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We derive new model independent constraints on the supersymmetric extensionsof the standard model from the new experimental measurements of B_s -\bar{B}_smass difference. We point out that supersymmetry can still give a significantcontribution to the CP asymmetry of B_s ->J/\psi \phi that can be measured atthe LHCb experiment. These new constraints on the LL and RR squark mixingseverely restricted their possible contributions to the CP asymmetries of B->\phi K and B - >\eta' K. Therefore, SUSY models with dominant LR flavor mixingis the only way to accommodate the apparent deviation of CP asymmetries fromthose expected in the standard model. Finally we present an example of SUSYnon-minimal flavor model that can accommodate the new \Delta M_{B_s} resultsand also induces significant CP asymmetries in B_s ->J/\psi \phi, B->\phi K andB ->\eta' K processes.Comment: 4 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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Supersymmetric contribution to theCPasymmetry ofB→J/ψϕin the light of recentBs