New signals for vector-like down-type quark in $U(1)$ of $E_6$

We consider the pair production of vector-like down-type quarks in an $E_6$ motivated model, where each of the produced down-type vector-like quark decays into an ordinary Standard Model light quark and a singlet scalar. Both the vector-like quark and singlet scalar appear naturally in the $E_6$ model with masses at the TeV scale with a favorable choice of symmetry breaking pattern. We focus on the non-standard decay of the vector-like quark and the new scalar which decays to two photons or two gluons. We analyze the signal for the vector-like quark production in the $2\gamma +\ge 2j$ channel and show how the scalar and vector-like quark masses can be determined at the Large Hadron Collider.