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We present a detailed and complete calculation of the neutralino contributionto the mass difference $\Delta m_{B_d^0}/m_{B_d^0}$\ within the MSSM. Weinclude the complete mixing matrices of the neutralinos and of the scalarpartners of the left and right handed bottom quark. We find that the neutralinocontribution is generally small but can be of the same order of the charginocontribution and much larger than that of the gluino over a small range of$m_S$, given $m_{g_2}$ and $\mu$ and for $\tan\beta\sim 50$.Comment: 8 pages, plain tex, 2 figures, not included, available under reques

Neutralino contribution to the mass difference of $$B_d^0 - \bar B_d^0 $$