Alternative framework for the left-right symmetric model including vector-like fermions

We extend the left-right symmetric model with an additional non-abelian $SU(2)$ gauge symmetry. The particle content is augmented by one generation of vector-like fermions transforming under the fundamental representation of this new gauge group. Consequently, new self-dual scalar fields have been introduced for the sake of breaking the symmetry and invoking the mixing of vector-like fermions with the chiral fermions. This model explains the smallness of the neutrinos masses, showing that the 1rst and 2nd generation neutrinos masses are governed by the seesaw relation of the LRSM, while the 3rd generation neutrino mass is controlled by a new seesaw relation which involves the VLN. We investigated the production of a resonant extra charged gauge boson which decays into vector-like quarks in association with 3rd generation or into heavy Majorana neutrinos. We exploited the {\tt run II} LHC data to set lower limits on the mass of $W^{\prime}$, and consequentially on the $Z^{\prime}$. We find that the most restrictive constraints come from the decay of the $W^{\prime}$ to the 2nd generation heavy Majorana neutrinos. We also examine the single production of the top vector-like quark with $t$ and $b$ quarks, where parton-shower is taken into account.