Universality of soft theorem from locality of soft vertex operators

We show the universal soft behavior of massless particles at the tree level by considering the operator product expansion of the soft vertex operator with the hard vertex operators. We find that after eliminating total derivative terms the world-sheet integral for the soft vertex is determined only by the regions that are close to the hard verteces. This analyses can be applied to massless particles in various theories such as bosonic closed string, closed superstring and heterotic string. When the hard particle is massive we find that a mixing with different vertex operators occurs.