  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.

High Energy Physics - Phenomenology;High Energy Physics - Theory