Self-energies of massive strings

An expression for the one-loop self-energy contribution to excited string states on the leading trajectory, J=2+α'm2, of closed superstrings is derived. Since the masses of such states are above threshold for decay, a useful formula has to depend analytically on m2 to allow the determination of finite real and imaginary parts by analytic continuation. This is achieved by factorization of a one-loop four-point amplitude. The procedure is tested by a calculation of δm2 for strings compactified to D dimensions in the limit of large m2. Results are obtained for D>6, but difficulties are encountered in lower dimensions. Possible explanations of this problem are discussed. (orig.)