Relations between tree-level closed string amplitudes and mixed string amplitudes at fewer points

Abstract

We formulated the relations between closed string amplitudes and mixed string amplitudes at tree level. In this paper we focus on fewer points of external states. We factorized the closed string amplitudes by analytical continuation of complex variables. With a careful examination of branch points, the results show that closed string amplitudes can be expressed in terms of products of mixed string amplitudes and additional terms with appropriate phase factors. In terms of five-point amplitudes, we introduced a one-parameter dependent amplitude to capture the results. Finally, some physical interpretations were provided.