# Research Topics and Main Issues

## B_{K} with high precision

We calculated
B_{K} in partially quenched QCD using MILC
gauge configurations. We tried both degenerate quark
mass combinations and non-degenerate quark mass
combinations. The results are analyzed using the
results of partially quenched (PQ) chiral perturbation
theory. The fitting of the data with non-degenerate
quark masses to the prediction of PQ chiral
perturbation theory illustrates that we can determine,
in principle, all the low energy constants using only
degenerate quark mass combinations. However, the
quality of fitting was significantly better with
non-degenerate quark mass combinations. We plan to
extend this preliminary study to large scale numerical
simulation such that we can fit the data to the form
suggested by the staggered chiral perturbation theory
in near future.
## Hadron spectrum

We plan to measure staggered meson spectrum
in quenched QCD in order to probe the improvement by
HYP/Fat7
fat links. First, we will have a look at
the pion multiplets to measure the splittings between
the Goldstone and non-Goldstone pions. Second, we will
investigate the rho, a1, a0, b1 spectrum to understand
the effect of improvement. By using
HYP/Fat7
fat links, we expect, the splitting would be reduced so
significantly that the chiral-log corrections
originating from the non-Goldstone pions become quite
important. Hence, this research will provide a basic
background work for other researches including weak
matrix elements. We also plan to measure the staggered
meson spectrum using MILC gauge configurations. The
results will be used to analyze the data of weak
matrix elements using the prediction of the staggered
chiral perturbation theory.
## ε'/ε

We are calculating the size of the
direct CP violation using lattice gauge theory. In
particluar, we use staggered fermions which preserve
enough chiral symmetry to calculate ε'/ε.
At the early stage of this work,
we calculated ε'/ε using
unimproved staggered fermions. The results for
B_{6} indicate a large quenching uncertainty.
In addition, the operators constructed out of
unimproved staggered fermions receive large
perturbative corrections (~100%). Hence it was
essential to reduce the large perturbative correction
by improving staggered fermions. In order to find the
best scheme, we calculated explicitly the one loop
matching coefficients for various improvement schemes
for the staggered fermion action and
operators. Through this study, we figure out that the
HYP and
Fat7
schemes lead to the smallest one loop
corrections. In order to fully match the lattice
calculation to the continuum, we calculated the one
loop renormalizations constants for the four-fermion
operators. It turns out that the matching coefficients
are reduced down to about 10% level using improved
staggered fermions. We also performed a numerical
study on ε'/ε using HYP staggered fermions
in quenched QCD.
We plan to calculate ε'/ε
in partially quenched QCD using MILC gauge configurations
in near future.
## Perturbative calculation of matching factors

In order to convert the numerical data into
physical quantity, we need to find the conversion
formula named "matching factors" which are, in general,
matrices. One possibility is to calculate the
matching factors using one-loop perturbation theory.
At present it is necessary to develop a method to
obtain matching factors in the mixed action
environment (HYP sea quarks and AsqTad valence
quarks). We also plan to develop a method to evaluate
the matching factor at the two-loop level. At the
same time, we will also search for a new method to
implement non-perturbative renormalization (NPR)
method for staggered fermions.
## Staggered chiral perturbation theory

In order to perform a data analysis as a
function of quark masses, it is important to
understand the chiral behavior of physical
observables. The best tool to calculate the chiral
behavior is the staggered chiral perturbation theory,
which was invented originally by Weonjong Lee and
Stephen Sharpe and developed later by Claude
Bernard. So far, for most of the weak matrix elements,
the chiral behavior is estimated based on the
(partially) qenched chiral perturbation theory. Since
we are using highly improved staggered fermions such
as HYP or Fat7 types,
the contribution from the non-Goldstone pions
becomes so important that we need to include them into
the data analysis. A systematic method to do this is
staggered chiral perturbation theory. We plan to
figure out the chiral behavior of hadron masses and
weak matrices relevant to CP violations in near future.
## Kl3 decay and form factors

We plan to calculate the vector form factor of the Kl3 decay channel
in order to determine V_{us} very precisely. The results will
be used to overconstrain the unitarity ansatz of the standard model.
## Non-perturbative renormalization for staggered fermions

We plan to calculate the matching factors for the B_{K} and
ε'/ε using the NPR method. This method is based on the
RI-MOM scheme. We will apply both exceptional momentum scheme and
non-exceptional momentum scheme in order to control the systematic
error. In the NPR, we trade the systematic error
due to the truncated higher
order with the statistical error.