Scattering of massive open strings in pure spinor

Abstract

In {\em Phys.\ Lett.} {\bf B 660}, 583 (2008), it was proposed that the D-brane geometry could be produced by open string quantum effects. In an effort to verify the proposal, we consider scattering amplitudes involving {\em massive} open superstrings. The main goal of this paper is to set the ground for two-loop "renormalization" of an oriented open superstring on a D-brane and to strengthen our skill in the pure spinor formulation of a superstring, an effective tool for multi-loop string diagrams. We start by reviewing scattering amplitudes of massless states in the 2D component method of the NSR formulation. A few examples of massive string scattering are worked out. The NSR results are then reproduced in the pure spinor formulation. We compute the amplitudes using the massive vertex operator constructed by Berkovits and Chandia in {\em JHEP} {\bf 0208}, 040 (2002). We point out that it may be possible to discover new Riemann type identities involving Jacobi $\vartheta$-functions by comparing a NSR computation and the corresponding pure spinor computation.