${\epsilon }_K^{\prime }/{\epsilon }_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model

Abstract

The Kaon direct CP violation $Re({\epsilon }_K^{\prime }/{\epsilon }_K)$ below the experimental data of a $2\sigma$ in the standard model, which is calculated using the RBC-UKQCD lattice and a large $N_c$ dual QCD, indicates the necessity of a new physics effect. In order to resolve the insufficient $Re({\epsilon }_K^{\prime }/{\epsilon }_K)$, we study the charged-Higgs contributions in a generic two-Higgs-doublet model. If we assume that the origin of the CP-violation phase is uniquely from the Kobayashi-Maskawa (KM) phase when the constraints from the $B$- and $K$-meson mixings, $B\to X_s\gamma$, and Kaon indirect CP violating parameter ${\epsilon }_K$ are simultaneously taken into account, it is found that the Kaon direct CP violation through the charged-Higgs effects can reach $Re({\epsilon }_K^{\prime }/{\epsilon }_K{)}_{H^{\pm }}\sim 8\times 10^{-4}$. Moreover, with the constrained values of the parameters, the branching ratios of the rare $K\to \pi \nu \bar{\nu }$ decays can be $BR(K^{+}\to {\pi }^{+}\nu \bar{\nu })\sim 14\times 10^{-11}$ and $BR(K_L\to {\pi }^0\nu \bar{\nu })\sim 3.6\times 10^{-11}$, where the results can be tested through the NA62 experiment at CERN and the KOTO experiment at J-PARC, respectively.

33 pages, 10 figures, version accepted for publication in JHEP

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Cited by in corpus (16)

• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• Search for $K_L\to {\pi }^0\nu \overline{\nu }$ and $K_L\to {\pi }^0{X}^0$ Decays at the J-PARC KOTO Experiment
• Explaining $(g-2{)}_{\mu ,e}$, the KOTO anomaly and the MiniBooNE excess in an extended Higgs model with sterile neutrinos
• Correlating ${\epsilon }^{\prime }/\epsilon$ to hadronic $B$ decays via $U(2{)}^3$ flavour symmetry
• Correlation between $R_{D^{(\ast )}}$ and top quark FCNC decays in leptoquark models
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Left-handed color-sextet diquark in the Kaon system
• Common explanation to the $R_{K^{(\ast )}}$, $R_{D^{(\ast )}}$ and ${\epsilon }^{\prime }/\epsilon$ anomalies in a 3HDM+${\nu }_R$ and connections to neutrino physics
• BSM Hadronic Matrix Elements for ${\epsilon }^{\prime }/\epsilon$ and $K\to \pi \pi$ Decays in the Dual QCD Approach
• Simultaneous interpretation of $K$ and $B$ anomalies in terms of chiral-flavorful vectors
• The direct CP violation in a general two Higgs doublet model
• Effect of the Pauli exclusion principle in the electric dipole moment of ${}^9$Be with $|\Delta S|=1$ interactions
• Observation of the $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ decay and measurement of its branching ratio
• ${\epsilon }_K$ and ${\epsilon }^{\prime }/\epsilon$ in a diquark model
• Strange processes in general two Higgs doublet model
• The Light Sgoldstino Phenomenology: Explanations for the Muon $(g-2)$ Deviation and KOTO Anomaly