Low energy processes associated with spontaneously broken N=2 supersymmetry

We consider low energy processes described by the N=2 supercurrent on its partially (to N=1) and spontaneously broken vacuum and the attendant Nambu-Goldstone fermion (NGF), which the presence of the electric and magnetic Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of amplitudes decaying into the NGF as its momentum becomes small. In the Lagrangian realization (namely, the model of arXiv:hep-th/0409060) of the conserved supercurrent, the NGF resides in the overall U(1), which is nonetheless not decoupled, and interacts with the SU(N) sector through non-derivative as well as derivative couplings. The low energy suppression is instead accomplished by a cancellation between the annihilation diagram from the Yukawa couplings and the contact four-Fermi terms. We give a complete form of the supercurrent and the model is recast in more transparent notation.