  The loop level flavor changing neutral currents transitions of the
$\Sigma_{b}\to n l^+l^-$ and $\Sigma_{c}\to p l^+l^-$ are investigated in full
QCD and heavy quark effective theory in the light cone QCD sum rules approach.
Using the most general form of the interpolating current for $\Sigma_{Q}$,
$Q=b$ or $c$, as members of the recently discovered sextet heavy baryons with
spin 1/2 and containing one heavy quark, the transition form factors are
calculated using two sets of input parameters entering the nucleon distribution
amplitudes, namely, QCD sum rules and lattice QCD inputs. The obtained results
are used to estimate the decay rates of the corresponding transitions. Since
such type transitions occurred at loop level in the standard model, they can be
considered as good candidates to search for the new physics effects beyond the
SM.
