Single Production of Fourth Family $t^{\mathrm{\prime }}$ Quarks at LHeC

We study the single production of fourth-family $t^{\mathrm{\prime }}$ quarks via the process $ep\to t^{\mathrm{\prime }}\nu$ at Large Hadron electron Collider (LHeC). We calculate the background and signal cross sections for the mass range 300-800 GeV. It is shown that the LHeC can discover single $t^{\mathrm{\prime }}$ quark up to the mass of 800 GeV for the optimized mixing parameters.