One-loop mass shifts in O(32) open superstring theory

One-loop amplitudes of O(N) open superstring with emission of massive bosons are studied. Divergences appearing at λ = 0 (λ: the over-all Teichmueller parameter) are shown to be canceled if N = 32 just as in the massless case. We explicitly evaluate the two-point on-shell amplitudes for all the levels of bosons lying on the leading (m2 = 2 l, J = l + 1, m:mass J:spin l:level number of an excited state) and the next-to-leading (m2 = 2 l, J = l) Regge trajectories and observe that they are nonvanishing even at N = 32. This implies that O(32) open super-string one-loop amplitudes with massive bosons generally suffer from external-line divergences. Further the obtained expressions of on-shell self energies (mass shifts δm2(l)) seem to have nontrivial dependences on l (being not proportional to l), although mass degeneracies remain. This strongly suggests that the Regge trajectories form a set of parallel polygonal lines at one-loop level so that the mass shifts cannot be absorbed by the shift of the slope parameter. The divergences would have to be cured by the vertex operator renormalizations at every excited level. (author)