???????
• ?????????????????
• ???????????
• ? ??????
• ????????0??? quark ??????????????????
• ??????????? quark ??????????S???????