Meson correlators of two-flavor QCD in the epsilon-regime

1
Meson correlators of two-flavor QCD in the
epsilon-regime

• Hidenori Fukaya (RIKEN)
• with S.Aoki, S.Hashimoto, T.Kaneko, H.Matsufuru,
  J.Noaki, K.Ogawa, T.Onogi and N.Yamada JLQCD
  collaboration

2
1. Introduction

• The chiral limit is difficult.
• The standard way requires before
  .
• Lattice QCD in
• ( )
• Necco (plenary), Akemann, DeGrand, Shindler
  (poster) , Cecile, Hierl (chiral), Hernandez
  (weak)
• Finite effects can be estimated within ChPT
• (
  ).
• is not very expensive.
• -gt the chiral symmetry is essential.
• -gt the dynamical overlap fermions.

3
1. Introduction

• JLQCD collaboration
• achieved 2-flavor QCD simulations with the
  dynamical overlap quarks on a 16332(1.7-2fm)
  lattice with a0.11-0.13fm at Q0 sector.
• the quark mass down to 3MeV ! (enough to reach
  the epsilon-regime.)
• The Dirac spectrum JLQCD, Phys.Rev.Lett.98,172001
  (2007)
• shows a good agreement with Banks-Casher
  relation.
• with finite V correction via Random Matrix Theory
  (RMT), we obtained the chiral condensate,

statistical
systematic
4
1. Introduction

• ChPT in the epsilon-regime Gasser Leutwyler,
  1987
• RMT does not know .
• Direct comparison with ChPT at
• -gt more accurate (condensate).
• -gt pion decay constant
• Meson correlators in the epsilon-regime
• 
  Hansen, 1990, 1991, Damgaard et
  al, 2002
• are quadratic function of t
• where A and B are expressed by the finite
  volume condensate,
• which is sensitive to m and topological charge Q.

5
1. Introduction

• Partially quenched ChPT in the epsilon-regime
• P.H.Damgaard HF, arXiv0707.3740,
  Bernardoni Hernandez, arXiv0707.3887
• The previous known results are limited to
  degenerate cases.
• We extend ChPT to the partially quenched theory.
• Pseudoscalar and scalar channels are done
• the correlators are expressed by of the
  partially quenched finite volume condensate,
• with which we can use the different valence
  quark masses to extract and .
• Axial vector and vector channels are in
  preparation.
• A0V0 calculated by the latter authors.

6
1. Introduction

• The goal of this work
• On a (1.8fm)4 lattice with a0.11fm,
• 2-flavor QCD simulation with m3MeV is achieved.
• The Dirac spectrum shows a qualitative agreement
  with RMT prediction, however, has 10 error
  of
• effects.
• Therefore, our goal is to determine
• to by comparing meson correlators
  with
• (partially quenched) ChPT.

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Contents

• Introduction
• Lattice simulations
• Results
• Conclusion

Related talks and posters

• Plenary talk by H.Matsufuru,
• meson spectrum by J.Noaki (chiral),
• 21 flavor simulations by S.Hashimoto (hadron
  spectroscopy),
• topology by T.W.Chiu and T.Onogi (chiral),
• pion form factor by T.Kaneko (hadron
  structure),
• pipi0 difference by E.Shintani (hadron
  spectroscopy),
• BK by N.Yamada (weak).

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2. Lattice simulations

• Lattice size 16332 (L1.8fm.).
• a0.11 fm. (determined by Sommer scale
  r00.49fm.)
• Iwasaki gauge action with .
• Extra topology fixing determinant.
• 2-flavor dynamical overlap quarks.
• ma 0.002 (3MeV).
• mv a0.0005, 0.001,0.002, 0.003 1-4MeV.
• topological sector is limited to Q0.
• 460 confs from 5000 trj.
• Details -gt Matsufurus plenary talk.

9
2. Lattice simulations

• Numerical cost
• Finite volume helps us to simulate very light
  quarks since the lowest eigenvalue of the Dirac
  operator are uplifted by an amount of 1/V.
• m3MeV is possible with L1.8fm !

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2. Lattice simulations

• Low-mode averaging
• DeGrand Schaefer, 2004,,
  Giusti,Hernandez,Laine,Weisz Wittig,2004.
• We calculate PS, S, V0, A0 correlation functions
  with a technique called low-mode averaging (LMA)
• with the lowest 100 Dirac-eigenmodes.
• PS, S -gt the fluctuation is drastically
  suppressed.
• V0, A0 -gt the improvement is marginal.

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3. Results

• Axial vector correlator (mvmsea3MeV)
• We use the ultra local definition of A0 which is
  not a conserved current -gt need
  renormalization.
• We calculate
• From 2-parameter fit with ChPT,
• chiral condensate
  ,
• pion decay const ,
• (Fit range t12-20, chi2/d.o.f. 0.01)
• are obtained.
• Note A0A0 is not very sensitive to .

12
3. Results

• Pseudoscalar correlators (mvmsea3MeV)
• With as an input,
  1-parameter fit of PP correlator works well and
• condensate is
  obtained.
• (fit range t12-20, chi2/d.o.f.0.07.)
• PP correlator is sensitive to .
• A0A0 is sensitive to .
• -gt With the simultaneous 2-parameter fit with
  PP and A0A0 correlator, we obtain to
• in lattice unit. (fit range t12-20,
  chi2/d.o.f.0.02.)

13
3. Results

• Consistency with SS and V0V0 (mvmsea3MeV)
• 
  are
  consistent with SS and V0V0 channels !
• (No free parameter left. )

14
3. Results

• Consistency with Partially quenched ChPT
• 
  are also
  consistent with partially quenched ChPT but the
  valence quark mass dependence is weak.
• (No free parameter left)

15
3. Results

• Consistency with Dirac spectrum
• If non-zero modes of ChPT are integrated out,
  there remains the zero-mode integral with
  effective chiral condensate,
• In fact, this value agree well with the value via
  Dirac spectrum compared with RMT,
• -gt support our estimate of
  correction.

16
3. Results

• Non-perturbative renormalization
• Since
  is the lattice bare value,
• it should be renormalized. We calculated
• the renormalization factor in a non-perturbative
  RI/MOM scheme on the lattice,
• match with MS bar scheme, with the perturbation
  theory,
• and obtained

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3. Results

• Systematic errors
• Different channels, PP, A0A0, SS, V0V0, their
  partially quenched correlators, and the Dirac
  spectrum are all consistent.
• Fit range from tmin10(1.1fm) to 15 (1.7fm),
  both
• are stable (within 1) with
  similar error-bars.
• Finite V
  taken into account in the analysis.
• Finite a overlap fermion is automatically free
  from O(a).
• Finite m m3MeV is already very close to the
  chiral limit.
• But 87.3(5.5)MeV slightly different from
  the value
• 78(3)(1)MeV (Noakis talk) in the p-regime.

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4. Conclusion

• On a (1.8fm)4 lattice with a0.11fm, 2-flavor
  QCD simulation with m3MeV is achieved, which is
  in the epsilon-regime.
• We calculate the various meson correlators with
  low-mode averaging (LMA).
• From PP (sensitive to ) and A0A0 (sensitive to
  ) channels, compared with ChPT,
• to accuracy, are obtained
  (preliminary).
• They are consistent with SS and V0V0 channels.
• Also consistent with partially quenched ChPT.
• Also consistent with result from Dirac spectrum.
• But slightly deviate from p-regime results.

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4. Conclusion

• Future works
• Larger volumes
• Smaller lattice spacings
• Partially quenched analysis for A0A0 and V0V0
  channels.
• 21 flavors