Calculation of Fayet-Iliopoulos D-term in type I string theory revisited: T6/Z3 orbifold case

The string one-loop computation of the Fayet-Iliopoulos D-term in type I string theory in the case of T6/Z3 orbifold compactification associated with annulus (planar) and the Möbius strip string worldsheet diagrams is reexamined. The mass extracted from the sum of these amplitudes through a limiting procedure is found to be non-vanishing, which is contrary to the earlier computation. The sum can be made finite by a rescaling of the modular parameter in the closed string channel.