On Discrete R-Symmetries in MSSM and its Extensions

We study possible anomaly-free discrete R-symmetries that avoid the \mu-problem and the dangerous D\leq 5 operators considering charge assignments that do not commute with the traditional grand unifying simple groups, such as SU(5) or SO(10), but commute instead with the so-called flipped-SU(5), with or without the operation of the GS mechanism. We find Z_N symmetries with N = 3, 6 in the anomaly-free case or N = 3, 4, 6, 8, 12, 24 in the case of anomaly cancellation through the Green-Schwartz mechanism. Non-unified cases (Z_5) have also been discussed. We also confront the construction of a 4D grand unified flipped-SU(5) model endowed with Z_N and find phenomenologically acceptable solutions with N = 2k+7 and N = 2k+10.