Toru T. Takahashi

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Lattice QCD study of g_A of N(1535) with
two flavors of dynamical quarks
Toru T. Takahashi with Teiji Kunihiro
Why N(1535)? Lattice QCD calculation Result
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Why lattice QCD ?
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Introduction
Want to understand the hadron dynamics
in terms of QCD
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Why N(1535) ?
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Why N(1535) ?
Importance of strange quarks in N(1535) Its
chiral structure
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Chiral symmetry
The original QCD lagrangian has a (approx.)
global symmetry. ( SU(3)_R x SU(3)_L invariant )
? chirality
This symmetry spontaneously broken to SU(3)_v and
NG bosons appear.
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Baryons are fermions composed of quarks.
Naively, Q Q Q
How are baryons transformed ??

• Naïve
• Mirror

?
Naïve assignment
Mirror assingment
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Naïve and mirror assignment
We hereby consider the situation where linear
combinations of two nucleon fields construct
physical N and N.
N1 and N2 is the original states of N and N
There are two possible realizations for N1 and N2.
NAÏVE and MIRROR
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Naïve assignment
Let us consider two nucleon fields.
Under the SU(2)LxSU(2)R transformation,
Chiral partner in
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Mirror assignment
In this case, we consider two nucleon fields,
Under the SU(2)LxSU(2)R transformation,
We can introduce chirally invariant mass term!
They can be massive even near the chirally
restored phase!
diagonalization
belong to the same multiplet and are chiral
partners of each other.
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Naive
Mixing between N1 and N2
s is responsible for mass generation.
Taken from the paper by D.Jido, Y.Nemoto, M.Oka,
A.Hosaka
Mirror
Massterm!
s is responsible for mass splitting.
They can be massive in restored phase.
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Naive
? diagonalization
Off-diagonal coupling vanishes. (in the soft pion
limit, where we can neglect the derivative
coupling.)
is small. Consistent?
Mirror
???
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gA for N(1535) is negative ? Mirror assignment
positive ? Naïve
assignment All we have to do is to investigate
the sign of gA for N(1535)
Couplings are related in the mirror
assignment. We can distinguish one from
another even in the chiral-broken phase?
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Lattice QCD
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g_A in Lattice QCD
Lattice QCD SIMPLY provides us with vacuum
expectation values of OPERATORS.

• RECIPE
• Construct or choose the interpolating field
• which couples to N(1535)
• 2. Compute the ratio of 2- and 3- point
  correlations

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PROBLEMS in lattice QCD calculations
CONTAMINATION of Signals
N(1535) is accompanied by N(1650) lying just
100MeV above.
N(1535) can decay.
Lattices are usually 4D torus-type.
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Signals in Lattice QCD
Difficulty in the lattice QCD calculation
We suffer from the contaminations of the other
scattering state.
Correlation between operators
N(1650) N(1535)
Creation at t0
Annihilation at tT
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Signals in Lattice QCD
We need to separate signals.
Remember pentaquark !
We employ two different types of operators.

• Diagonalize the 2x2 correlation matrix
• and separate the signals!

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PROBLEMS in lattice QCD calculations
CONTAMINATION of Signals
N(1535) is accompanied by N(1650) lying just
100MeV above.
N(1535) can decay.
Lattices are usually 4D torus-type.
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Contaminations from scattering states
It is quite difficult to extract higher-excited
state signals!
Finite volume Heavy quark masses
Infinite volume
Our setups
pN threshold
N(1650)
N(1650)
N(1650)
N(1535)
N(1535)
N(1535)
pN threshold
pN threshold
pN-scattering states do not bother us!
It implies the volumes and the quark masses are
far from realistic ones.
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PROBLEMS in lattice QCD calculations
CONTAMINATION of Signals
N(1535) is accompanied by N(1650) lying just
100MeV above.
N(1535) can decay.
Lattices are usually 4D torus-type.
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4D torus is harmful ???
Imaginary time dir.
Let us consider 2-point functions
What we want
We do not have
N p
N p
N
We impose Dirichlet boundary for quarks!
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PROBLEMS in lattice QCD calculations
CONTAMINATION of Signals
N(1535) is accompanied by N(1650) lying just
100MeV above.
N(1535) can decay.
Lattices are usually 4D torus-type.
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Simulation parameters
Generated by CP-PACS

• 163 x 32 lattice with two flavors of dynamical
  quarks
• The renormalization-group improved gauge action
  at ß1.95
• The mean field improved clover quark action
• with the clover coefficient c_SW1.530
• Lattice size (2.5fm)3 x (5.0fm)
• Hopping parameter ?0.1375, 0.1390, 0.1400
• ?pion mass 1.16 GeV, 0.947 GeV, 0.777 GeV

The quarks are heavier than the realistic ones.
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Masses - chiral extrapolation -
N(940) 1204( 4) MeV N(1440) 2019(141) MeV
N(1535) 1642(32) MeV N(1650) 1815(49) MeV
Diagonalization processes seem to work well.
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Lattice QCD results
gV and gA for N(940) gV for N(1535)
preliminary
? 1.26
? 1.00
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Lattice QCD results
gA for N(1535)
preliminary
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Lattice QCD results
Relative sign is - ? mirror assignment Relative
sign is ? naïve assignment
Even the relative sign is quark-mass-dependent.

• Finite size effect ?
• (2.5 fm)3 may be small for N(1535)
• Transition from naïve to mirror
• sea quark effect in the light-quark region ?

Model prediction
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Summary
We have studied the axial charge of N(1535) using
lattice QCD. g_A for N(1535) seems small as
g_A0.2. Even the sign is quark-mass-dependent.
The absolute value is quite small. ? Naïve
only with Yukawa terms is not likely? u- and d-
contributions are individually quite small.
Analysis on a large lattice 21 dynamical
calculations Possible mixture of mirror and
naïve assignments ?