Left-handed color-sextet diquark in the Kaon system

Abstract

We investigate whether a color-sextet scalar diquark (${\mathbf{H}}_6$) coupling to the left-handed quarks contributes to the $\Delta S=2$ process. It is found that the box diagrams mediated by $W$ and ${\mathbf{H}}_6$ bosons have no contributions to $\Delta S=2$ 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 $W-{\mathbf{H}}_6$ box diagrams significantly contributing to $\Delta S=2$, their effects can be as large as those from the ${\mathbf{H}}_6-{\mathbf{H}}_6$ box diagrams. Using the parameters that are constrained by the $K^0-{\bar{K}}^0$ mixing parameter $\Delta M_K$ and the Kaon indirect CP violation ${\epsilon }_K$, we find that the left-handed color-sextet diquark can lead to the Kaon direct CP violation being $Re({\epsilon }^{\prime }/\epsilon )\sim 0.4\times 10^{-3}$. In the chosen scheme, although the diquark contribution to $K_L\to {\pi }^0\nu \bar{\nu }$ is small, the branching ratio of $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ can reach the current experimental upper bound.

28 pages, 10 figures, version accepted for publication in PRD

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• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• Correlating ${\epsilon }^{\prime }/\epsilon$ to hadronic $B$ decays via $U(2{)}^3$ flavour symmetry
• Exploiting dijet resonance searches for flavor physics
• LHC Constraints on Scalar Diquarks