Transcript Naïve assignment

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
Why lattice QCD ?
Introduction
Nuclear or Hadron Physics
Quantum Chromodynamics
Quantum manybody system
proton
Hadrons neutron
……
SU(3) gauge theory
Mesons p, r, w,…..
GAP!!
Quarks
(fund. rep.)
Gluons
(adjoint rep.)
Want to understand the hadron dynamics
in terms of QCD
Strong coupling nature of QCD
Analytic study is still difficult
Lattice QCD calculation
Why N*(1535) ?
Why N*(1535) ?
・Importance of strange quarks in N*(1535)
・It’s chiral structure
Baryon sector in the linear sigma model
Two types of chiral realization
1) One may naively expect that nucleons become massless
as indicated using linear sigma mode.
Naïve assignment
2) DeTar and Kunihiro in 1989, Schafer and Shuryak in 1995
 They showed the possibility that nucleons are massive
even in the chiral-restored phase.
Mirror assignment
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.
Baryons are fermions composed of quarks.
Naively, Q + Q + Q
How are baryons transformed ??
?
N ´ q( qC° 5 q)
Naïve assignment
 Naïve
 Mirror
N ´ ° 5 q( qC° 5 q) ( q
¹ ° 5 q)
Mirror assingment
Naïve and mirror assignment
We hereby consider the situation
where linear combinations of two nucleon fields construct
physical N and N*.
N » aN 1 + bN 2
N ¤ » cN 1 + dN 2
N1 and N2 is the original states of N and N*
There are two possible realizations for N1 and N2.
NAÏVE and MIRROR
Naïve assignment
Let us consider two nucleon fields.
Under the SU(2)LxSU(2)R transformation,
Chiral partner in
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.
Naive
Mixing between N1 and N2
σ is responsible for
mass generation.
Taken from the paper by D.Jido, Y.Nemoto, M.Oka, A.Hosaka
Mirror
Massterm!
σ is responsible for
mass splitting.
They can be massive
in restored phase.
Naive
 diagonalization
Off-diagonal coupling vanishes.
(in the soft pion limit, where we
can neglect the derivative coupling.)
is small.
Consistent?
Mirror
逆符号
Couplings
areisrelated
mirror
assignment.
gA
for N(1535)
negativeinthe
Mirror
assignment
We can distinguish
from
another
positive one
Naïve
assignment
All we have
to do
to investigate
the sign phase…?
of gA for N(1535)
even
in isthe
chiral-broken
Lattice QCD
g_A in Lattice QCD
Lattice QCD SIMPLY provides us
with vacuum expectation values of OPERATORS.
here couples to the state
RECIPE
1. Construct or choose the interpolating field
which couples to N(1535)
2. Compute the ratio of 2- and 3- point correlations
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.
Signals in Lattice QCD
Difficulty in the lattice QCD calculation
We suffer from the contaminations of the other scattering state.
Correlation between operators
Euclidean time evolution by exp(-Ht)
N(1650)
N(1535)
Creation
at
t=0
Annihilation
at
t=T
Energy of the ground state
Signals in Lattice QCD
We need to separate signals.
Remember pentaquark !
We employ two different types of operators.
N^ 1 ´ u( u T C° 5 d)
N^ 2 ´ ° 5 u( u T Cd)

Diagonalize the 2x2 correlation matrix
and separate the signals!
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.
Contaminations from scattering states
It is quite difficult to extract higher-excited state signals!
Infinite volume
Finite volume
&
Heavy quark masses
Our setups
πN threshold
N(1650)
N(1535)
πN threshold
N(1650)
N(1535)
πN threshold
N(1650)
N(1535)
πN-scattering states do not bother us!
It implies the volumes and the quark masses are far from realistic ones.
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.
4D torus is harmful ???
Imaginary time dir.
Let us consider 2-point functions
What we want
N*
We do not have
N+π
We impose Dirichlet boundary for quarks!
N+π
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.
Simulation parameters
Generated by CP-PACS
16^3 x 32 lattice with two flavors of dynamical quarks
The renormalization-group improved gauge action at β=1.95
The mean field improved clover quark action
with the clover coefficient c_SW=1.530
Lattice size = (2.5fm)^3 x (5.0fm)
Hopping parameter κ=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.
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.
Lattice QCD results
gV and gA for N(940)
gV
for N(1535)
 1.26
 1.00
Lattice QCD results
gA
for N(1535)
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
Summary
We have studied the axial charge of N(1535) using lattice QCD.
g_A for N(1535) seems small as | g_A|～0.2.
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
2+1 dynamical calculations
Possible mixture of mirror and naïve assignments ?