${ϵ}^{\prime }/ϵ$ from charged-Higgs-induced gluonic dipole operators

Abstract

We study the effect of charged-Higgs-induced chromomagnetic operator, $Q_{8G}(-)\equiv \bar{s}{\sigma }^{\mu \nu }{T}^a{\gamma }_{5}d{G}_{\mu \nu }^a$, on the Kaon direct CP violation $Re({ϵ}^{\prime }/ϵ)$. Using the matrix element $⟨\pi \pi |O_{8G}(-)|K^0⟩$ recently obtained by a large $N_c$ dual QCD approach, we find that if the Kobayashi-Maskawa phase is the origin of CP violation, the charged-Higgs-induced gluon penguin dipole operator in the type-III two-Higgs-doublet model can explain the measured $Re({ϵ}^{\prime }/ϵ)$ when the constraints from the relevant low energy flavor physics, such as $\Delta B(K)=2$, $B\to X_s\gamma$, and Kaon indirect CP violation parameter $ϵ$, are included.

Comments: 15 pages, 4 figures, version accepted for publication in Physics Letters B