The Twisted String Vertex Algorithm Applied to the $Z_2$-Twisted Scalar String Four Vertex

Recently an algorithm was found by means of which one can calculate terms at arbitrary oscillator level in the four-Ramond vertex obtained by sewing. Here we show that this algorithm is applicable also to the case of ${\bf Z}_2$-twisted scalars and derive the full propagator for scalars on the Riemann sphere with two branch cuts. The relation to similar results previously derived in the literature by other means is discussed briefly.