A search for pair-production of heavy leptons ($\Sigma^{0}$, $\Sigma^{\pm}$)

predicted by the Type III seesaw mechanism to explain the origin of small

neutrino masses is presented. The decay channels for the heavy leptons $\Sigma^0

\rightarrow W^{\pm}e^{\mp}$ and $\Sigma^{\pm} \rightarrow

W^{\pm}\nu_{e}$ are considered. Multivariate

techniques versus a kinematic selection method are compared. The study is

based on proton-proton collisions recorded at the ATLAS detector at the Large

Hadron Collider at CERN during 2015 with a center-of-mass energy of

$13 \tev$. The data used corresponds to an integrated luminosity of $3.2~\ifb$

and no evidence of heavy lepton pair-production was observed.