Transcript Meson correlators of two-flavor QCD in theε

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]
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1. Introduction

The chiral limit is difficult.


The standard way requires
Lattice QCD in
(
before
.
)
[Necco (plenary), Akemann, DeGrand, Shindler (poster) , Cecile, Hierl (chiral), Hernandez
(weak)…]
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Finite
(
effects can be estimated within ChPT
).
is not very expensive.
-> the chiral symmetry is essential.
-> the dynamical overlap fermions.
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1. Introduction

JLQCD collaboration
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achieved 2-flavor QCD simulations with the dynamical
overlap quarks on a 16332(~1.7-2fm) lattice with a~0.110.13fm at Q=0 sector.
the quark mass down to ~3MeV ! (enough to reach the
epsilon-regime.)
The Dirac spectrum [JLQCD, Phys.Rev.Lett.98,172001(2007)]
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
shows a good agreement with Banks-Casher relation.
with finite V correction via Random Matrix Theory (RMT),
we obtained the chiral condensate,
statistical systematic
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1. Introduction

ChPT in the epsilon-regime [Gasser & Leutwyler, 1987]
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RMT does not know
.
Direct comparison with ChPT at
-> more accurate
(condensate).
-> 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.
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1. Introduction

Partially quenched ChPT in the epsilon-regime
[P.H.Damgaard & HF, arXiv:0707.3740, Bernardoni & Hernandez, arXiv:0707.3887]
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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.
A0+V0 calculated by the latter authors.
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1. Introduction

The goal of this work
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On a (1.8fm)4 lattice with a~0.11fm,
2-flavor QCD simulation with m~3MeV 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
 1. Introduction
2. Lattice simulations
3. Results
4. Conclusion
Related talks and posters
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Plenary talk by H.Matsufuru,
“meson spectrum” by J.Noaki (chiral),
“2+1 flavor simulations” by S.Hashimoto (hadron spectroscopy),
“topology” by T.W.Chiu and T.Onogi (chiral),
“pion form factor” by T.Kaneko (hadron structure),
“pi±pi0 difference” by E.Shintani (hadron spectroscopy),
“BK” by N.Yamada (weak).
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2. Lattice simulations
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Lattice size = 16332 (L~1.8fm.).
a~0.11 fm. (determined by Sommer scale
r0=0.49fm.)
Iwasaki gauge action with
.
Extra topology fixing determinant.
2-flavor dynamical overlap quarks.
ma = 0.002 (~3MeV).
mv a=0.0005, 0.001,0.002, 0.003 [1-4MeV].
topological sector is limited to Q=0.
460 confs from 5000 trj.
Details -> Matsufuru’s plenary talk.
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2. Lattice simulations
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Numerical cost
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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.
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m~3MeV is possible with L~1.8fm !
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2. Lattice simulations
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Low-mode averaging
[DeGrand & Schaefer, 2004,, Giusti,Hernandez,Laine,Weisz & Wittig,2004.]
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We calculate PS, S, V0, A0 correlation functions with a
technique called low-mode averaging (LMA)
with the lowest 100 Dirac-eigenmodes.
PS, S -> the fluctuation is drastically suppressed.
V0, A0 -> the improvement is marginal.
PS-PS
A0-A0
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3. Results
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Axial vector correlator (mv=msea=3MeV)
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We use the ultra local definition of A0 which is not a
conserved current -> need renormalization.
We calculate
From 2-parameter fit with ChPT,
 chiral condensate
 pion decay const
（Fit range : t=12-20, chi2/d.o.f. ~ 0.01)
are obtained.
Note: A0A0 is not very sensitive to
.
,
,
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3. Results
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Pseudoscalar correlators (mv=msea=3MeV)
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With
as an input, 1-parameter fit of PP
correlator works well and
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condensate
is obtained.
(fit range: t=12-20, chi2/d.o.f.=0.07.)
PP correlator is sensitive to
.
A0A0 is sensitive to
.
-> With the simultaneous 2-parameter fit with PP and A0A0
correlator, we obtain to
in lattice unit. (fit range : t=12-20, chi2/d.o.f.=0.02.)
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3. Results
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Consistency with SS and V0V0 (mv=msea=3MeV)
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are consistent with SS and V0V0 channels !
(No free parameter left. )
SS
V0V0
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3. Results
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Consistency with Partially quenched ChPT
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are also consistent with partially quenched ChPT but the
valence quark mass dependence is weak.
(No free parameter left)
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3. Results
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Consistency with Dirac spectrum
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If non-zero modes of ChPT are integrated out, there
remains the zero-mode integral with “effective” chiral
condensate,
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In fact, this value agree well with the value via Dirac
spectrum compared with RMT,
-> support our estimate of
correction.
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3. Results
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Non-perturbative renormalization
Since
is the lattice bare value,
it should be renormalized. We calculated
1. the renormalization factor in a non-perturbative RI/MOM
scheme on the lattice,
(non-perturbative)
(tree)
2. match with MS bar scheme, with the perturbation theory,
3. and obtained
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3. Results
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Systematic errors
1. Different channels, PP, A0A0, SS, V0V0, their partially
quenched correlators, and the Dirac spectrum are all
consistent.
2. Fit range : from tmin~10(1.1fm) to 15 (1.7fm), both
are stable (within 1%) with similar error-bars.
3. Finite V :
taken into account in the
analysis.
4. Finite a : overlap fermion is automatically free from O(a).
5. Finite m : m~3MeV is already very close to the chiral limit.
But
=87.3(5.5)MeV slightly different from the value
[~78(3)(1)MeV] (Noaki’s talk) in the p-regime.
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4. Conclusion
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On a (1.8fm)4 lattice with a~0.11fm, 2-flavor QCD
simulation with m~3MeV 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
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Future works
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Larger volumes
Smaller lattice spacings
Partially quenched analysis for A0A0 and V0V0 channels.
2+1 flavors…
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