# Research Topics and Main Issues

## Structure of chiral symmetry

Jeff Manudula has shown that there exist a countable infinite number
of chiral symmetries in the Ginsparg-Wilson (GW) fermion formulation.
Therefore, the construction of the chiral lagrangian is non-trivial.
We study the sturcture of the chiral symmetry systematically such that
we can understand the consequence of the extra chiral symmetries.
## B_{K} with high precision

Once we understand the structure of the chiral symmetries of the
GW fermions, we will construct the best operators to calculate
B_{K}. We will perform the numerical study using these
operators, which will cross-check the results obtained
using improved staggered fermions.
## Kl3 decay and form factors

Using the conserved vector current, we will calculate the vector
form factor of the Kl3 decay channel. The results will determine
V_{us} very precisely. This will overconstrain the unitarity
of the CKM matrix.
## Non-perturbative Renormalization (NPR)

We will apply the NPR method of the RI-MOM scheme to calculate the
matching factors for B_{K} and ε'/ε.
We will study both the exceptional momentum scheme and non-exceptional
momentum scheme to understand the systematic ambiguity in NPR.
## ε'/ε

We will calculate the direct CP violation parameter ε'/ε
in the neutral kaon system using the GW fermions. This will lead to
a direct test of the standard model.