Non-standard signatures of vector-like quarks in a leptophobic 221 model

We consider vector-like quarks in a leptophobic 221 model characterized by the gauge group $SU(2)_L\times SU(2)_2 \times U(1)_X$, where the $SU(2)_2$ is leptophobic in nature. We discuss about the pattern of mixing between Standard Model quarks and vector-like quarks and how we prevent tree level flavour-changing interactions in the model. The model also predicts tauphilic scalars decaying mostly to tau leptons. We consider a typical signal of the model in the form of pair production of top-type vector-like quarks which decays to the tauphilic scalars and a third generation quark. We analyze the resulting final state signal for the 13 TeV LHC, containing $\geq 3j(1b) \, + \geq 2\tau \, + \geq 1l$ and discuss the discovery prospects of such vector-like quarks with non-standard decay modes.