CP Violation in Hyperon Decays from SUSY with Hermitian Yukawa and A Matrices

We show that a large CP asymmetry in hyperon decays can be naturally realized in the framework of SUSY models. The possibility is implemented by the hermiticities of Yukawa and A matrices. And also, the observed values of ǫ and ǫ are explained. The origin of CP violation (CPV) is one of mysterious phenomena in particle physics since its discovery in the neutral kaon decays in 1964 [1]. Recently, another CP asymmetry, sin 2β, in the decay of B → J/ΨKs is observed by BARBAR [2] and BELLE [3]. Nevertheless, our understanding of CPV is still exiguous. In the standard model (SM), the unique source of CPV is from the Cabibbo-Kobayashi-Maskawa (CKM) matrix [4] induced from the threegeneration quark mixings and described by the three angles α, β and γ or φ2, φ1 and φ3. Even though the SM prediction on the indirect CP violating parameter ǫ in the kaon system can be fitted well with current experimental data, due to the large uncertainties from hadronic matrix elements, so far it is unclear whether the result in the SM is consistent with the observed value of the direct CP violating parameter ǫ measured by KTeV [5] and NA31 [6]. Furthermore, the problem of baryogenesis is insolvable in the SM. In addition, the predicted CP asymmetry of O(10) in hyperon decays of Ξ → Λπ → pππ is about one order of the magnitude smaller than that of O(10) proposed by the experiment E871 at Fermilab [7]. Hence, it is inevitable to look for new physics which gives observable CPV effects. Supersymmetric theories not only supply an elegant mechanism for the breaking of the electroweak symmetry and a solution to the hierarchy problem, but provide many new weak CP violating phases. These CP phases usually arise from the trilinear and bilinear supersymmetry (SUSY) soft breaking A and B terms, the μ parameter for the scalar mixing and gaugino masses, respectively. Unfortunately, it has been shown that with the universal assumption on soft breaking parameters, these phases are severely bounded by electric dipole moments (EDMs) [8] so that the contributions to ǫ and ǫ are far below the experimental values. In the literature, some strategies to escape the constraints of EDMs have been suggested. They are mainly (a) by setting the squark masses of the first two generations to be as heavy as few TeV [9] but allowing the third one being light; (b) by including all possible contributions to EDMs such that somewhat cancellations occur in some allowed parameter space [10, 11]; and (c) with the non-universal soft A terms instead of universal ones. In particular, those models with non-universal parameters have been demonstrated that they can be realized in some string-inspired models [12, 13, 14, 15]. Among the models with non-degenerate soft trilinear terms, for satisfying the bounds of EDMs, the phases in the diagonal elements of the A matrix should be set to be small in any basis artificially although the remaining large phases and the light sfermions are still allowed to explain the observed values of ǫ and ǫ. To overcome this problem, it is proposed in Ref. [16] to use hermitian Yukawa and A matrices. The construction of a hermitian Yukawa matrix can be implemented based on some symmetries such as the global (gauged) horizontal SU(3)H symmetry [17] and left-right symmetry [18]. Although the hermiticity will be broken by renormalization group (RG) effects, it is shown [16] that their contributions to EDMs are two orders of the magnitude below the present experimental limit. Moreover, due to the hermitian property, a special relation is obtained as