$K\to \pi \nu \overline{\nu }$ in the MSSM in Light of the ${\epsilon }_K^{\prime }/{\epsilon }_K$ Anomaly

Abstract

The Standard-Model (SM) prediction for the CP-violating quantity ${\epsilon }_K^{\prime }/{\epsilon }_K$ deviates from its measured value by 2.8 $\sigma$. It has been shown that this tension can be resolved within the Minimal Supersymmetric Standard Model (MSSM) through gluino-squark box diagrams, even if squarks and gluinos are much heavier than 1 TeV. The rare decays $K_L\to {\pi }^0\nu \bar{\nu }$ and $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ are similarly sensitive to very high mass scales and the first one also measures CP violation. In this article, we analyze the correlations between ${\epsilon }_K^{\prime }/{\epsilon }_K$ and $B(K_L\to {\pi }^0\nu \bar{\nu })$ and $B(K^{+}\to {\pi }^{+}\nu \bar{\nu })$ within the MSSM aiming at an explanation of ${\epsilon }_K^{\prime }/{\epsilon }_K$ via gluino-squark box diagrams. The dominant MSSM contribution to the $K\to \pi \nu \bar{\nu }$ branching fractions stems from box diagrams with squarks, sleptons, charginos, and neutralinos, and the pattern of the correlations is different from the widely studied $Z$-penguin scenarios. This is interesting in light of future precision measurements by KOTO and NA62 at J-PARC and CERN, respectively. We find $B(K_L\to {\pi }^0\nu \bar{\nu })/B^{SM}(K_L\to {\pi }^0\nu \bar{\nu })\lesssim 2(1.2)$ and $B(K^{+}\to {\pi }^{+}\nu \bar{\nu })/B^{SM}(K^{+}\to {\pi }^{+}\nu \bar{\nu })\lesssim 1.4(1.1)$, if all squark masses are above 1.5 TeV, gaugino masses obey GUT relations, and if one allows for a fine-tuning at the $1\%(10\%)$ level for the gluino mass. Larger values are possible for a tuned CP violating phase. Furthermore, the sign of the MSSM contribution to ${\epsilon }_K^{\prime }$ imposes a strict correlation between $B(K_L\to {\pi }^0\nu \bar{\nu })$ and the hierarchy between the masses $m_{\bar{U}}$, $m_{\bar{D}}$ of the right-handed up-squark and down-squark: sgn$[B(K_L\to {\pi }^0\nu \bar{\nu })-B^{SM}(K_L\to {\pi }^0\nu \bar{\nu })]=$sgn$(m_{\bar{U}}-m_{\bar{D}})$.

9 pages, 5 figures; references added, version published in PRD

References in corpus (9)

• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• An ${\epsilon }^{\prime }$ improvement from right-handed currents
• Revisiting Kaon Physics in General $Z$ Scenario
• Chargino contributions in light of recent ${\epsilon }^{\prime }/\epsilon$
• Experiments with K-Meson Decays
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• Do squarks have to be degenerate? Constraining the mass splitting with Kaon and D mixing

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• Physics Beyond Colliders at CERN: Beyond the Standard Model Working Group Report
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• Generic Loop Effects of New Scalars and Fermions in $b\to s{\ell }^{+}{\ell }^{-}$, $(g-2{)}_{\mu }$ and a Vector-like $4^{\mathrm{th}}$ Generation
• Direct $CP$ Violation in $K\to {\mu }^{+}{\mu }^{-}$
• Explaining $(g-2{)}_{\mu ,e}$, the KOTO anomaly and the MiniBooNE excess in an extended Higgs model with sterile neutrinos
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Master formula for ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• Gluino-mediated electroweak penguin with flavor-violating trilinear couplings
• ${\epsilon }^{\prime }/\epsilon$ from charged-Higgs-induced gluonic dipole operators
• Correlating ${\epsilon }^{\prime }/\epsilon$ to hadronic $B$ decays via $U(2{)}^3$ flavour symmetry
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Left-handed color-sextet diquark in the Kaon system
• Light vectors coupled to bosonic currents
• 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
• Flavour issues in warped custodial models: $B$ anomalies and rare $K$ decays
• The direct CP violation in a general two Higgs doublet model
• Probing SUSY effects in $K_S^0\to {\mu }^{+}{\mu }^{-}$
• Top-quark flavor-changing $tqZ$ couplings and rare $\Delta F=1$ processes
• The Light Sgoldstino Phenomenology: Explanations for the Muon $(g-2)$ Deviation and KOTO Anomaly
• Theory perspectives on rare Kaon decays and CPV