$B^0_d-{\bar B}^0_d$ mixing in the left-right supersymmetric model

We analyze $B^0_d-{\bar B}^0_d$ mixing in a fully left-right supersymmetric model. We give explicit expressions for all the chargino, gluino, gluino-neutralino and neutralino amplitudes involved in the process. We calculate the mass difference $\Delta m_d$ and CP asymmetry $a_{J/\psi K_s}$ in both the constrained case (where the only flavor violation comes from the Cabibbo-Kobayashi-Maskawa matrix) and the unconstrained case (including soft supersymmetry breaking terms). The constrained case does not contain any new information beyond the supergravity-inspired MSSM. In the unconstrained case, the main contribution to $B^0_d-{\bar B}^0_d$ and the CP asymmetry is due to either gluino diagrams, if the dominating flavor mixing arises in the down squark sector, or chargino diagrams, if the dominant flavor mixing comes from the up squark sector. We include numerical results and compare this analysis with the ones performed in other models.