Motivated by the recently observed anomalous large dimuon charge asymmetry in neutral B decays and the unexpected large CP phase in the mixing-induced CP asymmetry for B_s–>J/\psi\phi decay, we study the effects of the anomalous tensor couplings to pursue possible solution. With the constraints from the obsevables \phi^{J/\psi\phi}s, a{sl}^s and \Delta M_s, the parameter spaces are severely restricted. Numerically, we find the anomalies in B_s^0-\bar{B}s^0 mixing system could be moderated simultaneously by the contributions induced by the color-singlet or color-octet tensor operators with their respective nontrivial new weak phase \phi{T1}\approx28.0(15.6) degree or \phi_{T8}\approx-62.1(-74.2) degree and relevant strength parameters g_{T1}\approx6.7(8.5)\times10^{-2} or g_{T8}\approx1.9(2.4)\times10^{-2} for the CP-violating phase \phi^{J/\psi\phi}_s=-0.77(+0.29,-0.37)(-2.36(+0.37,-0.29)), respectively.

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