B0−B¯0mixing in supergravity models

We consider the supersymmetric contributions to $B_d^0-{\overline{B}}_d^0$ mixing in the supergravity (SUGRA) models, which arise from box diagrams where charginos and up-type squarks or charged Higgs bosons and up-type quarks are exchanged. We have calculated $R$, which is defined to be the ratio between the minimal supersymmetric standard model (MSSM) contributions to $x_d$ and the standard model one. By choosing a particular set of Cabibbo-Kobayashi-Maskawa parameters allowed by the present data along with the present experimental data on $x_d$ and $\epsilon$, which lead to $0.7\lesssim R\lesssim 1.4$ in the MSSM, we have demonstrated an indication of possible constraints on $m_{{\chi }_1^{\pm }}$ and $tan\beta$ in the SUGRA models. As a result, for $m_t\left(m_t\right)=170\mathrm{}$ GeV and $\mu >0\mathrm{}$, we obtain $m_{{\chi }_1^{\pm }}\gtrsim 112$ GeV for $tan\beta =2\mathrm{}$ in the no-scale SU(5)×U(1) SUGRA model and $m_{{\chi }_1^{\pm }}\gtrsim 107\left(66\right)\mathrm{}$ GeV for $tan\beta =2\mathrm{}\left(4\right)\mathrm{}$ in the dilaton SU(5)×U(1) SUGRA model. In the minimal SU(5) SUGRA model, however, we find no constraint from $R$. It will be very interesting for one to see what values for $R$ the future experimental data would prefer.