TTP08-43 ${\cal O}(\alpha\alpha_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold

We compute the last missing piece of the two-loop ${\cal O}(\alpha \alpha_s)$ corrections to $\gamma t \bar{t}$ vertex at the $t \bar{t}$ threshold due to the exchange of a $W$ boson and a gluon. This contribution constitutes a building block of the top quark threshold production cross section at electron positron colliders.