Left-handed color-sextet diquark in the Kaon system

Abstract

We investigate whether a color-sextet scalar diquark (${\bf H}_6$) coupling to the left-handed quarks contributes to the $ΔS=2$ process. It is found that the box diagrams mediated by $W$ and ${\bf H}_6$ bosons have no contributions to $ΔS=2$ when the limit of $m_t=0$ is used, and the flavor mixing matrices for diagonalizing quark mass matrices are introduced at the same time. When the heavy top-quark mass effects are taken into account, it is found that in addition to the $W-{\bf H}_6$ box diagrams significantly contributing to $ΔS=2$, their effects can be as large as those from the ${\bf H}_6-{\bf H}_6$ box diagrams. Using the parameters that are constrained by the $K^0-\bar K^0$ mixing parameter $ΔM_K$ and the Kaon indirect CP violation $ε_K$, we find that the left-handed color-sextet diquark can lead to the Kaon direct CP violation being $Re(ε'/ε) \sim 0.4 \times 10^{-3}$. In the chosen scheme, although the diquark contribution to $K_L\to π^0 ν\barν$ is small, the branching ratio of $K^+ \to π^+ ν\barν$ can reach the current experimental upper bound.