Fixed point and anomaly mediation in partial N = 2 supersymmetric standard models

Motivated by the simple toroidal compactification of extra-dimensional SUSY theories, we investigate a partial N = 2 supersymmetric (SUSY) extension of the standard model which has an N = 2 SUSY sector and an N = 1 SUSY sector. We point out that below the scale of the partial breaking of N = 2 to N = 1, the ratio of Yukawa to gauge couplings embedded in the original N = 2 gauge interaction in the N = 2 sector becomes greater due to a fixed point. Since at the partial breaking scale the sfermion masses in the N = 2 sector are suppressed due to the N = 2 non-renormalization theorem, the anomaly mediation effect becomes important. If dominant, the anomaly-induced masses for the sfermions in the N = 2 sector are almost UV-insensitive due to the fixed point. Interestingly, these masses are always positive, i.e. there is no tachyonic slepton problem. From an example model, we show interesting phenomena differing from ordinary MSSM. In particular, the dark matter particle can be a sbino, i.e. the scalar component of the N = 2 vector multiplet of U(1)_Y. To obtain the correct dark matter abundance, the mass of the sbino, as well as the MSSM sparticles in the N = 2 sector which have a typical mass pattern of anomaly mediation, is required to be small. Therefore, this scenario can be tested and confirmed in the LHC and may be further confirmed by the measurement of the N = 2 Yukawa couplings in future colliders. This model can explain dark matter, the muon anomaly, and gauge coupling unification, and relaxes some ordinary problems within the MSSM. It is also compatible with thermal leptogenesis.