Higgs and top production in the reaction $\gamma e \to$ $v$ $b$ $\bar{b}$ $W$ at TeV linear collider energies

For an electron-photon collider the complete tree-level cross sections of the reaction $\gamma e \rightarrow \nu b \bar{b} W$ are computed at center-of-mass energies between 0.5 and 2.0 TeV, for top masses of 160 to 200 GeV and Higgs masses between 80 and 140 GeV within the Standard Model. It is shown that most of the $\nu b \bar{b}$ events are due to Higgs and $Z/\gamma~*$ production (with $H, Z/\gamma~* \rightarrow b \bar{b}$ decay) while top production (with $t \rightarrow bW$ decay) is about 50% smaller. Multiperipheral background and interferences are small, respectively negligible, in the energy range studied. By convoluting the basic cross sections with an energy spectrum of the backscattered photon beam, and inserting linear collider luminosities as anticipated in present designs, realistic $\nu b \bar{b} W$ event rates are estimated. This results in large event rates for $\gamma e \rightarrow \nu t b$ and $\gamma e \rightarrow \nu H W$. We estimate that the CKM matrix element $|V_{tb}|$, can be probed from the $\nu t b$ final state to an accuracy of 1-3% at $\sqrt{s_{e~+e~-}} > 1 TeV$. Assuming an effective Lagrangian based on dimension-6 operators we discuss the sensitivity for detecting deviations of the HWW coupling from the Standard Model in the reaction $\gamma e \rightarrow \nu H W$