Fixed Point and Anomaly Mediation in Partially $N = 2$ Supersymmetric Standard Models

Abstract

Motivated by the simple toroidal compactification of extra-dimensional SUSY theories, we investigate on a partially $N=2$ 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 partially 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 partially breaking scale the sfermion masses in the $N=2$ sector is 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. no tachyonic slepton problem. From an example model, we show interesting phenomena differing from the ordinary MSSM. In particular, the dark matter can be a sbino, i.e. the scalar component of the $N=2$ vector multiplet of $\rm U(1)_Y$. To obtain the correct dark matter abundance, the mass of 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, muon $g-2$ anomaly, gauge coupling unification and relaxes some ordinary problems within the MSSM. Also, it is compatible with thermal leptogenesis.