Search

Rectification phenomenon caused by the simultaneous breaking of time reversal and spatial inversion symmetries has been extended to a wide range of (quasi)particles and waves; however, the nonreciprocal diffraction, which is the imbalance of upward and downward deflections, was previously observed only for photons and remained to be extended to other (quasi)particles. In this study, we present evidence of the nonreciprocal diffraction of surface acoustic wave (SAW) utilizing a magnetoelastic grating on a SAW device. Asymmetric diffraction intensities were observed when the ferromagnetic resonance was acoustically excited. Based on a theoretical model, we attribute the microscopic origin of this phenomenon to the resonant scattering involving ferromagnetic resonance excitations. The novel property may pave an avenue to further development of SAW devices for various purposes, including microwave communications and quantum engineering applications., Comment: 15 pages, 12 figures

Magnets are interesting materials for classical and quantum information technologies. However, the short decoherence and dephasing times that determine the scale and speed of information networks, severely limit the appeal of employing the ferromagnetic resonance. Here we show that the lifetime and coherence of the uniform Kittel mode can be enhanced by 3-magnon interaction-induced mixing with the long-lived magnons at the minima of the dispersion relation. Analytical and numerical calculations based on this model explain recent experimental results and predict experimental signatures of quantum coherence.

We study the interplay of New Physics (NP) among the lepton magnetic moment, the lepton flavor violation (LFV) and the electron electric dipole moment (EDM) in light of recent data of the muon $(g-2)_\mu$. The NP is discussed in the leptonic dipole operator with the $U(2)$ flavor symmetry of the charged leptons, where possible CP violating phases of the three family space are taken into account. It is remarked that the third-family contributes significantly to the LFV decay, $\mu \to e\gamma$, and the electron EDM. The experimental upper-bound on $\mu \to e\gamma$ decay gives a severe constraint on the parameters of the flavor model. The predicted electron EDM is rather large due to the CP violating phases in the three family space. In addition, we also study $(g-2)_{e,\tau}$ of the electron and tauon, and EDMs of the muon and tauon as well as the $\tau \to e \gamma$ and $\tau \to \mu \gamma$ decays. The $\tau_R \to \mu_L \gamma$ decay is predicted to be close to the experimental upper-bound., Comment: 25 pages, 14 figures. Published version in EPJ-C; minor comments added, typos corrected

Phonons and magnons are engineered by periodic potential landscapes in phononic and magnonic crystals, and their combined studies may enable valley phonon transport tunable by the magnetic field. Through nonreciprocal surface acoustic wave transmission, we demonstrate valley-selective phonon-magnon scattering in magnetoelastic superlattices. The lattice symmetry and the out-of-plane magnetization component control the sign of nonreciprocity. The phonons in the valleys play a crucial role in generating nonreciprocal transmission by inducing circularly polarized strains that couple with the magnons. The transmission spectra show a nonreciprocity peak near a transmission gap, matching the phononic band structure. Our results open the way for manipulating valley phonon transport through periodically varying magnon-phonon coupling.

Harnessing the causal relationships between mechanical and magnetic properties of van der Waals materials presents a wealth of untapped opportunity for scientific and technological advancement, from precision sensing to novel memories. This can, however, only be exploited if the means exist to efficiently interface with the magnetoelastic interaction. Here, we demonstrate acoustically-driven spin-wave resonance in a crystalline antiferromagnet, chromium trichloride, via surface acoustic wave irradiation. The resulting magnon-phonon coupling is found to depend strongly on sample temperature and external magnetic field orientation, and displays a high sensitivity to extremely weak magnetic anisotropy fields in the few~mT range. Our work demonstrates a natural pairing between power-efficient strain-wave technology and the excellent mechanical properties of van der Waals materials, representing a foothold towards widespread future adoption of dynamic magneto-acoustics., Comment: 14 pages, 7 figures (main text + supplemental material)

We have investigated an approach to determine the Majorana type-phases using the time evolution of lepton family numbers. The Majorana type-phases are related to the orientation of unitarity triangles for the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix, and the Majorana phases $\alpha_{21}$ and $\alpha_{31}$. After taking the second-order time derivative of the lepton family number expectation values, the dependencies on the summation of Majorana type-phases can be determined. Thus allowing for the extraction of the orientation of the unitarity triangles and the Majorana phases. We study how to extract the Majorana type-phases and the lightest neutrino mass for three massive neutrinos, and when a neutrino is massless, i.e., $m_{1,3}=0$. Our result can be complimentary to using neutrinoless double-beta decay for determining the orientation of PMNS unitarity triangles and the Majorana phases., Comment: 18 pages, 5 figures, In v2,one reference is cited in a correct place. The order of the author's addresses is corrected

We study the quark sector of the universal seesaw model with SU(2)$_L$ $\times$ SU(2)$_R$ $\times$ $U(1)$.The model incorporates the seesaw mechanism with the vector-like quarks (VLQs). The purpose of this work is to study the model with the effective theory. After integrating the heavy five VLQs, we derive the effective theory with four up-type quark and three down type quark. In this work, the FCNC of Z boson for top quark and top$^\prime$ quark is derived., Comment: 4 pages, Contribution to the proceedings for International Conference on Kaon Physics 2022

We classify a supersymmetric extension of the Standard Model by discrete symmetries originating from finite modular symmetries $\Gamma_N$. Since all the couplings in supersymmetric theories of finite modular symmetries $\Gamma_N$ are described by holomorphic modular forms with even modular weights, renormalizable and non-renormalizable operators such as baryon- and/or lepton-number violating operators are severely constrained. From the modular transformation of matter multiplets with modular weight $1/M$, we find $\mathbb{Z}_{2M}$ symmetries, including the generalized baryon and lepton parities, $R$-parity, $\mathbb{Z}_3$ baryon triality and $\mathbb{Z}_6$ proton hexality. Such $\mathbb{Z}_{2M}$ symmetries are enlarged to $\mathbb{Z}_{2M} \rtimes \mathbb{Z}_2^{\text{CP}}$ symmetries together with the CP transformation., Comment: 23 pagess, v2: published version

We study the lepton flavor violation (LFV), the leptonic magnetic moments $(g-2)_{\mu,\,e} $ and the electric dipole moment (EDM) of the electron in the Standard-Model Effective Field Theory with the $\Gamma_N$ modular flavor symmetry. We employ the stringy Ansatz on coupling structure that 4-point couplings of matter fields are written by a product of 3-point couplings of matter fields. We take the level 3 finite modular group, $\Gamma_3$ for the flavor symmetry, and discuss the dipole operators at nearby fixed point $\tau=i$, where observed lepton masses and mixing angles are well reproduced. Suppose the anomaly of the anomalous magnetic moment of the muon to be evidence of the new physics (NP), we have related it with $(g-2)_{e}$, LFV decays, and the electron EDM. It is found that the NP contribution to $(g-2)_{e}$ is proportional to the lepton masses squared likewise the naive scaling. We also discuss the correlations among the LFV processes $\mu\to e\gamma$, $\tau\to \mu\gamma$ and $\tau\to e\gamma$, which are testable in the future. The electron EDM requires the tiny imaginary part of the relevant Wilson coefficient in the basis of real positive charged lepton masses, which is related to the $\mu\to e\gamma$ transition in our framework., Comment: 33 pages, references added

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community., Comment: 356 pages, Large pdf file (40 MB) submitted to Snowmass 2021; v2 references to Snowmass contributions added, additional authors; v3 references added, some updates, additional authors

We experimentally and theoretically demonstrate that nonlinear spin-wave interactions suppress the hybrid magnon-photon quasiparticle or "magnon polariton" in microwave spectra of an yttrium iron garnet film detected by an on-chip split-ring resonator. We observe a strong coupling between the Kittel and microwave cavity modes in terms of an avoided crossing as a function of magnetic fields at low microwave input powers, but a complete closing of the gap at high powers. The experimental results are well explained by a theoretical model including the three-magnon decay of the Kittel magnon into spin waves. The gap closure originates from the saturation of the ferromagnetic resonance above the Suhl instability threshold by a coherent back reaction from the spin waves., Comment: 6 pages

Rare meson decays are among the most sensitive probes of both heavy and light new physics. Among them, new physics searches using kaons benefit from their small total decay widths and the availability of very large datasets. On the other hand, useful complementary information is provided by hyperon decay measurements. We summarize the relevant phenomenological models and the status of the searches in a comprehensive list of kaon and hyperon decay channels. We identify new search strategies for under-explored signatures, and demonstrate that the improved sensitivities from current and next-generation experiments could lead to a qualitative leap in the exploration of light dark sectors., Comment: 108 pages, 25 figures, 9 tables, matches the published version

We study a scenario to derive four-dimensional modular flavor symmetric models from higher dimensional theory by assuming the compactification consistent with the modular symmetry. In our scenario, wavefunctions in extra dimensional compact space are modular forms. That leads to constraints on combinations between modular weights and $\Gamma_N$ ($\Gamma_N')$ representations of matter fields. We also present illustrating examples., Comment: 21 pages, v2: published version

We study the modular symmetric standard-model effective field theory. We employ the stringy Ansatz on coupling structure that 4-point couplings $y^{(4)}$ of matter fields are written by a product of 3-point couplings $y^{(3)}$ of matter fields, i.e., $y^{(4)} = y^{(3)}y^{(3)}$. In this framework, we discuss the flavor structure of bilinear fermion operators and 4-fermion operators, where the holomorphic and anti-holomorphic modular forms appear. From the Ansatz, the $A_4$ modular-invariant semileptonic four-fermion operator $[\,\bar E_R \Gamma E_R][\,\bar D_R \Gamma D_R\,]$ does not lead to the flavor changing (FC) processes since this operator would be constructed in terms of gauge couplings $g$ as $y^{(3)} \sim g$. The chirality flipped bilinear operator $[\,\bar D_R \Gamma D_L\,]$ also does not lead FC if the mediated mode corresponds to the Higgs boson $H_d$. In this case, the flavor structure of this operator is the exactly same as the mass matrix. On the other hand, if the flavor structure of the operator is not the exactly same as the mass matrix, the situation would change drastically. Then, we obtain the non-trivial relations of FC transitions at nearby fixed points $\tau=i,\,\omega\,, i\infty$, which are testable in the future. As an application, we discuss the relations of the lepton flavor violation processes $ \mu\to e\gamma,\, \tau\to \mu\gamma$ and $\tau\to e\gamma$ at nearby $\tau_e=i$, where the successful lepton mass matrix was obtained. We also study the flavor changing 4-quark operators in the $A_4$ modular symmetry of quarks. As a result, the minimal flavor violation could be realized by taking relevant specific parameter sets of order one., Comment: 48 pages, 14 tables, revised discussion in Sec.4, several tables modified

The electric dipole moment (EDM) of electron is studied in the supersymmetric $\rm A_4$ modular invariant theory of flavors with CP invariance. The CP symmetry of the lepton sector is broken by fixing the modulus $\tau$. Lepton mass matrices are completely consistent with observed lepton masses and mixing angles in our model. In this framework, a fixed $\tau$ also causes the CP violation in the soft SUSY breaking terms. The elecrton EDM arises from the CP non-conserved soft SUSY breaking terms. The experimental upper bound of the electron EDM excludes the SUSY mass scale below $2-6$ TeV for five cases of the lepton mass matrices. In order to see the effect of CP phase of the modulus $\tau$, we examine the correlation between the electron EDM and the decay rate of the $\mu \rightarrow e \gamma$ decay, which is also predicted by the soft SUSY breaking terms. The correlations are clearly predicted in contrast to models of the conventional flavor symmetry. The SUSY mass scale will be constrained by the future sensitivity of the electron EDM, $|d_e/e| \simeq 10^{-30}$. Indeed, it could probe the SUSY mass range of $10-20$ TeV in our model. Thus, the electron EDM provides a severe test of the CP violation via the modulus $\tau$ in the supersymmetric modular invariant theory of flavors., Comment: 33 pages, 8 figures, 4 tables; v3: corrections for equations, discussion added, figures and tables changed, conclusions unchanged. arXiv admin note: text overlap with arXiv:2105.14292

We analyse how $U(3)^5$ and $U(2)^5$ flavour symmetries act on the Standard Model Effective Field Theory, providing an organising principle to classify the large number of dimension-six operators involving fermion fields. A detailed counting of such operators, at different order in the breaking terms of both these symmetries, is presented. A brief discussion about possible deviations from these two reference cases, and a simple example of the usefulness of this classification scheme for high-$p_T$ analyses at the LHC, are also presented., Comment: 31 pages, 13 Tables

Voltage induced magnetization dynamics of magnetic thin films is a valuable tool to study anisotropic fields, exchange couplings, magnetization damping and spin pumping mechanism. A particularly well established technique is the ferromagnetic resonance (FMR) generated by the coupling of microwave photons and magnetization eigenmodes in the GHz range. Here we review the basic concepts of the so-called acoustic ferromagnetic resonance technique (a-FMR) induced by the coupling of surface acoustic waves (SAW) and magnetization of thin films. Interestingly, additional to the benefits of the microwave excited FMR technique, the coupling between SAW and magnetization also offers fertile ground to study magnon-phonon and spin rotation couplings. We describe the in-plane magnetic field angle dependence of the a-FMR by measuring the absorption / transmission of SAW and the attenuation of SAW in the presence of rotational motion of the lattice, and show the consequent generation of spin current by acoustic spin pumping., Comment: 6 pages, 6 figures, short review

One of the most fundamental forms of magnon-phonon interaction is an intrinsic property of magnetic materials, the "magnetoelastic coupling". This particular form of interaction has been the basis for describing magnetic materials and their strain related applications, where strain induces changes of internal magnetic fields. Different from the magnetoelastic coupling, more than 40 years ago, it was proposed that surface acoustic waves may induce surface magnons via rotational motion of the lattice in anisotropic magnets. However, a signature of this magnon-phonon coupling mechanism, termed magneto-rotation coupling, has been elusive. Here, we report the first observation and theoretical framework of the magneto-rotation coupling in a perpendicularly anisotropic ultra-thin film Ta/CoFeB(1.6 nm)/MgO, which consequently induces nonreciprocal acoustic wave attenuation with a unprecedented ratio up to 100$\%$ rectification at the theoretically predicted optimized condition. Our work not only experimentally demonstrates a fundamentally new path for investigating magnon-phonon coupling, but also justify the feasibility of the magneto-rotation coupling based application., Comment: 30 pages, 12 figures

Motivated by the recent hints of lepton flavor universality violation observed in semileptonic $B$ decays, we analyze how to test flavor and helicity structures of the corresponding amplitudes in view of future data. We show that the general assumption that such non-standard effects are controlled by a $U(2)_q \times U(2)_\ell$ flavor symmetry, minimally broken as in the Standard Model Yukawa sector, leads to stringent predictions on leptonic and semileptonic $B$ decays. Future measurements of $R_{D^{(*)}}$, $R_{K^{(*)}}$, ${\mathcal B}(\bar B_{c,u}\to \ell \bar \nu)$, ${\mathcal B}(\bar B \to \pi \ell \bar\nu)$, ${\mathcal B}(B \to \pi \ell \bar\ell)$, ${\mathcal B}(B_{s,d}\to\ell\bar\ell^{(\prime)})$, as well as various polarization asymmetries in $\bar B\to D^{(*)} \tau \bar \nu$ decays, will allow to prove or falsify this general hypothesis independently of its dynamical origin., Comment: 12 pages, 4 figures (v2: very minor modifications)

We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological origin. For a class of classical systems that includes spin waves driven by dipole-dipole interactions, we show that the topology is characterized by vortex lines in the Brillouin zone in such a way that the symplectic structure of Hamiltonian mechanics plays an essential role. We define winding numbers around these vortex lines and identify them to be the bulk topological invariants for a class of semimetals. Exploiting the bulk-edge correspondence appropriately reformulated for these classical waves, we predict that surface modes appear but not in a gap of the bulk frequency spectrum. This feature, consistent with the magnetostatic surface spin waves, indicates a broader realm of topological phases of matter beyond spectrally gapped ones., Comment: 5 pages, 3 figures. To appear in PRL

The emerging field of magnonics employs spin waves and their quanta, magnons, to implement wave-based computing on the micro- and nanoscale. Multi-frequency magnon networks would allow for parallel data processing within single logic elements whereas this is not the case with conventional transistor-based electronic logic. However, a lack of experimentally proven solutions to efficiently combine and separate magnons of different frequencies has impeded the intensive use of this concept. In this Letter, the experimental realization of a spin-wave demultiplexer enabling frequency-dependent separation of magnonic signals in the GHz range is demonstrated. The device is based on two-dimensional magnon transport in the form of spin-wave beams in unpatterned magnetic films. The intrinsic frequency-dependence of the beam direction is exploited to realize a passive functioning obviating an external control and additional power consumption. This approach paves the way to magnonic multiplexing circuits enabling simultaneous information transport and processing., Comment: 16 pages, 3 figures

We address the presently reported significant flavor anomalies in the $K$ and $B$ meson systems such as the CP violating Kaon decay ($\epsilon'/\epsilon$) and lepton-flavor universality violation in $B$ meson decays ($R_{K^{(*)}},$ and also commenting ${R_{D^{(*)}}}$), by proposing flavorful and chiral vector bosons as the new physics constitution at $\sim 1\,\mathrm{TeV}$. Interestingly, if the new (composite) vector bosons are quite heavier than $\sim 1\,\mathrm{TeV}$, we face a difficulty in addressing the anomaly in $\epsilon'/\epsilon$ consistently with the constraint from the $K^0$-$\overline{K^0}$ mixing. Both of the anomalies can be addressed within $1\sigma$ confidence levels individually, where the relevant parameter space will be investigated by the NA62 and KOTO experiments, in addition to direct searches at the large hadron collider., Comment: 13 pages, 4 figures (v2, some references added); Contribution to the Proceedings of the Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2018), 31 August - 28 September, 2018, Corfu, Greece

Polarization measurements in $\bar{B} \to D^{(\ast)} \tau \overline{\nu}$ are useful to check consistency in new physics explanations for the $R_{D}$ and $R_{D^{\ast}}$ anomalies. In this paper, we investigate the $D^{\ast}$ and $\tau$ polarizations and focus on the new physics contributions to the fraction of a longitudinal $D^{\ast}$ polarization ($F_{L}^{D^{\ast}}$), which is recently measured by the Belle collaboration $F_{L}^{D^{\ast}} = 0.60 \pm 0.09$, in model-independent manner and in each single leptoquark model (${\rm R}_2$, ${\rm S}_1$ and ${\rm U}_1$) that can naturally explain the $R_{D^{(\ast)}}$ anomalies. It is found that $\mathcal{B}(B_c^{+} \to \tau^{+} \nu)$ severely restricts deviation from the Standard Model (SM) prediction of $F_{L, \textrm{SM}}^{D^{\ast}} = 0.46 \pm 0.04$ in the leptoquark models: [0.43, 0.44], [0.42, 0.48], and [0.43, 0.47] are predicted as a range of $F_{L}^{D^{\ast}}$ for the ${\rm R}_2$, ${\rm S}_1$, and ${\rm U}_1$ leptoquark models, respectively, where the current data of $R_{D^{(\ast)}}$ is satisfied at $1\,\sigma$ level. It is also shown that the $\tau$ polarization observables can much deviate from the SM predictions. The Belle II experiment, therefore, can check such correlations between $R_{D^{(\ast)}}$ and the polarization observables, and discriminate among the leptoquark models., Comment: 24 pages, 3 figures, 1 table; references added, version published in JHEP

We study spin-dependent electron transport through a ferromagnetic-antiferromagnetic-normal metal tunneling junction subject to a voltage or temperature bias, in the absence of spin-orbit coupling. We derive microscopic formulas for various types of spin torque acting on the antiferromagnet as well as for charge and spin currents flowing through the junction. The obtained results are applicable in the limit of slow magnetization dynamics. We identify a parameter regime in which an unconventional damping-like torque can become comparable in magnitude to the equivalent of the conventional Slonczewski's torque generalized to antiferromagnets. Moreover, we show that the antiferromagnetic sublattice structure opens up a channel of electron transport which does not have a ferromagnetic analogue and that this mechanism leads to a pronounced field-like torque. Both charge conductance and spin current transmission through the junction depend on the relative orientation of the ferromagnetic and the antiferromagnetic vectors (order parameters). The obtained formulas for charge and spin currents allow us to identify the microscopic mechanisms responsible for this angular dependence and to assess the efficiency of an antiferromagnetic metal acting as a spin current polarizer.

We address the presently reported significant flavor anomalies in the Kaon and $B$ meson systems such as the CP violating Kaon decay ($\epsilon'/\epsilon$) and lepton-flavor universality violation in $B$ meson decays ($R_{K^{(*)}},{R_{D^{(*)}}}$), by proposing flavorful and chiral vector bosons as the new physics constitution at around TeV scale. The chiral-flavorful vectors (CFVs) are introduced as a 63-plet of the global $SU(8)$ symmetry, identified as the one-family symmetry for left-handed quarks and leptons in the standard model (SM) forming the 8-dimensional vector. Thus the CFVs include massive gluons, vector leptoquarks, and $W',Z'$-type bosons, which are allowed to have flavorful couplings with left-handed quarks and leptons, and flavor-universal couplings to right-handed ones, where the latter arises from mixing with the SM gauge bosons. The flavor texture is assumed to possess a "minimal" structure to be consistent with the current flavor measurements on the $K$ and $B$ systems. Among the presently reported significant flavor anomalies in the Kaon and $B$ meson systems ($\epsilon'/\epsilon$, $R_{K^{(*)}}, {R_{D^{(*)}}}$), the first two $\epsilon'/\epsilon$ and $R_{K^{(*)}}$ anomalies can simultaneously be interpreted by the presence of CFVs, the ${R_{D^{(*)}}}$ anomaly is predicted not to survive, due to the approximate $SU(8)$ flavor symmetry. Remarkably, we find that as long as both of the $\epsilon'/\epsilon$ and $R_{K^{(*)}}$ anomalies persist beyond the SM, the CFVs predict the enhanced $K^+ \to \pi^+ \nu \bar{\nu}$ and $K_L \to \pi^0 \nu \bar{\nu}$ decay rates compared to the SM values, which will readily be explored by the NA62 and KOTO experiments, and they will also be explored in new resonance searches at the Large Hadron Collider., Comment: 52 pages, 14 figures, 1 table, version published in JHEP

Colossal magnetoresistance (CMR) refers to a large change in electrical conductivity induced by a magnetic field in the vicinity of a metal-insulator transition and has inspired extensive studies for decades\cite{Ramirez1997, Tokura2006}. Here we demonstrate an analogous spin effect near the N\'eel temperature $T_{\rm{N}}$=296 K of the antiferromagnetic insulator \CrO. Using a yttrium iron garnet \YIG/\CrO/Pt trilayer, we injected a spin current from the YIG into the \CrO layer, and collected via the inverse spin Hall effect the signal transmitted in the heavy metal Pt. We observed a change by two orders of magnitude in the transmitted spin current within 14 K of the N\'eel temperature. This transition between spin conducting and nonconducting states could be also modulated by a magnetic field in isothermal conditions. This effect, that we term spin colossal magnetoresistance (SCMR), has the potential to simplify the design of fundamental spintronics components, for instance enabling the realization of spin current switches or spin-current based memories.

Searching for novel spin caloric effects in antiferromagnets we study the properties of thermally activated magnons in the presence of an external spin current and temperature gradient. We predict the spin Peltier effect -- generation of a heat flux by spin accumulation -- in an antiferromagnetic insulator with cubic or uniaxial magnetic symmetry. This effect is related with spin-current induced splitting of the relaxation times of the magnons with opposite spin direction. We show that the Peltier effect can trigger antiferromagnetic domain wall motion with a force whose value grows with the temperature of a sample. At a temperature, larger than the energy of the low-frequency magnons, this force is much larger than the force caused by direct spin transfer between the spin current and the domain wall. We also demonstrate that the external spin current can induce the magnon spin Seebeck effect. The corresponding Seebeck coefficient is controlled by the current density. These spin-current assisted caloric effects open new ways for the manipulation of the magnetic states in antiferromagnets., Comment: SUbmitted to J.Phus. D as a part of special issue on Spin Caloritronics

In light of a discrepancy of the direct $CP$ violation in $K\to\pi\pi$ decays, $\varepsilon'/\varepsilon_K$, we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to $\Delta S = 2$ observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of $\varepsilon'/\varepsilon_K$ for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify $\mathcal{B}(K \to \pi \nu \overline{\nu})$, $\mathcal{B}(K_S \to \mu^+ \mu^-)_{\rm eff}$ and $\Delta A_{\rm CP}(b\to s\gamma)$. Such large effects could be measured in future experiments., Comment: 30 pages, 8 figures; references added, version published in JHEP

We explore supersymmetric contributions to the decay $K_S^0\rightarrow\mu^+\mu^-$, in light of current experimental data. The Standard Model (SM) predicts $\mathcal{B}(K_S^0\rightarrow\mu^+\mu^-)\approx5\times 10^{-12}$. We find that contributions arising from flavour violating Higgs penguins can enhance the branching fraction up to $\approx 35\times 10^{-12}$ within different scenarios of the Minimal Supersymmetric Standard Model (MSSM), as well as suppress it down to $\approx 0.78\times 10^{-12}$. Regions with fine-tuned parameters can bring the branching fraction up to the current experimental upper bound, $8\times 10^{-10}$. The mass degeneracy of the heavy Higgs bosons in MSSM induces correlations between $\mathcal{B}(K_S^0\rightarrow\mu^+\mu^-)$ and $\mathcal{B}(K_L^0\rightarrow\mu^+\mu^-)$. Predictions for the $CP$ asymmetry in $K^0\rightarrow\mu^+\mu^-$ decays in the context of MSSM are also given, and can be up to eight times bigger than in the SM., Comment: 36 pages, 31 figs