${\epsilon }_K$ and ${\epsilon }^{\prime }/\epsilon$ in a diquark model

Abstract

Based on the calculations using the lattice QCD by RBC-UKQCD collaboration and a large $N_c$ dual QCD, the resulted ${\epsilon }^{\prime }/\epsilon$, which is less than the experimental data by more than a $2\sigma$ in the standard model (SM), suggests the necessity of a new physics effect. In order to complement the insufficient ${\epsilon }^{\prime }/\epsilon$, we study the extension of the SM with a colored scalar in a diquark model. In addition to the pure diquark box diagrams, it is found that the box diagrams with one $W$-boson and one diquark, ignored in the literature, play an important role in the $\Delta S=2$ process. The mass difference between $K_L$ and $K_S$ in the diquark model is well below the current data, whereas the Kaon indirect CP violation ${\epsilon }_K$ gives a strict constraint on the new parameters. Three mechanisms are classified in the study of ${\epsilon }^{\prime }/\epsilon$, and they include: tree-level diagram, QCD and electroweak penguins, and chromomagnetic dipole. Taking the Kobayashi-Maskawa phase as the unique CP source, we analyze each contribution of the three mechanisms in detail and conclude that these diquark-mediated effects can singly enhance ${\epsilon }^{\prime }/\epsilon$ to be of $\mathcal{O}(10^{-3})$, depending on the values of free parameters, when the bound from ${\epsilon }_K$ is satisfied.

44 pages, 10 figures, typos corrected, references added, and charged-Goldstone-boson effects included

References in corpus (17)

• Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• Search for narrow and broad dijet resonances in proton-proton collisions at $\sqrt{s}=$ 13 TeV and constraints on dark matter mediators and other new particles
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• An ${\epsilon }^{\prime }$ improvement from right-handed currents
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Leptoquarks meet ${\epsilon }^{\prime }/\epsilon$ and rare Kaon processes
• Chargino contributions in light of recent ${\epsilon }^{\prime }/\epsilon$
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• ${\epsilon }^{\prime }/\epsilon$ from charged-Higgs-induced gluonic dipole operators
• BSM Hadronic Matrix Elements for ${\epsilon }^{\prime }/\epsilon$ and $K\to \pi \pi$ Decays in the Dual QCD Approach
• ${\epsilon }_K^{\prime }/{\epsilon }_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model
• Simultaneous interpretation of $K$ and $B$ anomalies in terms of chiral-flavorful vectors
• $K\to \pi \pi$ and $K-\pi$ Matrix Elements of the Chromomagnetic Operators from Dual QCD
• $K\to \pi$ matrix elements of the chromomagnetic operator on the lattice
• ${\epsilon }^{\prime }/\epsilon$ Anomaly and Neutron EDM in $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ model with Charge Symmetry
• Direct CP Violation in Cabibbo-Favored Charmed Meson Decays and ${\epsilon }^{\prime }/\epsilon$ in $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}$ Model

Cited by in corpus (6)

• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Left-handed color-sextet diquark in the Kaon system
• On the LHC signatures of $SU(5)\times U(1{)}^{\prime }$ F-theory motivated models
• Updated Standard Model Prediction for ${\epsilon }^{\prime }/\epsilon$
• Doubling down on down-type diquarks