$K\to\pi\pi$ from electroweak penguins in $N_f=2$ domain-wall QCD

Abstract

We present the calculation of $K\to\pi\pi$ matrix elements of electroweak penguin operators {\it i.e.} $Q_7$ and $Q_8$. In the numerical simulation, we use the gauge configurations generated by the combination of $N_f=2$ domain-wall fermions and DBW2 gauge action. From $K\to\pi$ and $K\to 0$ matrix elements on the lattice, we construct $K\to\pi\pi$ matrix elements at next-to-leading order in the chiral expansion by using recent analytic results. Renormalization factor of these matrix elements are obtained by the non-perturbative renormalization technique in RI/MOM scheme. Brief discussion based on our results are made as well as a comparison with previous works.