  We present a systematic light-cone QCD sum rule study of the exclusive rare
radiative decay $\Lambda_b\rightarrow\Lambda\gamma$ and rare semileptonic decay
$\Lambda_b\rightarrow\Lambda l^+l^-$ within the framework of the standard
model. Although some LCSR studies on these rare processes can be found in
different literatures, it is necessary to reanalyze them systematically for the
reason that either the baryonic distribution amplitudes are improved or
different interpolating currents for the $\Lambda_b$ baryon may lead to quite
different results. In addition, the rare process
$\Lambda_b\rightarrow\Lambda\gamma$ has not yet been analyzed by LCSR with the
Ioffe-type current. Taking all these reasons into account, we perform LCSR
calculations of both the processes with two types of interpolating currents.
Our calculations show that the choice of the interpolating current for the
$\Lambda_b$ baryon can affect the predictions significantly, especially for the
rare radiative decay process.
