A relation between massive and massless string tree amplitudes

Abstract

We uncover a relation between the scattering amplitudes of massive strings and the ${\alpha }^{\prime }$ expansion of the massless string amplitude at tree level. More precisely, the n-point tree amplitude of n-1 massless and one massive state is written as a linear combination of n+1 massless string amplitudes at the ${\alpha }^{\prime 2}$ order.